Characterization of main ion properties for the optimization of future fusion power plants

University of Seville Doctoral Thesis Characterization of main ion properties for the optimization of future fusion power plants Author: Pilar Cano Meg´ıas Supervisor: Prof. Dr. Ricardo Chacartegui Prof. Dr. Eleonora Viezzer A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in the Plasma Science and Fusion Technology Group Department of Energy Engineering PhD program in Energy, Chemistry and Environmental Engineering September 26, 2022 iii Declaration of Authorship I, Pilar Cano Meg´ıas, declare that the thesis “Characterization of main ion properties for the optimization of future fusion power plants” and the related work are my own. I confirm that:  This work was done wholly or mainly during candidature for a research degree at the University of Seville.  Where any part of this thesis has previously been submitted for a degree or any other qualification at the University of Seville or any other institution, this has been clearly stated.  Where I have consulted the published work of others, this is always clearly attributed.  Where I have quoted from the work of others, the source is always given. Except for such quotations, this thesis is my own work.  I have acknowledged all main supporting sources.  Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself. Signed: Date: v A mis padres vii UNIVERSITY OF SEVILLE Abstract Higher Technical School of Engineering Department of Energy Engineering Characterization of main ion properties for the optimization of future fusion power plants by Pilar Cano Meg´ıas In the search for a clean and sustainable energy source for our society, fusion energy emerges as a promising candidate. The realization of a fusion power plant on Earth faces important technological and physical challenges. This thesis is a multidisciplinary project that addresses the optimization of future fusion devices from a plasma physics and engineering perspective. From the plasma physics perspective, the performance of future fusion reactors depends on the properties of the plasma, the fusion fuel. The main ion properties (in present experimental devices, deuterium) are particularly important as they determine the fusion power, which sets the electricity production. Traditionally, the main ions have been rarely diagnosed and their properties have typically been inferred from minority impurity measurements and theoretical models. In this thesis, a novel diagnostic method has been established that enables the direct experimental measurement of the main ions with a focus on the plasma edge. The plasma edge is a critical region, as it prescribes the boundary conditions for the plasma core performance, while it must enable a heat exhaust solution that limits the power loads to the plasma facing components, keeping the integrity of the fusion reactor. Plasma edge diagnostics are demanding in terms of spatial and temporal resolution, as they need to resolve fast transient events and strong spatial gradients. From an engineering perspective, the efficiency of the power conversion cycle coupled to a fusion reactor has been studied and optimized to maximize the electric power output. Cogeneration schemes as opportunities for boosting the efficiency of future fusion power plants have also been investigated. In the framework of this thesis, a new edge main ion diagnostic based on the Charge Exchange Recombination Spectroscopy technique has been installed and exploited at the ASDEX Upgrade experimental reactor, a full metal wall device, to provide main ion temperature and toroidal rotation velocity measurements. A new in-vessel optical head has been installed, which covers the outermost plasma region with a resolution down to 3 mm. A forward model, based on the collisional radiative model implemented in the fidasim code, and data analysis tools have been developed to enable an accurate interpretation of the main ion data. These are state-of-the-art measurements of edge deuterium temperature and toroidal rotation profiles in a tungsten environment, which resembles conditions relevant for future fusion reactors. viii Several experiments have been carried out at the ASDEX Upgrade tokamak to characterize the main ion temperature and toroidal rotation in a variety of plasma conditions. The role of plasma collisionality and heating scheme on the main ion temperature and toroidal rotation has been addressed. The main ion properties have been compared to minority impurity ion and electron measurements and serve as a testbed for theoretical transport models. In particular, the measurements are compared against neoclassical transport theory. The main ion properties in high and low confinement regimes, such as the high confinement mode (H-mode), low confinement mode (L-mode), improved energy confinement mode (I-mode) and quiescent high confinement mode (QH-mode), have been documented. It has been found that the impurity ion temperature does not always give a good description of the main ion properties, and the thermal equilibration between main and impurity ions is a complex function of heating scheme and collisionality. In H-mode, the main ion toroidal rotation is in remarkably good agreement with neoclassical theory in the steep gradient region of the plasma edge. The detailed diagnosis of the edge plasma properties is essential for understanding plasmas in present experimental devices, and consequently, for the projection towards future fusion power plants and their optimization. The integration of a portfolio of Rankine and Brayton power conversion cycles with a fusion reactor has been studied in a framework that couples the engineering equation solver and the process systems code. The fusion reactor is based on the European DEMO Baseline 2018, which sets the temperature and power boundary conditions. In the intermediate temperature range envisaged for the EU-DEMO Baseline 2018, supercritical carbon dioxide power conversion cycles constitute a very attractive technology. Nuclear fusion cogeneration of heat and electricity has been put forward as a strategy for boosting the efficiency of future fusion devices. The use of district heating networks for the recovery of low-grade heat yields efficiency improvements for all power cycle layouts. The economic viability has been studied by the definition of the levelized cost of hybrid production, which is an indicator that integrates cost estimates from process and production and distribution costs. The cogeneration scheme is feasible from an economic point of view for Rankine and supercritical carbon dioxide power cycles. This work expands potential fusion energy applications and its deployment in the energy market. ix UNIVERSIDAD DE SEVILLA Resumen Escuela T´ecnica Superior de Ingenier´ıa Departmento de Ingenier´ıa Energ´etica Caracterizaci´on de las propiedades de la especie i´onica mayoritaria para la optimizaci´on de futuras plantas de potencia basadas en la fusion nuclear por Pilar Cano Meg´ıas La fusi´on nuclear se presenta como una de las grandes opciones tecnol´ogicas para cubrir de manera limpia y sostenible la demanda energ´etica. Sin embargo, lograr la producci´on de energ´ıa en una planta de potencia basada en la fusi´on nuclear en la Tierra enfrenta importantes desaf´ıos tecnol´ogicos y f´ısicos. Esta tesis es un proyecto multidisciplinar que aborda la optimizaci´on de futuros reactores de fusi´on desde una perspectiva de ingenier´ıa y f´ısica del plasma. Desde la perspectiva de la f´ısica del plasma, el rendimiento de los futuros reactores de fusi´on depende de las propiedades del plasma, el combustible de fusi´on. Las propiedades de la especie i´onica mayoritaria (en los dispositivos experimentales actuales, el deuterio) son particularmente importantes ya que determinan la energ´ıa producida por la fusi´on nuclear, que a su vez establece la producci´on de electricidad. Tradicionalmente, las propiedades del deuterio no se miden de manera directa en reactores experimentales, sino que son inferidas a partir de las propiedades de otras especies i´onicas minoritarias (impurezas) y modelos te´oricos. En esta tesis, se ha establecido un nuevo m´etodo de diagn´ostico que permite la caracterizaci´on experimental directa de la temperatura y la velocidad de rotaci´on toroidal del deuterio en el borde del plasma. El borde del plasma es una regi´on cr´ıtica, ya que prescribe las condiciones de contorno que determinan el desempe˜no global del plasma y que deben ser compatibles con estrategias de disipaci´on de calor que garanticen la integridad del reactor de fusi´on. Los diagn´osticos de borde de plasma son exigentes en t´erminos de resoluci´on espacial y temporal, ya que necesitan resolver eventos transitorios r´apidos y fuertes gradientes espaciales. Desde la perspectiva de la ingenier´ıa, se ha estudiado y optimizado la eficiencia del ciclo de potencia acoplado a un reactor de fusi´on, maximizando la producci´on de energ´ıa el´ectrica. Igualmente, se han investigado esquemas de cogeneraci´on como oportunidades para aumentar la eficiencia de las futuras plantas de potencia de fusi´on. xvi 5.1 Total, active and passive experimental spectra and syntehtic contributions to the edge main ion spectrum calculated with fidasim ...... 63 5.2 (a) Splitting due to Stark effect. (b) Separation of BES from thermal Dα64 5.3 Workflow of the forward modelling framework for the interpretation of the main ion spectra ............................. 65 5.4 Evolution of main ion profiles and spectrum in sucessive iterations with the forward model .............................. 66 5.5 Neutral density of beam, halo and DCX calculated with the fidasim code 67 5.6 Sensitivity study synthetic fidasim spectra to input profiles ....... 69 5.7 Impact of the main ion input profiles to fidasim on the synthetic main ion CX spectra and apparent properties .................. 70 5.8 Corrections due to the halo effect to edge main ion temperature and toroidal rotation ............................... 71 5.9 Correction factor to the main ion temperature due to Zeeman, Stark and fine structure effects ............................. 72 5.10 Evolution of passive and total main ion integrated radiance in the ELM cycle ...................................... 74 5.11 Main ion spectrum with significant FIDA contribution .......... 75 5.12 Correction to the main ion properties due to the fast-ion contribution . 75 6.1 Overview of H-mode discharges for main ion characterization . . . . . . 78 6.2 ECRH and NBI power deposition profiles ................. 79 6.3 Main ion temperature and toroidal rotation in the validation case (high collisionality H-mode) ............................ 80 6.4 Radial force balance for (a) impurity ion and (b) main ions and (c) main ion poloidal rotation ............................. 81 6.5 Main ion temperature and rotation at the collisionality banana limit. . . 82 6.6 (a) Ion heat diffusivity (b) ion heat flux evaluated with the transp transport code ................................ 83 6.7 Impact of ECRH power scan on edge temperature and toroidal rotation 84 6.8 Temperature profiles in a NBI scan at PECRH = 3.8 MW ........ 85 6.9 Temperature profiles in a NBI scan at PECRH = 2.3 MW ........ 85 6.10 Ion toroidal rotation profiles in a NBI scan at PECRH = 3.8 MW . . . . 86 6.11 Ion toroidal rotation profiles in a NBI scan at PECRH = 2.3 MW . . . . 86 6.12 Temperature profiles in L-mode, I-mode and QH-mode .......... 87 6.13 Ion toroidal rotation profiles in L-mode, I-mode and QH-mode ..... 88 6.14 Beam-based and gas-puff based main ion temperature measurements . . 89 6.15 Inter-species temperature difference and difference between experimental and neoclassical-theory based main ion toroidal rotation as a function of collisionality .................................. 90 7.1 Framework integrating process and ees .................. 96 7.2 (a) Integration of the power conversion cycle, thermal energy storage and reactor heat sources. (b) Thermal energy as a function of time during a full cycle .................................... 97 7.3 (a) Power split between divertor and blanket (b) Cycle electric efficiency for different working fluids .......................... 99 7.4 Rankine cycle for the DEMO Baseline 2018 with mixers in preheating train ...................................... 101 7.5 Rankine cycle for the DEMO Baseline 2018 ................ 103 7.6 Efficiency of Rankine fusion power plant as a function of pressure . . . . 104 xvii 7.7 Efficiency of supercritical Rankine fusion power plant ........... 105 7.8 sCO2cycle-based fusion power plant .................... 106 7.9 Helium Brayton cycle-based fusion power plant .............. 108 7.10 Efficiency of helium Brayton cycle-based fusion power plant . . . . . . . 108 7.11 Levelized cost of electricity as a function of (a) the net electrical power output and (b) cycle electric efficiency and recirculated power ...... 111 7.12 Cycle electric efficiency as a function of temperature and power fraction to the divertor ................................ 113 7.13 Efficiency parameters for spherical tokamaks ............... 114 8.1 Sankey diagram for pure electric and hybrid production ......... 118 8.2 Rankine cycle for a fission nuclear power plant .............. 119 8.3 Cogeneration parameters for a fission nuclear power plant ........ 120 8.4 Cogeneration parameters for a Rankine cycle for a fusion power plant based on the DEMO Baseline 2018 ..................... 121 8.5 Cogeneration parameters for a sCO2cycle for a fusion power plant based on the DEMO Baseline 2018 ......................... 122 8.6 Cogeneration parameters sCO2cycle-based fusion nuclear power plant . 122 8.7 Cogeneration parameters helium Brayton cycle-based fusion nuclear power plant ...................................... 123 8.8 Levelized cost of hybrid production and primary energy savings . . . . . 125 8.9 Heat and electricity efficiency ratios for primary energy savings . . . . . 127 xix List of Tables 3.1 Technical data for the ASDEX Upgrade tokamak ............. 27 3.2 Details on the Neutral Beam Injection system at the ASDEX Upgrade tokamak .................................... 28 3.3 Properties of primary coolants for the DEMO tokamak .......... 42 3.4 Direct costs breakdown for the EU-DEMO Baseline 2018 ........ 45 3.5 Total capital investment breakdown for the EU-DEMO Baseline 2018 . 45 3.6 Relevant machine parameters for the EU-DEMO Baseline 2018 ..... 46 6.1 Relevant parameters for the H-mode discharges .............. 79 7.1 Boundary conditions for the DEMO Baseline 2018 scenario ....... 96 7.2 Performance parameters for fusion Rankine cycle layouts ......... 102 7.3 Economic parameters for the analysis of the LCOE ............ 110 7.4 Levelized cost of electricity breakdown for the DEMO Baseline 2018 . . 110 7.5 Thermodynamic and economic performance of selected layouts . . . . . 112 7.6 Fluid properties for Rankine and Brayton Power Conversion Systems integrated with the DEMO Baseline 2018 ................. 113 8.1 Fluid properties for the fission power conversion system ......... 120 xxi List of Abbreviations AUG ASDEX Upgrade BES Beam Emission Spectroscopy CCD Charge Coupled Device COE Cost OfElectricity CX Charge Exchange CXRS Charge Exchange Recombination Spectroscopy DCX Direct Charge Exchange DEMO European Demonstration tokamak DH District Heating DHN District Heating Network ECRH Electron Cyclotron Resonance Heating ELM Edge Localized Mode ETB Edge Transport Barrier HPT High Pressure Turbine HTR High Temperature Recuperator HX Heat Exchanger FIDA Fast Ion D-Alpha FPP Fusion Power Plants GHG Greenhouse Gases HCPB Helium Cooled Pebble Bed HFS High Field Side HTR High Temperature Recuperator HX Heat Exchanger LCHP Levelized Cost Of Hybrid Production LCOE Levelized Cost OfElectricity LFS Low Field Side LOS Line(s) OfSight LPT Low Pressure Turbine LSN Lower Single Null LTR Low Temperature Recuperator MPT Medium Pressure Turbine NBI Neutral Beam Injection NPP Nuclear Power Plants PCS Power Conversion System PES Primary Energy Savings PWR Pressurized Water Reactor SOL Scrape-OffLayer TES Thermal Energy Storage USN Upper Single Null xxiii List of Symbols Aspect ratio A Blanket temperature Tbnk Boltzmann constant kB Cycle efficiency ηcycle Cyclotron Frequency ωc=qB/m Collisionality ν Divertor temperature Tdiv Effective charge Zeff Electron temperature Te Energy E Enthalpy h Entropy s Impurity temperature Tz Inverse aspect ratio ε Ion heat diffusivity χi Larmor radius rL=mv⊥/qB Magnetic moment µ=mv2 ⊥/2B Main ion deuterium temperature TD Magnetic field B Major radius R0 Plant efficiency ηplant Poloidal coordinate θ Poloidal rotation velocity vθ Power P Pressure p Radial electric field Er Rotation velocity v Temperature T Temperature increase in each pre-heating stage ∆TPH Toroidal coordinate ϕ Toroidal rotation velocity vϕ Safety factor q= ∆ϕ/2π Wavelength λ Power W Speed of light c Steam quality x xxiv “Compartir es vivir” 1 Chapter 1 Introduction 1.1 Fusion energy The world’s primary energy consumption exceeded 580 EJ for the first time in 2019, with a growth of 1.3% compared to 2018, as shown in Figure 1.1(a). The predictions indicate that the energy consumption will continue to increase in the future, closely following the growing trend of the population and economy [2]. The improvement of life standards and the electrification of sectors such as transport and space conditioning will further increase electricity demand. Despite the climate emergency and the urgent need to reduce CO2emissions, the electricity generation mix is currently dominated by the use of fossil fuels, as shown in Figure 1.1(b). The search for alternatives to fossil fuels is one of the greatest technological challenges and compromises of society with the environment and future generations: fossil fuel reserves are limited to the next decades1and their usage has a harmful effect on the environment. International efforts are being made to reduce, and ultimately eliminate, fossil fuel consumption to comply with the Intergovernmental Panel on Climate Change goals and limit the temperature increase below 2 ° C with respect to the pre-industrial level [4]. (a)                         (b)                   Figure 1.1: (a) Time history of primary energy consumption by region, adapted from [5]. (b) Time history of electricity generation by fuel type, adapted from [6]. Carbon-free alternatives to the use of fossil fuels comprise renewable (mainly, hydropower, solar and wind power) and non-renewable (nuclear fission) energy sources, as shown in Figure 1.1(b). While a further deployment of these technologies to replace fossil fuels is underway, a complete replacement of fossil fuels by this means is uncertain and requires solving several challenges. Hydroelectric plants’ emplacements 1Global reserves-to-production ratios show that oil, natural gas and coal in 2019 account for 50, 50 and 132 years of current production, respectively [3]. 8Chapter 1. Introduction in Chapter 5. The main ion measurements in different confinement and collisionality regimes are presented in Chapter 6. The main ion properties are compared against those of impurity ions and electrons and to neoclassical theory. The study of the integration of future fusion power plants and power cycles is presented in Chapter 7, while the opportunities for boosting the efficiency and economic performance of future fusion devices are addressed in Chapter 8. An overview and a summary of the main outcomes of this thesis is given in Chapter 9, which also provides an outlook and directions for future work. The contents of Chapter 4and Chapter 5have partially been published in the article Feasibility study for an edge main ion charge exchange recombination spectroscopy system at ASDEX Upgrade in the journal Journal of Instrumentation on 2019. This article demonstrates the feasibility of the diagnostic and presents the first measurements. The work presented in Chapter 8has also resulted in the publication of a journal article Boosting the Efficiency of Future Fusion Power Plants Combining Energy and Heat Production in the journal IEEE Transactions on Plasma Science on 2022, which studies cogeneration strategies for boosting the efficiency of future fusion power plants. The thesis author is the first author of both publications, for which the full citations are given in Appendix A. 9 Chapter 2 Theoretical background In this Chapter, the relation between main ion and impurity properties based on neoclassical transport theory is described. The structure of neoclassical plasma flows is derived starting from the motion of a single charged particle in the tokamak’s magnetic field and its interaction with other particles via collisions. The confinement regimes relevant to this work are characterized. 2.1 Single particle motion The basic idea of magnetic confinement of charged particles can be retrieved from the equation of motion of a charged particle in an electromagnetic field. A charged particle in the presence of magnetic and electric fields feels the Lorentz force. The motion of a single charged particle is described by:  F=mdv dt=q·( E+v × B),(2.1) where qis the particle charge, v is the velocity of the particle,  Eis the electric field and  Bis the magnetic field. The particle velocity can be decomposed in a parallel (v∥) and perpendicular (v⊥) component to  B, which in the simplified case of a uniform magnetic field (  E= 0,  B=Bez, and constant B) yields: mdv⊥ dt=q·(v⊥× B),(2.2) mdv∥ dt=q·(v∥× B)=0.(2.3) The velocity in the direction parallel to the magnetic field is constant, and the particle gyrates around the magnetic field lines with uniform circular motion. This is the basic idea behind magnetic confinement: a charged particle motion is constrained to a helical trajectory around the magnetic field line as illustrated in Figure 2.1. The characteristic temporal and spatial scales of the gyromotion are the cyclotron frequency (ωc) and the Larmor radius (rL), defined as: ωc=|q|B m;rL=mv⊥ |q|B=v⊥ ωc .(2.4) Note that ions and electrons gyrate in opposite directions due to their charge. Electrons gyrate faster and closer to the magnetic field lines due to the mass dependence of ωcand rL. If B/∇B >> rLand ˙ B/B << ωc, the guiding center approximation can be applied, which is valid in the fusion plasmas considered in this thesis. The guiding center motion is illustrated in Figure 2.1 in blue. In the guiding center approximation, the effect of 10 Chapter 2. Theoretical background rL X guiding center X(t) rL B Figure 2.1: Decomposition of particle motion in its gyration around  B(in red) and the guiding center motion (in blue), rLis the Larmor radius (in magenta) and X(t) the position of the guiding center. In the presence of inhomogeneous magnetic or electric fields, the guiding center does not follow the magnetic field line (in black). Adapted from [18]. an external  Fon the particle trajectory is usually gyro-averaged and approximated to act on the guiding center. A force acting in the direction parallel to  Bwould lead to an acceleration of the guiding center, while a force perpendicular to  Bwill lead to a drift of the guiding center. 2.2 Guiding center and fluid drifts The magnetic field structure in a tokamak is not uniform, leading to guiding center drifts. The general expression for a drift velocity (vd) due to an external force  Fext is: vd=1 q  Fext × B B2.(2.5) The magnetic field dependence on the major radius and the toroidal geometry of the tokamak lead to the ∇ Band curvature drifts. These drifts have an important role in the particle orbit topology, as explained in Subsection 2.3. Other important drifts for this work are the  E× Band diamagnetic drift, which are a particle-like and fluid drift, respectively, and apply in different pictures of the plasma. The typical directions for these drifts in the ASDEX Upgrade (AUG) tokamak are illustrated in Figure 3.5. 2.2.1 ∇Bdrift The magnetic field gradient in the direction of the major radius (B∝1/R) leads to a force perpendicular to both the magnetic field and its gradient. This is the ∇ Bdrift, which is given by: v∇B=−mv2 ⊥ 2qB3∇B× B. (2.6) The direction of the ∇Bdrift with respect to the X-point is an important ingredient for access to different confinement regimes, as discussed in Subsections 2.7.3-2.7.4. 2.2.2 Curvature drift In their motion, particles will feel a centrifugal force due to the toroidal field line geometry in a tokamak, and a curvature drift (vcurv) arises. If we assume constant 2.3. Radial transport 11 radius of curvature of the field lines (Rc) and the average centrifugal force  Fcurv, the associated curvature drift velocity (vcurv) is:  Fcurv =mv2 ∥  Rc R2 c ;vcurv =−mv2 ∥ qB3∇B× B. (2.7) Note that both the ∇ Band curvature drift depend on the charge and lead to charge separation. This motivates the need for introducing a poloidal magnetic field. 2.2.3  E× Bdrift If there is an electric field perpendicular to the magnetic field, particles will feel a force  F=q E. The  E× Bdrift is given by: vE×B= E× B B2.(2.8) Note that the  E× Bdrift does not depend on the charge nor mass of the particle, and therefore it points into the same direction for ions and electrons. 2.2.4 Diamagnetic drift The diamagnetic drift (vdia) is due to a pressure gradient (∇p) perpendicular to the magnetic field. Strictly speaking it is not a guiding center drift, as it does not act on the guiding center of individual particles. The diamagnetic drift is caused by both a gradient in the density and temperature (i.e., a pressure gradient). In a given reference area, a differential fluid velocity will arise from a gradient in temperature (T) and/or density (n). In the presence of a density gradient, the number of particles with a positive and negative velocity are unbalanced, while in the presence of a temperature gradient, particles with higher temperature (and energy) gyrate faster. This leads to an apparent fluid drift, given by: vdia =−∇p× B qnB2.(2.9) 2.3 Radial transport Although charged particles are bound to the magnetic field lines, particles can move across magnetic flux surfaces due transport. The outward movement of particles and energy perpendicular to the magnetic field leads to radial transport. Understanding and controlling radial transport are fundamental for the success of magnetically confined fusion plasmas. On the one hand, the minimization of radial transport of D and T is essential to achieve fusion energy. On the other hand, the confinement of the helium fusion product should be long enough to allow energy transfer from the alpha particles to the bulk plasma while ensuring its efficient removal to avoid fuel dilution. In addition, knowledge of impurity transport is key for control of the radiation profile and detachment, which is crucial for the achievement of a power exhaust solution in future fusion devices. Radial diffusive particle transport can be described using Fick’s law, according to: Γ = −D∇n, (2.10) where Dis the diffusion coefficient, ∇nis the radial density gradient and Γ is the radial particle flux. The drive for the radial flux is the gradient in the plasma quantity, and 12 Chapter 2. Theoretical background the flux is directed opposite to the gradient to counteract it. The radial heat flux (Q) is related to the radial temperature gradient (∇T) via the heat diffusivity (χ) [19]: Q=ZPdV=−nχ∇T, (2.11) where Pis the power and Vthe plasma volume. A similar expression can be written for momentum transport (driven by gradients in velocity). The values for the diffusion coefficients depend on the transport mechanism. The main transport mechanisms discussed in the next subsections are collisional and turbulent transport. 2.3.1 Collisional transport In their gyromotion, particles can collide leading to radial transport. Classical collisional transport considers the random walk of a particle due to Coulomb collisions. The characteristic spatial and time scales are the Larmor radius (rL) and the collision time (τ), respectively. The classical diffusivity (Dclass) is defined as: Dclass =r2 L 2τ.(2.12) In the following subsection, the role of the collision frequency (ν= 1/τ) as an important parameter for the characterization of plasma transport is discussed. 2.3.2 Neoclassical transport In a tokamak, radial transport is expected to be larger than classical transport due to the toroidal geometry of the magnetic field. The neoclassical transport theory [20] includes the effects of toroidal geometry for the derivation of the diffusion coefficients. The main effect of the toroidal geometry, which enhances diffusion is the occurrence of magnetic mirrors. Magnetic mirrors form due to the ∇Band curvature drifts and lead to particle trapping, affecting the spatial scale for diffusion. Particle trapping can be understood from energy (E=1 2m(v2 ∥+v2 ⊥)) conservation and magnetic moment (µ=mv2 ⊥ 2B) invariance (in the limit of slow variations of  B,µis an adiabatic invariant [9]). As a particle moves from the LFS to the HFS, Bincreases. Consequently, v⊥increases (such that µis constant), while v∥decreases (due to energy conservation). If v∥= 0 along the trajectory, the particle cannot penetrate further in the high magnetic field region and is reflected to the LFS. In addition, the ∇Band curvature drifts lead to a deviation of the particle from its corresponding magnetic flux surface. The projection of this trajectory in the poloidal plane leads to the characteristic banana orbit, illustrated in Figure 2.2 in a red-yellow color code. The characteristic spatial scale for diffusion of trapped particles is the banana orbit width rb, which is larger than rL, given as [20]: rb=rL,pol√ε, (2.13) where rL,pol is the Larmor radius evaluated with the poloidal field and εis the inverse aspect ratio of the machine (where ε=r/R, i.e., the ratio between the minor (r) and major (R) radius). Instead, the particles with sufficient energy and v∥/v (such that v∥>0) are so called passing particles, illustrated in Figure 2.2 in blue-green. Note that 2.3. Radial transport 13 Poloidal view Trapped Toroidal view Passing Figure 2.2: Representation of a particle in a banana (red-yellow) and passing (blue-green) orbit in a toroidal and poloidal view. the trapped particle fraction depends on rand is given by [9]: ft=2r R0+r1/2 ,(2.14) where R0is the major radius at the magnetic axis. Collisional transport can be classified in three regimes which are introduced in the following subsection. Collisionality regimes The collisionality (ν∗,α) of species αis a dimensionless parameter that reflects the role of banana particles on overall collisional transport. It is expressed as the effective collision frequency (να) normalized to the trapped particle bounce frequency (ωb) [9]: ν∗α=να εωb =qR ε3/2vth,α να=qR ε3/2vth,α X β ναβ,(2.15) where vth,α is the thermal velocity. The effective ion collision frequency (να) considers collisions of the species αwith itself and with other ion species. The binary collision frequency between plasma species αand β(ναβ) is given by [21,22]: ναβ =4√2πe4 3rmαmβ mα+mβ Z2 αZ2 β mα nβ T3/2Λαβ,(2.16) where mis the mass, Zis the atomic number, nthe density, Tthe temperature and Λαβ is the Coulomb logarithm [9] given by Λαβ = 23.46−ln ZαZβ T3/2 αqnαZ2 α+nβZ2 β[21]. Note that the collisionality is directly proportional to the density and inversely proportional to the temperature. As collisions are the main mechanism for de-trapping particles, three collisionality regimes can be found depending on whether trapped or passing particles dominate the transport, which will affect the diffusion coefficient.  Banana regime (ν∗<1): at low collisionality, trapped particles dominate the 14 Chapter 2. Theoretical background (a) Banana Plateau PS D 1ν* -3/2 ε classical Pfirsch-Schlüter Banana-Plateau Figure 2.3: Neoclassical diffusion coefficient as a function of collisionality at constant temperature. Adapted from [24]. transport, as particles complete several banana orbits before experiencing a collision [9]. Dneo banana ≈q2 ε3/2Dclass,(2.17) the diffusivity depends linearly on the collision frequency and is larger than the classical diffusivity by a large fraction. This is true even when the trapped particle fraction is proportional to ε1/2.  Plateau regime (ε−3/2> ν∗>1): in this intermediate regime, the bounce and collision frequencies are comparable. The diffusivity is given by [23]: Dneo plateau =vthr2 Lq R.(2.18) In this regime the diffusion coefficient is roughly constant, such that it does not depend on collisionality.  Pfirsch-Schl¨uter regime (ν∗> ε−3/2): at high collisionality, trapped particles cannot complete a full orbit before experiencing a collision. In the Pfirsch-Schl¨uter regime, the diffusivity is given by [9]: Dneo PS =q2Dclass.(2.19) The diffusivity also depends linearly on the collision frequency and is larger than the classical value. The collisionality regimes are illustrated in Figure 2.3, and it can be seen that the total transport is due to the sum of the classical, banana-plateau and Pfirsch-Schl¨uter contributions [24]. Collisional heat transfer between thermal species Besides particle transport, collisions also lead to energy transport. The energy exchange term between thermal plasma species is proportional to the temperature difference between them: the larger the temperature difference, the higher the exchange term. 2.3. Radial transport 15 (a) 0.0 0.2 0.4 0.6 0.8 1.0 pol 0.2 0.4 0.6 0.8 Power fraction #38539 t = 2.50 s to ions to electrons Injection energy 93 keV 60 keV (b) 0.0 0.2 0.4 0.6 0.8 1.0 pol 10 5 10 4 10 3 10 2 10 1 100 101 102 Time [s] #38539, t = 2.50 s zD ze eD tr Figure 2.4: (a) Power fraction to ions (red) and electrons (green) from NBI for a 60 keV (dashed) and 93 keV (solid) injection energy using analytical expressions from Equations (2.21)-(2.23). (b) Thermal equilibration time scale for impurity-ion (τzD in red), impurity-electron (τze in green), electron-main ion (τeD in blue) and particle transport time (τtr in black). The power density thermal equipartition between two species αand βis given by [25, 26]: pαβ =ceqΛαβ (AαAβ)1/2 (TβAα+TαAβ)3/2Z2 αZ2 βnαnβ(Tα−Tβ),(2.20) where ceq is a constant that can be derived from the heat exchange time [9,25] and Λαβ is the Coulomb logarithm for Coulomb collisions between the species αand β. Collisional heat transfer from energetic particles to thermal plasma Energetic ions, which can be born in the plasma from fusion reactions or generated by external heating (such as Neutral Beam Injection (NBI)), transfer their energy to the thermal plasma via collisions. The energy transferred to ions and electrons depends on the local density and temperature of the plasma, as they affect the probability of a collision with the species. The local heating fraction to ions (Gi) can be calculated analytically using [27]: Gi=Ec E0ZE0/Ec 0 y 1 + y3/2,(2.21) where E0is fast particle energy and Ecthe critical energy. Consequently the local heating fraction to electrons (Ge) is Ge= 1 −Gi.(2.22) The critical energy (Ec) is defined as the energy at which the loss rate to ions and electrons is the same. Ec= 14.8Te A3/2 neX i niZ2 i Ai!2/3 ,(2.23) where Tis the temperature, nis the density, Aand Zare the atomic and mass numbers and the subindex erefers to the electrons and ito the ion species. Figure 2.4(a) shows 16 Chapter 2. Theoretical background Electron Main ion Impurity E = 60 keV E = 93 keV Electron Main ion Impurity Electron Main ion Impurity E = 60 keV E = 93 keV E = 60 keV E = 93 keV Figure 2.5: (a) Power density deposited, (b) integrated power and (c) power per particle for electrons (green), main ions (red) and impurities (blue) as a function of radius as calculated with the orbit following ascot code for discharge #38540 for a 60 (solid) and 93 (dashed) keV NBI source. the heating fraction to ions (red) and electrons (green) for fast-neutrals at 93 and 60 keV, which resemble the NBI sources at AUG. It can be seen that at the plasma edge, the power deposition to electrons is dominant, while in the plasma core, most of the power is transferred to the ions. The power deposited to the ions increases, as temperature increases and as density decreases. Interestingly, the more energetic beams deliver more power to the electrons. The power deposition to the three species (electrons, main ions and impurity ions) as calculated with the Monte Carlo orbit following ascot code [28] is illustrated in Figure 2.5(a-c) for the plasma discharge #38539. The calculated heating source power density shown in Figure 2.5(a) is consistent with the analytical calculation shown in Figure 2.4(b). Figure 2.5(b) shows the volume integrated power deposited on each species. It can be seen that the main ions receive the largest fraction of NBI power. Note that the impurities are receiving a higher heating power per particle compared to the main ions and electrons across the full plasma radius (see Figure 2.5(c)). 2.3.3 Anomalous transport Radial transport in tokamaks is typically larger than that expected from neoclassical transport. Anomalous, or turbulent transport, is due to fluctuations in the density, temperature, electrostatic potential and/or magnetic field. The anomalous transport is typically 2-5 times larger than neoclassical transport. Only in regions with reduced turbulence levels, such as the steep gradient region in the edge transport barrier of H- mode plasmas (see Section 2.7.2) or internal transport barriers [29], tokamak transport has been found to be at the neoclassical level. 2.4 Transport time scales The transport and confinement of the plasma can be characterized in terms of the macroscopic energy confinement time. The energy confinement time (τE) is defined as τE=W/(P−dW/dt),(2.24) where Wis the global plasma energy content and Pthe total input power. 2.5. The radial force balance equation 17 Another important time scale is the collisional thermal equilibration time (ταβ) between the species αand β, which can be determined using [26]: ταβ =1 1.8×10−19 (mαTβ+mβTα)3/2 pmαmβ)(ZαZβ)2nβln Λ,(2.25) where mα,mβare the masses in g, Tα,Tβthe temperatures in eV and Zα,Zβthe charge states of the particle species αand β, nβis the density of species βin cm−3and ln Λ the Coulomb logarithm. Note that the general assumption of TD∼Tzis motivated by the short thermal equilibration time between main ions and impurities (τDz, in the order of µ s) compared to the local particle transport time scale (τtr, in the order of ms), as shown in Figure 2.4(b). 2.5 The radial force balance equation In this section, the expression for the radial electric field is derived, starting from the statistical description of the plasma species αby means of its distribution function. 2.5.1 The kinetic equation In a statistical approach, the description of a plasma species is given by its distribution function. The distribution function fα(x,v, t) of the species αmeasures the probability density for a single particle in the six-dimensional phase space (x,v) at time t. If the number of particles is conserved along the trajectories of the system, fαobeys the conservation equation [9,30,31]: dfα dt=∂fα ∂t +∂fα ∂x ∂x ∂t +∂fα ∂v ∂v ∂t = 0,(2.26) using v =∂x/∂t and Equation (2.1): ∂fα ∂t +v ∇fα+qα mα ( E+v × B)∇vfα= 0.(2.27) This is the Vlasov equation, which is valid in the absence of collisions (low density or short time scales compared to the collisional time scale). The distribution function can change over time due to particle interactions, in particular, due to collisions. The change of the distribution function due to Coulomb collisions is considered by [22,32]: dfα dt=Cα(fα),(2.28) where Cα(fα) is the Fokker-Planck collision operator, which is a sum of contributions due to collisions of the species (α) with other particle species (β), Cα=PβCαβ(fα, fβ). The Fokker-Planck kinetic equation for a particle species αin a plasma reads [9,22, 30]: ∂fα ∂t +v ∇fα+qα mα ( E+v × B)∇vfα=Cα(fα).(2.29) An important property of the collision operator is that it drives the distribution function towards local thermodynamic equilibrium [22]. The relevant information on the statistical distribution fαis contained in its moments. The k-th moment of the distribution function is defined as Rv kfα(v)dv, with k≥0 [30]. Importantly, the zeroth 24 Chapter 2. Theoretical background 0 2 4 ne[m2] 1e19 (f) #39318 H-1 H-5 0 1 2 3 PNBI [MW] (g) Q4 Q5 Q7 Q8 0 2 4 6 P [MW] (h) ECRH NBI 1.00 1.25 1.50 pol (i) Program RT 4.50 4.75 5.00 5.25 5.50 5.75 6.00 Time [s] 0 5 10 Idiv [kA] (j) QH-mode EHO 15 0 fELM coils [kHz] 0 5 ne[m2] 1e19 (a) L-mode I-mode #40223 H-1 H-5 0 2 PNBI [MW] (b) Q3 Q8 0 1 2 PECRH [MW] (c) 0.0 0.5 1.0 pol (d) Program RT 2.5 3.0 3.5 4.0 4.5 Time [s] 0 1 2 D[part/s] 1e21 (e) -5 5 0 N Figure 2.7: Time traces of (a) the core (black) and edge (red) line integrated electron density, (b) NBI power, (c) ECRH power, (d) programmed and real-time βpol and (e) gas fuelling for the USN discharge #40223. The L-mode and I-mode phases are highlighted in cyan and green, respectively. Time traces of (f) the core (black) and edge (red) line integrated electron density, (g) NBI power, (h) total power, (i) programmed and real-time βpol and (j) divertor current for the USN discharge #39318. The phase where EHOs are observed is highlighted in cyan. stability against ELMs. Experimentally, the QH-mode is accessed at low density and low collisionality. A strong  E× Brotational shear is a key ingredient for entering the QH-mode [72]. The time traces of the USN discharge #39318 (Bϕ=−2.5 T, Ip= 0.6 MA), for which main ion measurements are presented in Chapter 6, are shown in Figure 2.7(fj). A βpol feedback control scan is implemented in this case using the NBI at 2 MW per source at constant ECRH power. A drop of the divertor currents can be seen in Figure 2.7(j) at 5s, which indicates a change in the particle recycling. This change is concomitant with the transient appearance of the EHO in the magnetic spectrogram, which is visible up to t= 6 s. In this time window, highlighted in cyan, the EHO co-exists with the ELMs, which indicates that it is not yet fully established and able to replace the ELMs completely. 2.8 Summary In this chapter, single particle motion in tokamaks has been explained. The operation regimes investigated in this thesis have been introduced. The characterization of the main ion properties in these confinement regimes are presented in Chapter 6, with a special focus on the H-mode, which is currently considered the primary operating mode for future fusion devices. In the next chapter, the ASDEX Upgrade tokamak, in which experiments have been carried out in this thesis, is described. The conceptual design of 2.8. Summary 25 the European DEMO tokamak is also reviewed. The integration of the DEMO Baseline 2018 reactor with a power conversion system is studied in Chapters 7and 8. 27 Chapter 3 The ASDEX Upgrade and the European DEMO tokamak In the framework of this thesis, experiments have been carried out at the ASDEX Upgrade tokamak. A description of the ASDEX Upgrade tokamak and its heating and diagnostic systems, which are crucial for this thesis, is given. The conceptual design of the European Demonstration (DEMO) tokamak is reviewed. The prediction of the DEMO performance requires the use of modelling tools, in particular, reactor systems codes. The process system code is explained and the reference baseline, which is considered in this work, is introduced. The baseline will be used as reference scenario for the study of the integration of a future fusion reactor and a power conversion cycle. 3.1 The ASDEX Upgrade tokamak The ASDEX Upgrade (AUG) tokamak is a medium sized diverted magnetic fusion device located at the Max-Planck Institute for Plasma Physics in Garching (Germany). The goal of AUG is to establish a scientific basis for the optimization of the tokamak approach to achieve fusion energy and to prepare for next step devices such as ITER and DEMO [73,74]. AUG makes a world-wide unique contribution to tokamak research, as it features tungsten plasma facing components, a powerful and flexible external heating installation (see Subsection 3.1.1) and an excellent diagnostic suite (see Subsection 3.1.2), with matched conditions to those envisaged for next step devices. 120 MW of NBI, 5-6 MW of ECRH and 6 MW of Ion Cyclotron Resonance Frequency. Total height of the device [m]9 Major plasma radius [m]1.65 Minor plasma radii [m]0.5 - 0.8 Magnetic field [T]3.1 Plasma current [MA]1.6 Pulse length [s]10 External heating [MW]321 Plasma volume [m3]13 Plasma mass [mg]3 Plasma composition H, D, He Plasma density [particles/m3]2·1020 Plasma temperature [M ° C]100 Table 3.1: Technical data for the ASDEX Upgrade tokamak, taken from [1]. 28 Chapter 3. The ASDEX Upgrade and the DEMO tokamak Note that the methodology for the planning and execution of experiments is discussed in Appendix C. Relevant technical data about the tokamak is summarized in Table 3.1. 3.1.1 Heating systems In the absence of external heating, plasmas are resistively heated. These are the ohmic plasmas. Resistive heating is however inefficient to achieve fusion conditions, as it decreases with increasing plasma temperature with T−3/2, due to a decrease of plasma resistivity [44]. To achieve the conditions necessary for fusion, external or auxiliary heating is required. AUG is equipped with 32 MW of input power. In this subsection, two plasma heating methods are presented. The first method consists of injecting energetic neutrals (Neutral Beam Injection), which transfer their energy to the plasma particles by collisions. The second method relies on the wave-particle resonant interaction and specifically targets electrons (Electron Cyclotron Resonance Heating). Neutral Beam Injection The Neutral Beam Injection (NBI) system at AUG consists of two positive-ion-based injectors, box 1 and box 2, located in sectors 15 and 7, respectively. Each injector is equipped with 4 ion sources, of 2.5 MW nominal power each. The NBI sources inject energetic neutrals (typically D) which can penetrate the magnetic field and ionize as they interact with the plasma, giving rise to the fast-ions. The fast-ions then transfer their energy via Coulomb collisions to ions and electrons, as described in Subsection 2.3.2. The main energy component (E0) is 60 keV and 93 keV for box 1 and 2, respectively. In the ion source, D+ions as well as D+ 2and D+ 3molecules are generated. Since all are accelerated with the same electric potential, this results in three populations with decreasing energy gains per D atom, leading to three energy components: E1=E0for D+,E2=E0/2 for D+ 2and E3=E0/3 for D+ 3. Besides the injection energy, the NBI sources differ in their geometry. A summary of the characteristics of each beam box and sources is given in Table 3.2. Compared to radial beams, tangential beams favour the injection of passing particles, because of a higher v∥component. The off-axis injection favours the creation of edge fastions compared to on-axis injection. NBI Q3 and Q8 are particularly important for this work, as they are the diagnostic beams for impurity and main ion CXRS measurements, respectively (see Subsection 3.1.2). Box 1 Box 2 Sector 15 7 Number of sources 4 4 Injection Energy 60 93 E1:E2:E3ratio (%) 65 : 25 : 10 62 : 29 : 12 Sources 1 Radial 5 Tangential 2 Tangential 6 Off-axis 3 Tangential 7 Off-axis 4 Radial 8 Tangential Table 3.2: Details on the Neutral Beam Injection system at the ASDEX Upgrade tokamak [1]. 3.1. The ASDEX Upgrade tokamak 29 (a) edge tor. CXRS ECE Li beam Q5/8 core tor. LFS/HFS CXRS TS core tor. CXRS 1412 1311 x [m] -3 -2 -1 0 3 21 10 8 7 9 y [m] 3-3 2 1 0 -2-1 Q2/3 edge pol. CXRS DCN He beam edge tor. CXRS 1 16 15 2 6 5 4 3 #38540 t = 2.5s edge tor./pol. gp CXRS edge pol. gp CXRS (b) 1.0 2.51.5 2.0 R [m] -0.5 0.0 0.5 1.0 -1.0 #38540 t = 2.5s z [m] separatrix edge tor. CXRS Q8/Q3 edge pol. CXRS gp/Q3 core tor. CXRS Q3/Q8 Q8 Q3 edge /tor. pol HFS gp CXRS DCN Li beam He beam ECE TS edge tor. gp CXRS H-1 H-0 H-2 H-5 H-4 Figure 3.1: Overview of AUG diagnostics relevant to the work in a (a) toroidal and (b) poloidal view. For simplicity, only the innermost and outermost line of sight for each CXRS optical head are shown. Electron Cyclotron Resonance Heating Heating of the plasma is possible by resonant interaction of plasma particles with electromagnetic waves. The Electron Cyclotron Resonance Heating (ECRH) working principle relies on the acceleration of electrons in their gyromotion, by launching high frequency microwaves (of the order of mm), which are comparable to their cyclotron frequency (ωc). The power deposition is well localized in radius as the launched waves are resonant at a given magnetic field strength, which strongly depends on R. At AUG, the deposition location can be fine tuned by adjusting the launching angle of the turnable mirrors. A specific flux surface can be targeted, as the deposition in (R, z) is determined by the intersection of the beam with the resonance radial location. The ECRH system at AUG consists of eight gyrotrons which deliver up to 6 MW (typically, each gyrotron delivers 700 kW). The gyrotrons generate 140 GHz and 105 GHz waves for core deposition for a central magnetic field of -2.5 T and -1.8 T, which in standard configuration corresponds to the second harmonic of the cyclotron frequency, respectively [75]. In this thesis, ECRH has been used as an auxiliary heating method in all discharges. The use of ECRH at the AUG full-tungsten wall is important to avoid core impurity accumulation, which can lead to plasma termination due to radiative collapse [76]. 3.1.2 Measurement of plasma properties In this section, the diagnostics that are important for this thesis are explained. A toroidal and a poloidal view of the diagnostics are shown in Figures 3.1(a,b), respectively. Charge Exchange Recombination Spectroscopy Charge Exchange Recombination Spectroscopy (CXRS) is the most wide-spread technique for radially and time-resolved diagnosis of ion temperature, velocity and density 30 Chapter 3. The ASDEX Upgrade and the DEMO tokamak 493.75 494.00 494.25 494.50 494.75 495.00 495.25 Wavelength [nm] 0.5 1.0 1.5 2.0 2.5 3.0 Intensity [Ph/ ( m 2 nm sr s ) ] 1e17 B 5 + (7 6) B 5 + 0 FWHM L 0 CMR-1-6 #38540, t = 2.70s Total fit Active B 5 + (7 6) Passive B 5 + B 2 + Figure 3.2: Spectral line of B5+(7 →6 transition) at 494.467 nm with the total fit (red) including the passive (orange) and active line (magenta). in tokamak plasmas [77,78]. It is based on the observation of spectral lines emitted by electrons after a Charge Exchange (CX) reaction of an ion (A) with a donor neutral. The donor neutral gives an electron to the ion, which is subsequently in an excited state. The electron decays to a lower binding energy state and a photon of characteristic energy (hν) is emitted in the process, according to Equation (3.1): AZ++D→A(Z−1)+∗+D+→A(Z−1)+ +D++hν. (3.1) The energy is released due to the transition of the electron from the binding energy level E2to the lower binding energy level E1. The energy difference between the two levels is emitted as radiation of characteristic energy (and wavelength, following E=hc/λ, where cis the speed of light). Typically the donor neutral is a fast NBI neutral, which may be used for plasma heating and/or as a diagnostic beam. The emitted light is collected by an optical system that views the neutral source and is analyzed by means of a spectrometer, as described in Chapter 4. At AUG, neutral injection systems at thermal energies for CXRS are also available at the LFS and HFS [79,80]. The fast or thermal donor neutrals are externally injected to induce the CX reaction. The transitions B5+(7 →6) at 494.467 nm, N7+(9 →8) at 566.937 nm, He2+(4 →3) at 468.571 nm and C5+(7 → 6) at 529.059 nm are typically observed at AUG. These transitions can be conveniently measured using standard spectroscopic instrumentation for the visible range. The CXRS technique provides radially localized measurements. The localization of the ion properties in (R, z) coordinates is given by the intersection of the viewing optics (or lines of sight (LOS)) and the neutral gas cloud. The radial resolution of CXRS diagnostics is optimized by careful in-vessel alignment of the optical head (see Subsection 4.3.3) and is down to the mm range. The CXRS method focuses on low-Z impurities, as they are generally fully ionized across the full plasma volume, enabling full radial profiles from the core to the separatrix. Fully ionized impurities do not strongly radiate and perturb the plasma, and give good signal-to-noise ratios in concentrations below 1%. They can be naturally present in the machine or introduced by external fuelling [78]. Figure 3.2 shows the spectrum of the B5+(7 →6) transition at 494.467 nm. The spectral line contains information on the impurity distribution. If the impurity ions are thermalized, their distribution can be described by a Maxwellian, which leads to a 3.1. The ASDEX Upgrade tokamak 31 Gaussian-shaped spectral line, whose intensity (LCX ) can be described as: LCX =L0exp −mzc2 2kBTz (λ−λ0)2 λ2 0,(3.2) where L0is the maximum intensity of the spectral line, kBis the Boltzmann constant, cis the speed of light, λ0is the theoretical wavelength of the emission and Tz and mzare the impurity temperature and mass. The signal consists of an active component, due to CX reactions with the localized diagnostic neutral source (in this case, the NBI) and a passive component, which is present in the absence of an active neutral source due to electron impact excitation and CX with background thermal neutrals. The active emission is localized at the intersection of the LOS with the NBI, while the passive emission originates in a broader region and is collected along the LOS path. In order to extract localized information, the passive emission must be removed by passive background substraction (see Subsection 5.4.1) or both components need to be considered for the fit, as shown in Figure 3.2. The Gaussian spectral line contains information on the impurity temperature and rotation velocity. The impurity temperature (Tz) is related to the Gaussian full width at half maximum (FWHM) due to the Doppler broadening of the line according to: Tz=mzc2 8 ln(2)λ2 0eFWHM2,(3.3) where mzis the impurity ion mass, cthe speed of light, λ0the theoretical wavelength of the emission and ethe electron charge. The Doppler shift of the line (∆λ, the difference between the measured central wavelength and the theoretical wavelength of the emission) is related to the impurity rotation velocity due to the Doppler effect (the finite velocity of the emitting ion), according to: ∆λ λ0 =vrot,z ·eLOS c,(3.4) where eLOS is the unit vector along the LOS. The Doppler shift depends on the velocity of the emitting ion and the projection of the velocity on the LOS direction. For this reason, LOS in the poloidal and toroidal direction are required to characterize vϕand vθaccurately (see Subsection 2.5.3). The relation between the intensity of the spectral line (LCX ) and the impurity density (nz) and the donor neutral density (nN,n) is given by LCX =hν 4πZLOS nmax X n=1 nznN,n⟨σnν⟩eff dl, (3.5) where ⟨σnν⟩is the effective CX rate coefficient, the subindex nrefers to the quantum number and the integral refers to the path of the LOS. In this way, CXRS measurements enable time-resolved radial profiles of the impurity ion temperature, velocity and density. The AUG CXRS suite is illustrated in Figure 3.1. It consists of core and edge spectroscopy systems on NBI sources Q3 and Q8 (in dashed green), as well as gas puff based edge systems in both the HFS [79,81] and LFS [80]. The core systems have a temporal resolution down to 4 ms and spatial resolution down to 1.5 cm [82,83]. The edge systems consist of poloidal and toroidal optical heads at both the HFS and LFS, which enable the determination of the Erprofile at two poloidal locations. The standard temporal resolution of the edge diagnostics is 2.5 ms and can be down to 50 µs [84], with a spatial resolution of 3 and 5 mm for the toroidal and poloidal views, respectively [82]. The edge toroidal optical head on Q8 32 Chapter 3. The ASDEX Upgrade and the DEMO tokamak has been installed in the framework of this thesis, and enables the simultaneous direct measurement of impurity and main ions. Note that in the absence of a direct main ion diagnostic system, the main ion properties may be inferred from the impurity properties. In general Tz≈TDis assumed based on the short thermal equilibration times scales (discussed in Subsection 2.3.2). The main ion toroidal rotation at the plasma edge has been typically inferred using impurity toroidal rotation measurements in combination with neoclassical theory (see Subsection 2.6.3). In this work, the CXRS technique (traditionally performed on impurities) has been extended to the main ions. While the working principle for main ion spectroscopy is the same as for impurities, the main ion photo-emission processes and atomic effects prevent a simple interpretation of its spectrum. A detailed description of the edge main ion system and the tools developed in this thesis for the interpretation of the main ion spectrum are given in Chapter 4and 5, respectively. Electron measurements Detailed knowledge of electron temperature and density is crucial for its comparison to the ion measurements, for the characterization of the edge transport barrier and transport modelling. In addition, edge electron density and temperature profiles are inputs for the forward modelling of the main ion spectra using the fidasim code (see Subsection 5.2.1). In this subsection, the diagnostic capabilities at AUG for the experimental determination of the electron temperature (Te) and density (ne) are described.  Thomson Scattering The Thomson Scattering (TS) diagnostic is the most extended technique to provide simultaneous measurement of Teand nefrom a given plasma volume, and therefore allows for consistent alignment of the electron temperature and density profiles. The working principle of the TS diagnostic relies on the elastic scattering of a coherent wave by charged particles. Because of their low mass in comparison to ions, the electrons are accelerated by the incident laser wave, and scatter the radiation. The scattered light is collected by means of a polychromator. The measured spectrum provides information on the electron properties: nedepends on the total amount of scattered power, while Tecan be inferred from the Doppler broadening of the scattered radiation. The TS suite at AUG consists of a core, an edge and a divertor system [85,86]. The systems use 6 (core), 4 (edge) and 1 (divertor) pulsed Nd-YAG (neodymium yttrium aluminium garnet) lasers with a wavelength of 1064 nm. The temporal resolution of the edge and core system is 8 ms, and 50 ms for the divertor system. The spatial resolutions are 3 mm, 8 mm and 25 mm for the edge, divertor and core systems, respectively.  Interferometry Interferometry allows the determination of nedue to the dependence of the refractive index on the plasma density. The phase shift (φ) of a laser beam (of vacuum wavelength λ0) relative to a reference beam that propagates in vacuum depends on the local electron density (ne(x)) [9] according to: φ=λ0reZne(x)dl, (3.6) here, xis the spatial coordinate along the beam path and reis the classical electron radius re=e2/(4πε0meω2 0), where ω0is the vacuum angular frequency of the electromagnetic wave. The interferometer system at AUG uses a deuterium 3.1. The ASDEX Upgrade tokamak 33 cyanide (DCN) laser and a Mach–Zehnder-type interferometer [87] with heterodyne detection system [88]. The system consists of five lines of sight, which traverse different plasma volumes that are representative of core to edge lineintegrated densities (H-1 to H-5 as illustrated in Figure 3.1(b)). The measured phase difference between the waves launched across the plasma and a reference wave launched through vacuum enables the determination of the line-integrated electron density. The line-integrated measurements can be combined to provide radial profiles using an Abel inversion. Due to its fast temporal resolution, of 300 µ s, the diagnostic enables real-time control of the plasma density during experiments.  Electron Cyclotron Emission The Electron Cyclotron Emission (ECE) is a well-established technique to provide radially localized Teinformation. The working principle of the ECE diagnostic is based on black-body radiation, i.e., the electromagnetic emission of an opaque, non-reflective body that depends only on the body temperature. The temperature of the electrons can be derived from the spectral radiance (Iω) using the Rayleigh- Jeans expression: Iω=ω2 8π3c2kBTe,(3.7) where ωis the angular frequency and Teis the electron temperature. This expression is correct in optically thick plasmas, for which black-body radiation can be assumed (the plasma efficiently absorbs radiation at cyclotron frequency, such that no radiation is reflected). Because of their gyration around magnetic field lines, electrons emit radiation at the angular electron cyclotron frequency (ωc,e =eB me) and its harmonics (ωk=kωc,e). The localization of the emission can be performed due to the 1/R dependence of the magnetic field. At AUG, the electron cyclotron intensity spectrum is measured by a 60-channel heterodyne radiometer receiver [89], which covers a frequency range of 95-167 GHz. The spatial and temporal resolutions are down to 5 mm for the edge and 1.2 cm in the core, with a sampling rate of 1 MHz [90]. The direct diagnosis of Te by its identification with the radiation temperature is limited to Tene= 3 ·1018 keV m3at AUG. In the steep gradient region, a forward model is needed to interpret the measurement [90,91] and correct for the shine-through effect, i.e., an over-prediction of the radiation temperature.  Lithium beam emission spectroscopy This spectroscopic technique enables the determination of nein the edge region up to the pedestal top due to the interaction of a high lithium energy beam (45 keV) with the plasma. The interaction of the lithium atoms with the plasma leads to a population of excited atomic states. In particular, the Li2p→Li2s transition at 670.9 nm is measured [92]. The attenuation of the beam restricts the measurement to the plasma edge. The beam is observed with an optical head of 35 LOS. The measurement is combined with a probabilistic method [93] to resolve newith a temporal and spatial resolution down to 50 µ s and 6 mm, respectively.  Thermal helium beam emission The thermal helium beam emission technique enables plasma edge measurements of both neand Te. The technique is based on the detection of seven He Ilines in the visible range. The diagnostic takes advantage of the different dependency of singlet and triplet states densities on neand Te. Therefore, the experimental 40 Chapter 3. The ASDEX Upgrade and the DEMO tokamak There are close links between the breeding blanket (materials and coolant) and the PCS [117]. On the one hand, the choice of the primary coolant depends on the design and requirements for heat extraction from the blanket. The design and materials used for the blanket and structural elements will limit the maximum temperature for the primary coolant. On the other hand, the primary coolant temperature limits the secondary coolant temperature. The maximum temperature for the PCS working fluid limits the cycle performance (higher temperatures generally lead to higher efficiencies, due to the Carnot efficiency limit) and conditions the best choice for the working fluid: the performance of water/steam, helium and sCO2PCS depends on the temperature range, as will be discussed in Section 7.4. Another important parameter regarding the electricity production for future fusion power plants is the inner auxiliary power or recirculated power needs, i.e., how the electricity production compares to the electricity consumption of the device. In the following paragraphs, the characteristics of the heat sources in DEMO and the temperature constraints are discussed, the primary coolant properties and requirements are outlined and the power balance of the plant is explained. Heat sources characteristics In a future fusion device, the plasma facing components must handle extreme heat fluxes in a reactor environment, i.e., when exposed to radiation and neutron bombardment. In addition, if the operation of the machine is pulsed, the materials must withstand several duty cycles. From a thermodynamic point of view, a high temperature source is desirable, as it enables higher efficiencies according to the Carnot limit. In practice, the maximum achievable temperature in the PCS for a future fusion power plant (FPP) is limited by present day structural materials. Depending on the tritium-breeding blanket concept, the design power surface density to the blanket is typically limited to 1-2 MW/m2[118–120]. In the more conservative breeding blanket models, EUROFER97 is foreseen as structural material (see Subsection 3.2.1). The use of EUROFER97 as structural material poses an important temperature limit that conditions the power cycle performance. The EUROFER97 strength declines over 550 ° C, while below 200-250 ° C radiation causes embrittlement [117]. Both factors define its operation temperature window. In the DEMO Baseline 2018, the use of EUROFER97 limits the blanket temperature to 500 ° C. Larger heat loads are expected in the vessel components that are directly exposed to the plasma (the first wall and divertor). Special attention must be paid to the divertor targets, which collect escaping particles crossing the separatrix in a very narrow area adjacent to the strike points. This is the well-known power exhaust challenge confronted in the design of a commercial fusion reactor: the divertor and first wall will be exposed to extreme heat fluxes, over an order of magnitude higher compared to those expected in the blanket. The heat loads foreseen in the blanket are substantially higher than the highest heat flux for structural materials in fission reactors (∼1 MW/m2for the fuel cladding) [121]. In the divertor, peak heat loads of 6-7 MW/m2[120] are expected in steady-state. The operation of mono-block divertor target in DEMO-relevant high heat fluxes in conditions (up to 25 MW/m2) has been demonstrated [122]. In transient events, such as disruptions, peak radiative heat loads in the range of 500 MW/m2 are expected [123], which calls for the development of mitigation strategies. These extreme conditions demand the use of a highly efficient coolant. Because of its high heat capacity, active water-cooling of the divertor is envisaged in the DEMO Baseline 2018, as water enables efficient heat removal from the divertor. However, water evaporation 3.2. The European Demonstration DEMO tokamak 41 introduces a lower achievable temperature in the divertor in comparison to the blanket, of 150 ° C. This leads to the separation of the heat sources in blanket, divertor and first wall and shield. The temperature limits in each heat source may differ depending on the components materials and the expected heat and particle fluxes. Temperature limitations At this stage, the temperature limits at the heat sources are uncertain. In particular, the temperature limit at the divertor conditions its integration with the PCS. Possible scenarios, from more advanced to more conservative, depending on the temperature limit in the divertor, are:  Advanced structural material enabling high temperatures. Because the heat flux will be naturally higher in the divertor than in the blanket, the divertor temperature can be expected to be higher than the blanket temperature. If advancements in structural material make water-cooling of the divertor unnecessary, the high temperature divertor heat can be integrated with the PCS for superheating [117].  The divertor temperature is in the same range as the blanket temperature. In this case, the integration of the divertor and the blanket in the PCS can be unified. This could either be a fully water-cooled reactor (with efficiencies similar to Pressurized Water Reactors (PWR)) or a fully helium cooled-reactor.  The divertor needs to be water-cooled (based on ITER extrapolation), which limits its maximum temperature to 150 ° C. Because of its low temperature, the integration of the divertor with the PCS is expected to lower its thermodynamic efficiency. However, optimized integration of the divertor could result in improved efficiencies, e.g. when used for preheating [124]. The integration of a low temperature divertor with the PCS must be studied to evaluate whether its inclusion penalizes the efficiency of the cycle because of the temperature constraint that it poses or benefits the electrical power output. Primary coolant: fast neutrons and tritium recovery The PCS layout that can be integrated is conditioned by the choice of the primary coolant. The primary coolants considered include water, helium, molten lithiumlead, molten salt (containing lithium) and carbon dioxide (CO2) [117]. The secondary coolants are water, helium and CO2, as will be discussed in Chapter 7. Important factors to consider when choosing the primary coolant are its interaction with fast neutrons (produced in the fusion reaction) and with the tritium bred in the blanket. Neutron bombardment can induce transmutation (change of nuclear and chemical composition) of all reactor materials and radiation damage to the crystalline lattice (important for structural materials). An overview of the primary coolants and their properties are summarized in Table 3.3. In this context, the primary coolant should: 1. Be easily separated from tritium: Demonstrating tritium self-sufficiency is amongst the biggest challenges for DEMO. To achieve the tritium production goals, it becomes important to efficiently produce and separate the tritium bred in the blanket from other systems. One of the systems in close contact with the breeding blanket are the cooling and PCS system. As the tritium concentration in the primary loop is expected to be high [117], indirect cycles are generally assumed 42 Chapter 3. The ASDEX Upgrade and the DEMO tokamak Water Steam Helium SCO2FLiBe Liquid LiPb BB Model A,B AB,B,C B C C,D Pressure [MPa]15 8 8 8 Trange [ ° C]265-325 300-500 300-500 300-500 700-1100 500-700 ∆hv[MJ/m3]220 15 5.1 13 600 920 µ[10−6Pa s]90 24 35 31 650 10200 κ[W/m/K]0.57 0.07 0.28 0.049 25 1 Heat transfer 1.00 0.06 0.06 0.05 N/A 0.18 Pumping power 1.00 5000.00 23931.62 11382.11 N/A 5.60 Table 3.3: Breeding blanket concept, pressure, temperature range (Trange), volumetric enthalpy increase (∆hv), viscosity (µ), thermal conductivity (κ), heat transfer and pumping power indicators (normalized to water) for plausible primary coolants for DEMO (water, steam, helium, carbon dioxide, molten salts (FLiBe) and liquid lithium-lead). Adapted from [117]. to minimize tritium contamination of the PCS and facilitate its separation. In particular, the tritium permeation to the cooling channel in the divertor region is expected to be large, due to the high particle flux [104]. In this regard, the use of helium, sCO2, molten salts and liquid metals is preferred to the use of water. Permeated T from the plasma facing components or blanket to water coolant easily produces diluted triated water (HTO) due to isotopic exchange, from which T recovery is very cost-consuming. 2. Withstand fast neutron irradiation: interactions with a neutron can lead to the transmutation of atom nuclei. In the case of water, 16O irradiated with fast neutrons can form radioactive 16N which rapidly decays leading to the emission of energetic gamma rays. In contrast, helium is stable against neutron bombardment. The cross-section for neutron capture by carbon stable isotopes is very low, so its transmutation to a radioactive isotope (14C) is expected to be low in a fusion device [106]. In this regard, helium and CO2are preferred to water. 3. Not absorb neutrons: As discussed in Section 3.2, tritium will be bred by thermal transmutation of 6Li, according to Equation (3.8), in the test breeding blanket modules for ITER. This reaction occurs for thermal and fast neutrons, but no neutrons are produced in the reaction (see Equation (3.8)). The coolant must be chosen such that it does not absorb neutrons, as it would penalize the tritium breeding ratio. Water has a high specific heat capacity and is a low pumping power consumption coolant. Water is used with success in nuclear environments such as fission reactors. However, there are open issues for its use in FPP regarding tritium separation, corrosion, stability against fast neutron radiation and strong interaction with lithium. Helium is chemically and radiologically inert and compatible with liquid metals, and its use may enable higher thermodynamic efficiencies at higher temperatures. Carbon dioxide also enables higher thermodynamic efficiencies with reduced power consumption compared to helium, and is compatible with SiC structures [125] (formation of 16Nshould be investigated). The use of molten salts and liquid lithium is a possibility for advanced designs and will enable high PCS efficiency. Helium-cooling is preferred to water-cooling because of helium chemical inertness and stability against radiation at high temperatures, rather than due to the benefit of its use due to cycle efficiency gains at higher temperatures [116]. This is because the improvement in cycle efficiency due to the higher attainable temperatures is counteracted by the high pumping consumption in the primary loop, due to its high compressibility, in comparison with the use of 3.2. The European Demonstration DEMO tokamak 43 (a) Fusion Power 2008MW Plasma 2059MW Blanket/etc. 2060MW Energy Mult. 382MW Primary Heat 2442MW Gross electric 992MW Losses 1450MW Net elec. 500MW Recirc. Power 492MW Core Systems 364MW Heating System 128MW Plasma Heating 51MW Losses 76MW (b) Figure 3.7: (a) Sankey diagram for the DEMO Baseline 2018 fusion power plant. (b) Recirculated power breakdown for the DEMO Baseline 2018: toroidal (TFC) and poloidal field (PFC) coils consumption, tritium and cryogenic plants, primary pumps (He-cooled blanket), vacuum pumps and heating and current drive (H&CD). The total recirculated power is 491.5 MW. water [117]. In the DEMO Baseline 2018, helium is used as blanket coolant, while the divertor is water-cooled. Power balance and recirculated power The net electrical power output in a FPP is limited by the thermodynamic (or PCS) efficiency and the recirculated power. The recirculated power (auxiliary or inner reactor consumption) in a FPP is expected to be high. This has an important impact on the balance of the plant, as combined with the cycle efficiency limit (in practice, below 60% due to the ideal Carnot limit), it can lead to a negative power balance even if the fusion power is in the order of a few 100 MW. Figure 3.7(a) shows the Sankey diagram for DEMO Baseline 2018. It can be seen that the recirculated power is of the same order of magnitude (491.5 MW) as the net electrical power output (500 MW). A breakdown of the inner reactor consumptions for the DEMO Baseline 2018 is shown in Figure 3.7(b). The primary pumping power accounts for almost half of the recirculated power, which is due to the use of helium as blanket primary coolant. Although most of this power is kept within the cycle (over 87% of the compression electrical power will be deposited in the helium) it has a negative effect on the efficiency, as it is not part of the net electrical power output. The second biggest share is due to heating and current drive (H&CD). DEMO foresees an auxiliary input power of 50 MW, which combined with a H&CD efficiency below 40%, leads to an electricity consumption of 127.5 MW. To achieve a high performing FPP it becomes mandatory to minimize the inner consumptions as much as possible, and maximize the PCS efficiency. The latter is the subject of Chapter 7. 3.2.4 The PROCESS systems code Reactor systems codes enable the study of the performance of future fusion devices. In particular, the process systems code5has been used in this work [102,103]. process 5The code has been developed at the Culham Centre for Fusion Energy (CCFE), which belongs to the United Kingdom Atomic Energy Agency (UKAEA) 44 Chapter 3. The ASDEX Upgrade and the DEMO tokamak integrates simplified, yet comprehensive, engineering, plasma physics and economic models to assess the engineering and economic viability of a future fusion power plant. process can be run in a non-optimization and optimization mode [126]. The code is more commonly run in the optimization mode, in which the user specifies a figure of merit to be optimized. In the optimization mode, the constraint (inequalities) and consistency equations are enforced and process maximizes/minimizes a figure of merit by adjusting a selection of iteration variables within user-defined limits. The constraint equations ensure that physics or engineering limits are not exceeded, while consistency equations are usually equalities that ensure that the machine produced by process is self-consistent (many of them should always be activated). The number of iteration variables must be at least equal to the number of equations. In process, there are over 100 iteration variables. In the non-optimization mode only the consistency equations are enforced. In both cases, only the user-specified constraints are implemented. Typical engineering figures of merit are the toroidal magnetic field, major radius or net electrical power output. Economic parameters, such as the cost of electricity (COE) (see Subsection 7.4.4 for its definition), are alternative optimization targets. Engineering models process is one of the most flexible system codes [103]. The engineering models focus on describing the machine geometry and the main components, which include the toroidal and poloidal field coils, first wall, blanket and shield. From an engineering perspective, the coil characterization module is particularly outstanding. The constructive feasibility of the machine is verified, and the limits on forces, stresses, temperatures and current densities can be ensured. An important module for this work is the power balance routine. As highlighted in the previous subsection, the recirculated power can play a key role in the power balance of a future FPP. In process, the primary loop consumption for the blanket and first wall is calculated assuming a pressure loss of helium due to friction in the heat exchangers (HX)s and pipes of 5.5 bar and the Poisson equation for perfect gasses. This pressure drop is justified by estimations of a total pressure drop below 3 bar [127–129] (which give a total electric circulator power consumption of 90 MW in the primary heat transfer system [127,130]). The pumping consumption of the water-cooled divertor and shield are calculated as fractions of the total power deposited in these systems. For the DEMO Baseline 2018 the fractions are 0.5%. Physics models The main physics routines evaluate the plasma parameters and fusion power. These models also describe the current drive and divertor systems. Several models are available for the evaluation of the plasma performance, and each of them has its own usercontrolled switches or flags. Generally, the user is encouraged to use the well-tested default models. These models include limits and projections for plasma performance and stability, and may be based on zero-dimensional models and scaling laws. Important models are the plasma current limit, density limit, βlimit and the confinement scaling and power threshold scaling laws. The models used for the DEMO Baseline 2018 are discussed in Subsection 3.2.4. The plasma profiles in process can include a pedestal structure. The impact of different ion and electron temperatures on fusion power is illustrated in Figure 3.8(b). As the main ion temperature decreases, the fusion power drops, which leads to an increase in the COE. This highlights the importance of maximizing the main ion temperature for the viability of a future FPP. 3.2. The European Demonstration DEMO tokamak 45 Direct costs [M $ ] Structures and site 780.74 Fusion island 3907.51 Turbine system 196.68 Electric system 34.47 Heat rejection system 56.97 Miscellaneous 22.12 Total 4998.49 Table 3.4: Direct costs breakdown for the EUDEMO Baseline 2018. Total Capital Investment [M $ ] Constructed cost 7361.23 Direct cost 4998.49 Indirect cost 1402.58 Contingency cost 960.16 Interest during construction 1104.18 Total 8465.41 Table 3.5: Total capital investment breakdown for the EU-DEMO Baseline 2018. Cost model The process cost model combines methods used in the tetra code [131] and Generomak scheme [132]. The model used in this work evaluates the capital costs and variable costs for a future FPP [133,134]. All the costs and algorithms correspond to 1990 US dollars. The capital costs consider the constructed cost and the interest during construction. The constructed costs are comprised of direct, indirect and contingency costs. Figure 3.8 illustrates the direct costs, which include the fusion island (reactor system, magnets, power injection and vacuum systems, power conditioning, heat transport, fuel handling, instrumentation and control and maintenance equipment), turbine, heat rejection and electric system, structures and site and miscellaneous. An example of the direct costs provided by process is shown in Table 3.4 and Figure 3.8(a) for the DEMO Baseline 2018, with a net electric output of 500 MW and thermodynamic efficiency of 37.5%. The indirect costs (CID) are proportional to the direct costs (CD), by a fraction (find) ranging from 0.244 to 0.290, depending on the level of safety assurance, and the owner factor (fowner, which is set to 0.15), and calculated as: CID =find ·CD·(1 + fowner). The contingency costs (Ccont) are a function of both the direct and indirect costs and are an allowance for incomplete design specification and unforeseen events during the plant construction [126]: Ccont =fcont ·(CD+CID), where fcont is 0.195. The factors are estimated from commercial plant experience [126]. The total capital investment is shown in Table 3.5. The variable costs include the operation and maintenance (O&M), decommissioning fund, replaceable systems (such as blanket, first wall and divertors), auxiliary heating, fuel and waste disposal. The DEMO Baseline 2018 The European DEMO Baseline 2018 generated by process establishes a reference design point that is consistent from an engineering and physics point of view and serves as a starting point for studies [15]. It also facilitates the comparison among different studies. The process simulation results presented in this thesis have been carried out with process version 1.0.17 Release Date 2020-02-25. The relevant machine parameters are consistent with the EU-DEMO Baseline 2018 as presented in Table 1 of [15]. A comparison of the parameters is given in Table 3.6. 46 Chapter 3. The ASDEX Upgrade and the DEMO tokamak (a) (b) Figure 3.8: (a) Direct costs and (b) fusion power and cost of electricity as a function of the Ti/Teratio for the DEMO Baseline 2018. PROCESS PROCESS reference [15] R [m] 9.17 9 A3.1 3.1 B0[T] 5.27 5.86 q95 3.5 3.89 δ95 0.33 0.33 κ95 1.65 1.65 Ip[MA] 18 17.75 Pfus [MW] 2000 2000 PLH [MW] 113.4 120.8 H-factor 1.1 0.98 ⟨n⟩/nGW 1.2 1.2 ⟨T⟩12.27 12.49 βN[% mT/MA] 2.3 2.5 Zeff 2.12 2.12 Psep/R [MW/m] 18.9 18.9 Pulse length [s] 7200 7200 Table 3.6: Relevant machine parameters used for this work compared to those for the EU-DEMO Baseline 2018 as presented in [15] obtained with process. In this work, the DEMO Baseline 2018 has been taken as the reference design point for the power cycle studies presented in Chapter 7. The DEMO Baseline 2018 constitutes the latest official design point that has been released during the Pre-Concept Design Phase [15]. It uses the IPB98(y,2) (H-mode) scaling [45] for the confinement, the Greenwald density limit [135] and the Martin 2008 scaling for the power threshold [136]. Baselines for different confinement regimes Although the scenarios based on ITER will have the strongest experimental support for later devices, not all ITER solutions are directly applicable to DEMO because of the differences in machine size and ITER’s wider mission. Therefore, it becomes interesting to explore not only H-mode but also other high confinement regimes without ELMs for DEMO. Although the ELM-free regimes that can be tested in ITER have an advantage to qualify for DEMO, a system code such as process can be used to study the impact of different plasma profiles on the economic feasibility of the machine. In particular, L-mode, I-mode and QH-mode Baselines (see Chapter 2) have been established using 3.3. Summary 47 Figure 3.9: Density and temperature profile for the H-mode (red), QH-mode (purple), I-mode (black) and L-mode (blue) DEMO Baselines established in [137]. Rmajor [13.8 m] Bt [7.54 T] Ip [21.37 MA] Pnet,elec [500 MW] Ccost [16306 M€] COE [984 €/MWh] Figure 3.10: Major radius (Rmajor), toroidal magnetic field (Bt), plasma current (Ip), net electrical power output (Pnet,elec), capital cost (Ccost) and cost of electricity (COE) comparison for the QH-mode (purple), I-mode (black), L-mode (blue) and H-mode (red) baselines established with the process code in [137]. The values have been normalized to the values in brackets. the process system code [137]. The I-mode Baseline uses the H98(y, 2) scaling for the confinement (adding a correction factor of fcorr = 0.8) and the empirical L-I power threshold [62]. The QH-mode baseline considers an increased power input for achieving higher edge rotation. Figure 3.9 shows the plasma profiles corresponding to different regimes as produced with process [137], based on the current understanding of the confinement regimes. For all regimes the electron and ion temperatures are assumed to be equal. This assumption is justified by the large machine size. Figure 3.10 shows some relevant parameters that correspond to the different confinement regimes, as obtained with process. The L-mode scenario is the most demanding one from an engineering perspective, as it requires the largest engineering parameters (largest machine and highest Bϕ). Regarding the economic parameters, the H-mode (DEMO Baseline 2018) and QH-mode give the best performance, as they feature the lowest COE. In contrast, the I-mode features the largest. This is due to the low net electrical power output (Pnet,el) in I-mode, that is in turn related to the low core ion density. These results highlight the importance of achieving high main ion temperature and density for the economic feasibility of a future FPP. 3.3 Summary The future DEMO reactor and the experimental ASDEX Upgrade tokamak have been described in this chapter. The conceptual design of the DEMO tokamak and the prediction of its performance by means of the process system code has been introduced. 48 Chapter 3. The ASDEX Upgrade and the DEMO tokamak The relevant systems of the ASDEX Upgrade tokamak and the methodology for experiment execution in this device have been discussed. Importantly, the Charge Exchange Recombination Spectroscopy technique has been explained. In the next chapter, a detailed description of the edge main ion charge exchange recombination spectroscopy system installed at the ASDEX Upgrade tokamak is given. 49 Chapter 4 A new edge main ion charge exchange recombination spectroscopy diagnostic at ASDEX Upgrade The first step for studying the transport of energy and momentum in plasmas relies on the experimental characterization of plasma temperature and velocity. This chapter describes the edge main ion Charge Exchange Recombination Spectroscopy diagnostic. The working principle, the experimental set up and the components of the diagnostic are specified. The detailed calibration and characterization of the optics and the spectrometer are fundamental for an accurate determination of the main ion temperature and toroidal rotation velocity. The methodology for the calibrations required for the precise reconstruction of the charge exchange spectra are explained. Note that part of this chapter has been published in [138], of which the thesis author is the first author. 4.1 The edge main ion toroidal system The edge main ion diagnostic at AUG isaCharge Exchange Recombination Spectroscopy (CXRS) system, based on the observation of the emission of thermal deuterium after a CX reaction with beam neutrals [138]. The main hardware components of the edge main ion system are an in-vessel optical head, the transmission fibres from the vessel to the spectroscopy laboratory and a spectrometer. The edge main ion diagnostic is also the edge the fast-ion Dα(FIDA) diagnostic [139], as the hardware components are shared (the information on the main ions and fast-ions is contained in the same spectra, as explained in Chapter 5). In the framework of this work, a new toroidal optical head has been installed inside the vacuum vessel. The optical head provides a total of 30 LOS and enables the simultaneous measurement of main ion and impurity properties. The optical head features f/2.7 plano-convex lenses with a focal length of 85 mm, and is a replica of the edge toroidal optical head installed in sector 15 for impurity measurements. The new optical head is installed in sector 8 and therefore called CMR-8. A subset of 15 LOS is used for the edge main ion system, which covers 6.5 cm of the plasma edge region. The geometry of the LOS and diagnostic beam is shown in toroidal and poloidal views of the AUG tokamak in Figures 4.1(a) and (b). The impurity CXRS systems and their diagnostic beams and gas puffs are also included. The edge main ion diagnostic features high temporal and spatial resolution. The standard integration time for the 15 channels is 1.5 ms, although it can be tuned down to the microsecond time scale if only one channel is to be imaged. The spatial resolution 56 Chapter 4. A new edge main ion charge exchange recombination spectroscopy diagnostic at ASDEX Upgrade red) and the outermost (CMR-8 16, black) LOS of the diagnostic. The NBI density as calculated by fidasim and the flux surfaces are shown in dashed gray and blue lines for reference, respectively. A radial histogram can be built for each LOS, as shown in Figure 4.7(b). The histograms are fitted with a Gaussian. For LOS outside the separatrix, a significant part of light comes from the confined region. The radial resolution of the LOS cannot be properly described by a single Gaussian, and two Gaussians are needed to characterize the inner and outer resolution (see [138]). The widths of the Gaussians are related to the spatial resolution of the diagnostic, while the centers of the Gaussians determine the center of emission for each LOS. The center of emission is always taken into account for the mapping of the profiles onto the normalized poloidal flux coordinate ρpol. An overview of the spatial resolution of the CMR-8 optical head is illustrated in Figure 4.7(c), which shows that the radial resolution is between 3 and 8 mm across the pedestal. The resolution of the system is minimal just inside the separatrix and increases inwards as the tangency of the LOS to the flux surfaces at the intersection with the beam decreases. The toroidal (CMR-1 and CMR-2 optical heads) and poloidal (CPR head) systems measuring the Dαspectra on NBI source Q3 (60 keV) have a spatial resolution of 2 and 10 mm, respectively [138]. The poloidal LOS receive light from a broader region as the poloidal curvature of the plasma is larger compared to the toroidal one. These results agree with previous characterizations of the impurity systems [84]. 4.3.4 Intensity calibration The absolute intensity calibration characterizes the system sensitivity to light and enables the conversion from the camera digital counts to photons (Ph/sr/m2/s/nm), i.e., how efficiently the system converts light into counts. The sensitivity of the full system is characterized by measuring the signal produced when the system is exposed to a standardized light source (Labsphere, Model Unisource 1200). The spectral radiance of the integrating sphere (Lλ) is well known and depends on the wavelength, as shown in Figure 4.8(a). The number of counts (N) measured in the calibration will depend on the sensitivity of the system (S) and the radiance of the emission source: N=SLλtexp∆λpix,(4.4) where texp is the exposure time and ∆λpix is the wavelength range detected by a pixel. Note that Sis a function of the pixels in the x-direction, y-direction (spectrometer channel) and wavelength. The sensitivity of the system can be separated in two contributions: the sensitivity of the spectrometer (Sspec) and the transmission of the optics from the vessel to the laboratory (TLOS): N=SspecTLOSLλtexp,(4.5) For the sensitivity calibration of the full system (S), an in-vessel intensity calibration is performed. The optical head is exposed to the integrating sphere, such that the viewing cone of the optics is covered by the sphere aperture. The in-vessel set up is shown in Figure 4.9. The sensitivity of the spectrometer (Sspec) is calibrated in the spectroscopy laboratory. In this case, the spectrometer fibres are exposed to the integrating sphere. The combination of the two calibrations enables the determination of the line of sight transmission as TLOS =S/Sspec. The separate calibration of spectrometers and optical heads facilitates the exchange of fibres between spectrometers when the experimental plan requires it. The transmission for each line of sight depends only on the wavelength. 4.3. Characterization of the diagnostic 57 (a) 400 500 600 700 [nm] 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Spectral radiance [ph/m 2 /nm/s/sr] 1e18 (b) 5 10 15 Spectrometer channel 0.0 0.5 1.0 1.5 2.0 S spec [counts/(ph/sr/m 2 /pixel)] 1e 10 = 650 nm (c) 5 10 15 CMR-8 LOS 0 5 10 15 20 25 30 35 Transmission [%] = 650 nm Figure 4.8: (a) Spectral radiance of the Ulbricht sphere. (b) Central sensitivity for the CEF spectrometer channels at λ= 650 nm. (c) Transmission of the optical fibers. Figure 4.9: Experimental set up for the in-vessel intensity calibration of CMR-8. The sensitivity of the CXRS systems is generally calibrated for a central wavelength of λ0= [400,720] nm by turning the grating, as impurity spectral lines at different wavelengths are of interest. For the main ion CXRS system, the spectrometer sensitivity calibration is limited to 650 nm central wavelength. The sensitivity for the CEF spectrometer channels is shown in Figure 4.8(b). The main ion spectrometer sensitivity rapidly decays at other wavelengths. The LOS transmission can be calibrated for the full wavelength range using the CUR spectrometer. The transmission of the CMR-8 LOS used for the main ion diagnostic is shown in Figure 4.8(c). The sensitivity of the system may degrade over time due to damage or coating of the optical components. The evolution of the sensitivity is monitored by performing pre-campaign and post-campaign calibrations. 4.3.5 Camera calibration The main ion spectrometer uses a Princeton Instruments ProEM charged couple device (CCD) [146]. The working principle of a CCD is based on the photoelectric effect, which leads to the conversion of incident light into a current. Each pixel is a semiconductor element that accumulates charge as photons impinge on it during the data acquisition. At the end of the exposure time, a cyclic electric potential variation is applied that leads to the transfer of the electrons produced in each pixel, i.e., the read-out. The spectrometer camera is ideal for low light applications while maintaining short acquisition times, as it has an extended serial register that allows for on-chip electron multiplication. In the multiplication register, secondary electrons are generated by 58 Chapter 4. A new edge main ion charge exchange recombination spectroscopy diagnostic at ASDEX Upgrade impact ionization. The camera sensor features high quantum efficiency (over 90%) combined with a high dynamic range (16 bits). For the main ion diagnostic, the camera is typically operated using a medium controller (analog) gain and 10 MHz read-out rate. Uncertainty in the spectra The statistical uncertainty in the number of counts (σ) results from a combination of the photon (σc,photon) and the read-out (σADC) noise: σ2=σ2 c,photon +σ2 ADC.(4.6) The photon noise is represented by the intensity fluctuation when the device is exposed to a uniform light, while the read-out noise is due to electronics and independent of the light level. The photon noise follows a Poisson statistic and can be described as σphoton =√nphoton. Here nphoton is the number of photons. The photon noise translates to a count noise σc,photon =σphoton/fconv, where fconv is the number of photons per count, i.e., nphoton =ncfconv, where ncis the number of counts. The photon and readout noise calibration is simultaneously performed by the acquisition of measurements at different count levels. For this calibration, a set of frames is acquired at increasing exposure times or count rates under a uniform light source. The average (¯nc) and standard deviation (σ, the uncertainty) of counts per region of interest at different exposure times is fitted to the following expression: σ=r¯nc fconv +σ2 ACD.(4.7) (a) 0 2500 5000 7500 10000 12500 Counts 0 10 20 30 40 50 60 Std. dev. of counts CG1 fconv = 7.65 ADC = 14 (b) 0 2 4 6 8 10 12 14 16 18 20 Set EM Gain 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 Measured EM Gain CG1 20MHz Counts 1000.0 2500.0 5000.0 10000.0 20000.0 30000.0 Figure 4.10: (a) Standard deviation of counts as a function of count level for controller gain (CG) 1. From fitting the data to Equation (4.7), the photon (fconv) and read-out (σADC ) noise are characterized. (b) Electron multiplication (EM) gain calibration for a controller gain (CG) 1 and read-out rate of 20 MHz. The effective or measured EM gain as a function of the EM gain set in the software. The fit parameters fconv and σADC provide the photon and read-out noise characterization, respectively. Note that the photon conversion and read-out noise depend on the camera settings, in particular, on the controller gain and read-out rate, such that independent characterizations are required when the camera is operated with different controller gain settings. Figure 4.10(a) shows the photon and read-out noise calibration 4.4. Summary 59 for controller gain 1. The photon conversion factor decreases while the read-out noise increases as the controller gain is increased. Electron multiplication gain calibration The main ion camera is typically operated with an electron multiplication (EM) gain of 20. The instrument response to the application of EM gain needs to be characterized for accurate conversion of counts to photons. This calibration is performed by increasing the EM gain setting sequentially and adjusting the exposure time to match a certain amount of counts. Then, the counts are normalized with respect to the case where no EM gain is used. The results of the EM gain calibration are shown in Figure 4.10(b). As can be seen, the signal amplification by the EM gain is non-linear in gain (the effective multiplication does not follow a 1:1 line) and level of counts (shown in different colors). 4.4 Summary The edge main ion Charge Exchange Recombination Spectroscopy diagnostic has been described in this chapter. The methodology for the accurate hardware calibration of the system, which enables high precision temperature and rotation velocity measurements, is explained. The next chapter details the analysis and modelling techniques required for a correct interpretation of the experimental main ion spectra. 61 Chapter 5 Interpretation of the edge main ion spectra This chapter introduces the working principle of main ion Charge Exchange Recombination Spectroscopy and the differences with standard impurity Charge Exchange Recombination Spectroscopy. The forward modelling framework developed in this thesis for the interpretation of the main ion data is explained. The core of the forward model is the collisional radiative model implemented in the fidasim code [145,147, 148], which is described. The corrections due to atomic physics effects and considerations that are important for the analysis of the main ion spectroscopic data are discussed. Note that part of this chapter has been published in [138], of which the thesis author is the first author. 5.1 The Dαmain ion spectrum Knowledge of the main ion properties is fundamental for the success of future fusion devices, as the fusion power directly depends on the main ion energy (temperature and velocity). Main ion Charge Exchange Recombination Spectroscopy (CXRS) is one of the few diagnostic techniques that enables the direct measurement of main ion temperature (TD) and toroidal rotation velocity (vϕ,D). The working principle for main ion CXRS is the same as for impurities, described in Section 3.1.2: based on the charge transfer between a neutral and a plasma ion. In the particular case of hydrogenic main ions, the donor and the receiver of the electron are the same species; at AUG, typically deuterium (D). The direct measurement of hydrogenic main ion properties has not been performed routinely in magnetic confinement devices. Instead, impurity CXRS has been traditionally used for the measurement of the ion temperature and velocity, and main ion properties are assumed equal or inferred from them using neoclassical models. This is due to the complexity of the main ion D spectrum, which makes its interpretation more challenging in comparison to the impurity CXRS spectrum [149,150]. The multiple photoemission processes and the overlap of different features in the same spectral range have prevented the analysis of main ion spectra for the direct determination of main ion profiles for many years. The main issues for the routine analysis of main ion spectra are [151]: (i) Thermal halo emission from multiple CX reactions. The thermal neutral deuterium (originally a thermal ion) becomes a donor for a subsequent CX reaction, giving rise to the halo population. The halo neutrals are born in multiple generations and enhance line integration effects, which may compromise the resolution of the diagnostic. 62 Chapter 5. Interpretation of the edge main ion spectra (ii) Bright emission from cold neutrals at the plasma edge, which can lead to malfunctioning or damage of the instrumentation (camera saturation) and fully prevent the feasibility of the measurement. (iii) Cross-section distortions due to the energy dependence of the CX reaction rate. (iv) The finite lifetime of excited states. Since deuterium only has one proton, the deuterium ion becomes neutral after the CX reaction. As a neutral, deuterium does not feel the magnetic field and travels ballistically, such that diffusion across flux surfaces is enhanced. (v) Overlap of features, such as beam emission (BES) in the same spectral range. In recent years, developments in CCD diagnostics, comprehensive spectral fitting and code development for the modelling of the main ion spectra have enabled the feasibility of main ion CXRS analysis [17,151–156]. In this work, the donor neutrals for main ion CX reactions originally come from the NBI. The first generation of CX reactions between the plasma ion (D+) and the fast neutral (DNBI ) gives rise to the direct charge exchange (DCX) neutral population: D++DNBI →D∗ DCX +D+ NBI →DDCX +D+ NBI +hν. (5.1) The thermal neutral (DDCX) can charge exchange with the thermal main ions, producing the first generation of halo neutrals. The halo neutral population is born in multiple generations, from CX between D+and DCX neutrals (Equation (5.2) in the first generation) and halo neutrals themselves (Equation (5.3), for subsequent generations): D++DDCX →D∗ haloi=1 +D+ DCX →Dhaloi=1 +D+ DCX +hν. (5.2) D++Dhaloi=j→D∗ haloi=j+1 +D+ haloi=j→Dhaloi=j+1 +D+ haloi=j+hν. (5.3) where the subindex iindicates the halo generation. After the CX reaction, the original DCX or halo neutral becomes part of the D ion distribution. The thermal CX D emission consists of two contributions depending on the energy of the donor neutral. The DCX emission originates from CX of thermal ions with high energy neutrals (NBI) while the halo emission is due to thermal-thermal CX. The Doppler shift between the two contributions cannot be resolved spectroscopically, such that the two features are superposed in the spectra. The different nature of these emissions implies that each of them is subject to different atomic physics processes which may lead to distortions of the spectral line that need to be corrected for (see Section 5.3). The halo extends to a larger region in real space, as discussed in Section 5.2.1. The reaction rate for DCX depends on the relative velocity between the beam neutral (which is also non uniform, as it is composed of three energy populations at AUG) and the thermal ion, while for halo CX both particles feature thermal velocities. These two effects lead to a line integration and cross-section effect, which are discussed in Subsections 5.3.1 and 5.3.2, respectively. Figures 5.1(a-b) show two examples of the main ion spectra. For main ion spectroscopy, the Balmer Dα(D n= 3 →2, λ= 656.1 nm) transition is of interest as it leads to radiation in the visible range. As can be seen, the main ion spectrum is substantially more complex compared to the impurity spectrum (see Figure 3.2), with a total of seven contributions. The total (black), active (red) and passive (blue) experimental Dαspectrum is shown in Figure 5.1(a). In the absence of an external source of neutrals (here, the NBI), the spectrum consists only of passive components, (1) the 5.1. The Dαmain ion spectrum 63 (a) 652 653 654 655 656 657 658 659 Wavelength [nm] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Spect. Radiance [ph/s/sr/m 2 /nm] 1e18 CMR8-01 R = 2.062 m CII cold BES thermal CX (DCX + halo) cold CX #38540 t = 2.83s Total Passive Active Active (w/o ELM sync) (b) 653 654 655 656 657 658 659 Wavelength [nm] 1015 1016 1017 1018 Spect. Radiance [ph/s/sr/m 2 /nm] #38540 t = 2.83s CMR8-01 R = 2.062 m FIDASIM Th. CX Halo DCX Full Half Third BES Exp. data Figure 5.1: (a) Total (black) and passive (blue) experimental edge main ion spectra. Active (after background substraction) edge main ion spectra with (red) and without (gray) ELM synchronization. (b) Active main ion spectrum and synthetic contributions as simulated by the fidasim code. thermal component due to charge exchange with the thermal background neutrals (not localized), (2) the cold emission from the neutrals at the plasma edge and (3) the impurity carbon CII lines. The passive signal is subtracted to suppress these contributions, which are not localized and/or difficult to model (more details are given in Section 5.4.1). The active components derive from the interaction of the NBI with the plasma, which leads to the four active features: (4) the DCX, (5) the halo emission, (6) the beam emission (BES) and (7) the fast-ion Dα(FIDA) emission. Figure 5.1(b) shows the experimental active spectra and active contributions. The CX Dαemission (in cyan) appears as a single Gaussian feature and is due to the superposition of the DCX and halo, shown in gray and magenta, respectively. The DCX and halo contributions are of the same order of magnitude for typical AUG plasmas parameters. As for the impurity CXRS spectra, TDand vϕ,D are derived from the width and the Doppler shift of the thermal CX emission line, respectively. The CX Dαemission appears together with (6) the beam emission (BES, due to excitation of beam neutrals, shown in blue) [157] and (7) FIDA (negligible in this case) [158] contribution. The BES contribution is due to the emission of diagnostic beam itself, and it is split in the full (yellow), half (green), and third (red) energy components (see Subsection 3.1.1). The FIDA emission is typically several orders of magnitude smaller than the thermal emission at the plasma edge, due to the low fast-ion content in this region. The impact of FIDA emission on the main ion spectra analysis is discussed in Subsection 5.4.2. The edge main ion system at AUG uses an NBI as source of neutral. In particular, the optics of the diagnostic view NBI source Q8, with a first energy component of 93 keV, as can be seen in Figure 4.1. The BES emission is strongly affected by the Stark effect due to the high velocity of the beam (vb), as the Stark effect scales with vb× B. The Stark effect leads to line splitting of the individual σand πspectral lines, which are shown with transparency in Figure 5.1(b). The energy splitting due to the Stark effect is shown in Figure 5.2(a). The high velocity of the beam neutrals also results in a significant Doppler shift of the BES, so that it is separated in wavelength from the thermal component. This separation facilitates the fitting of the spectra and depends on the viewing geometry, according to Equation (3.4). The more perpendicular the LOS are to the beam, the smaller the projection of the velocity, and therefore the separation between the BES and the thermal component decreases. This effect is shown in Figure 5.2(b), where it can be seen that the separation is highest for the edge LOS, which 64 Chapter 5. Interpretation of the edge main ion spectra (a) energy E +6ΔE 3 E +3ΔE E E - 3 ΔE E - 6 ΔE E +2ΔE E E - 2 ΔE 3 3 3 3 2 2 2 n=3 n=2 ΔE 2π+3π+4π+ 2π- 3π- 4π-0σ 1σ-1σ+ (b) 652 654 656 658 Wavelength [nm] 2.08 2.09 2.10 2.11 2.12 2.13 RLOS [m] BES C II D #40221 t = 3.05s 1016 1017 1018 1019 Intensity [ph/s/sr/m 2 /nm] Figure 5.2: (a) Illustration of the energy level splitting due to the linear Stark effect, and resulting transitions allowed by selection rules. Reproduced with permission from [159]. (b) 2D contour of the main ion spectra as a function of the wavelength and LOS. The separation of the BES from the thermal DαCX decreases as the LOS become perpendicular to the beam. are the less perpendicular to the beam, as shown in Figure 4.1(a). The geometry of these LOS is also optimized in terms of radial resolution (tangency to the magnetic field lines), as discussed in Subsection 4.3.3. 5.2 Forward modelling framework for main ion spectra A forward modelling framework has been developed in order to correct for the halo, cross-section and line integration effects. This forward model is inspired by the work done at the DIII-D tokamak [152,156]. The core of the forward model is the collisional radiative model implemented in fidasim [145,147,148]. The different contributions to the Dαspectra can be modelled with fidasim, such that the predicted spectra for a specific input can be compared with the experimentally measured spectra. fidasim has been previously used to interpret the core Dαspectra by the definition of correction factors [157] and the construction of look-up tables [152]. At the plasma edge, these approaches are insufficient. The adopted approach for resolving the halo effects at the plasma edge is to run fidasim iteratively and compare the profiles inferred from the synthetic spectra to the experimental profiles [138,156]. The following steps, illustrated in the workflow in Figure 5.3, are taken for the interpretation of the main ion spectra: 1. The experimental spectra are fitted, which gives a set of apparent profiles. 2. A fidasim simulation is performed. For the first simulation, an initial guess is given for the main ion profiles. These are typically the impurity properties, flat or the apparent profiles. 3. The synthetic spectra (fidasim output) are fitted, which gives the synthetic profiles. 4. The synthetic and experimental profiles are compared, and a correction factor is defined. The correction factor is used to generate a new set of profiles, according to Equation (5.4): 5.2. Forward modelling framework for main ion spectra 65 Synt. spectra Equilibrium Beam geometry Diagnostic geom. Kinetic profiles Exp. spectra vsynt ID synt TD synt ID app TD app vϕ,D jID j TD j v FIDASIM 5 4 2 1 ID j+1 3 vapp ϕ,D ϕ,D j+1 vϕ,D TD j+1 Figure 5.3: Workflow of the forward modelling framework for the interpretation of the main ion spectra. Xj+1 =Xj Xapp Xsynt ,(5.4) where X is the variable, which can be the main ion temperature (TD), toroidal rotation (vϕ,D) or intensity (ID), and jrefers to the simulation number. These profiles will be the input profiles for the subsequent fidasim simulation. A check for convergency is done based on the profiles (it is checked whether the modification of the profiles is below the experimental uncertainty) and a direct comparison of the experimental and synthetic spectra is done. 5. The next fidasim run is initiated with a modified set of input profiles. After each simulation, the experimental and synthetic spectra are compared and convergency is reached when agreement is found within the experimental uncertainty. At this point, also the experimental and synthetic apparent profiles match and the true underlying deuterium properties are given by the input profiles to fidasim. Figure 5.4 shows the evolution of the synthetic spectra and main ion TDand ωϕ,D input profiles to fidasim during the forward modelling process. The colors represent the iteration (simulation) number. In this case, the initial guess for the fidasim input profiles are flat TDand vϕ,D profiles at 700 eV and 10 krad/s, respectively. The synthetic spectrum is compared to the experimental spectrum (shown in squares). It can be seen that the agreement between the synthetic and the experimental spectra substantially improves after the first iteration. The iterative corrections to the input profiles are applied until a good agreement is found across the full profile (i.e., for all the LOS). Typically, 4-5 iterations are required to achieve convergency. Convergency to the same final profiles is achieved when different initial profiles are provided (although more realistic profiles typically require 1-2 fewer simulations, reducing computational time). The profile uncertainty consists of a contribution from the experimental measurement (σexp, derived from the fitting parameters, which take into account the statistical uncertainty in the measurement, as described in Subsection 4.3.5) and a contribution from the forward model (σmodel), such that: σ2 profile =σ2 exp +σ2 model, 72 Chapter 5. Interpretation of the edge main ion spectra 5.3.4 Corrections due to Zeeman, fine structure and Stark effect The Zeeman and Stark effects lead to the splitting of spectral lines in the presence of a magnetic or electric field, respectively. Each Zeeman component is a Gaussian line itself with a Doppler width representing the true ion temperature. When these lines add up, a line shape that is well described by a Gaussian is produced for the magnetic fields at AUG (a few T). However, the width of the resulting Gaussian gives an apparent ion temperature which overestimates the real ion temperature [165]. An estimation of the maximal symmetrical splitting [166], gives a splitting of 0.0404 nm for D (n= 3 →2), compared to 0.0229 nm for B5+ (n= 7 →6) at B = 2 T. At AUG, all CXRS Tzand vzmeasurements are routinely corrected for Zeeman and fine structure broadening by using correction factors [167], which relate the apparent and true properties depending on the magnetic field and diagnostic geometry [83,162]. The calculation of the correction factors assumes statistical equilibrium of the sublevels of the quantum number n, which is checked to be a reasonable assumption using the empirical formula in [168], that gives a critical density for collisional coupling for a given transition. The critical density for the main ions (ncrit,D = 1.04 ·1017 m−3) is two orders of magnitude smaller than typical densities at the plasma edge of AUG (∼ne= 1019 m−3). (a) 0 100 200 300 Tapp [eV] 0.0 0.2 0.4 0.6 0.8 1.0 Ttrue / Tapp D - Rosato D - Hey B 5 + - Hey B = 2 T = 0° = 90° (b) 656.05 656.10 656.15 λ [nm] 0.0 0.2 0.4 0.6 0.8 1.0 Line profile [nm -1 ] B = 2.0T θ = 90º -3 n = 5·10 m e 19 Rosato Hey Database Figure 5.9: (a) Temperature correction factor as a function of apparent temperature due to Zeeman and fine structure effects (Hey) for Dn=3→2(dashed) and B5+ n=7→6(circles) and Zeeman and Stark effects (Rosato, Te= 30 eV) for Dn=3→2(solid) for B= 2T and viewing angles parallel (θ= 0 ° , in black) and perpendicular (θ= 90 ° , in red) to  B. (b) Line splitting for Dn=3→2at B= 2T, θ = 90 ° according to Rosato [169] and Hey databases [167]. For the main ions, these correction factors have been compared with Rosato’s database [169], which combines the Zeeman and Stark effects. Figure 5.9(a) shows a comparison of correction factors based on [169] and [167] databases for D (n= 3 →2) at B= 2 T and viewing angles parallel (θ= 0 ° ) and perpendicular (θ= 90 ° ) to the magnetic field. The correction factors for B5+ (n= 7 →6) are also shown. The main ion correction factors according to the two databases are comparable, and smaller compared to that of the impurity ions. Figure 5.9(b) shows the line profile splitting according to Rosato (in red, includes Zeeman and Stark splitting, for Te= 30 eV) and Hey (black, includes Zeeman and fine structure). Note that the splitting is in good agreement with the estimation based on [166]. The Stark effect has been evaluated for 5.4. Analysis and experimental techniques 73 an electron density and temperature of ne= 5 ·1019 m−3and T= 30 eV, respectively. The fine structure effect results in broader and asymmetric lines, while the Stark splitting has a small impact1. Thus, the correction for Zeeman and fine structure effects is included for the main ions according to the [167] database. The correction increases with decreasing apparent temperature and views parallel to the magnetic field (σ-lines become dominant), and is typically under 10 eV at the plasma edge. For routine analysis of main ion spectra, the full Zeeman pattern is convolved with the instrument function and included in the fit to the experimental data. The full Zeeman pattern for the D (n= 3 →2) consists of 54 lines [167]. Since the Zeeman splitting is not included in fidasim, the synthetic spectrum is convolved with both the Zeeman pattern and the instrument function for a comparison with the experimental spectrum. 5.4 Analysis and experimental techniques 5.4.1 Background subtraction In the absence of an active neutral source, the main ion spectra are purely passive. The bright feature at 656.1 nm in the passive main ion spectrum, shown in blue in Figure 5.1(a), is due to electron impact excitation of background neutral deuterium (Dbck) and its charge exchange reaction with the main plasma ions: e−+Dbck →D∗ bck +e−→Dbck +e−+hν. (5.13) D+ th +Dbck →D∗ th +D+ bck →Dth +D+ bck +hν. (5.14) Note that the first leads to the emission of the background neutrals (cold) while the second leads to the emission of the thermal plasma ions (warm). Modelling both of these contributions is complicated because of the large uncertainties in the background neutral density profile and its 3D structure [170,171]. The background deuterium neutral density maximizes at the wall and rapidly decays towards the plasma core. This leads to a very bright emission at the plasma edge, which is always collected as the LOS cross the SOL twice in their optical path. This contribution to the spectra is therefore unavoidable. For these reasons, the removal of this contribution from the spectra is a very important step in the analysis of the main ion data. This is achieved by performing passive background subtraction, which relies on beam modulation. There are mainly two experimental strategies for programming the NBI source time trace that enable passive background subtraction, which are: 1. Beam blip: the active beam is switched on for a short phase (15-20 ms), providing the active measurement. The passive signal is taken from the closest frames before and/or after the blip. This approach is only used for L-mode measurements in favorable configuration, as a constant NBI source of 2.5 MW would suffice for a transition into H-mode. Ideally, the fast blip does not perturb the main ion profiles, and the measurement is representative of the L-mode phase. 2. Beam compensation: an active and a passive beam are alternated such that the total input power is constant. The active and passive signals are taken when the 1The wings caused by the Stark effect are attenuated at the typical temperatures in the steep gradient region. 74 Chapter 5. Interpretation of the edge main ion spectra (a) 5 0 5 tELM [ms] 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Intensity [Ph/ ( m 2 sr s ) ] 1e17 CMR8-03 R = 2.071 m = [656.5, 656.6] nm #38540 t = [2.2, 3.5]s (b) 5 0 5 tELM [ms] 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 Intensity [Ph/ ( m 2 sr s ) ] 1e17 CMR8-28 R = 2.112 m = [656.5, 656.6] nm #38540 t = [2.2, 3.5]s Figure 5.10: Total (blue) and passive (red) integrated radiance at λ= [656.7,656.9] nm with respect to the ELM onset time for (a) inner LOS and (b) outer LOS. active and passive beams are switched on, respectively. These phases maybe fast (60:40 ms) or long (a few hundreds of ms). Note that this technique assumes that the background neutral density does not depend on the NBI source at use and that there is no significant temporal evolution of the passive and active signals, i.e., there are no significant differences in the main plasma parameters between the active and the passive time windows. This is however not true in ELMy H-modes. During the ELM cycle, several plasma parameters are affected, as discussed in Subsection 2.7.2. This leads to a variation of both the passive and the active main ion properties and, thus, also the spectra are affected across the ELM cycle. Figures 5.10(a,b) show the temporal evolution of the total (blue) and passive (red) signals with respect to the ELM onset for two LOS. The signal at λ= [656.5,656.6] nm has been integrated, and synchronized with respect to the ELMsatt=[2.2,3.5] s for discharge #38540. It can be seen that the main ion signal rises at the ELM onset and recovers to its pre-ELM value about 4 ms after the ELM crash. Therefore, it becomes essential for the analysis of main ion spectra in ELMy H-modes to ELM synchronize the passive and the active spectra (following the method 2 explained in Subsection 3.1.3) before the background subtraction. The ELM synchronized passive spectra are subtracted from the active spectra which correspond to analogous time windows with respect to the ELM onset. Note that all the H-mode measurements presented in Chapter 6have been background subtracted and refer to spectra within the time window t = [-4,-2] ms with respect to the ELM onset. An example of passive background subtraction with (red) and without (gray) ELM synchronization is illustrated in Figure 5.1(a). It can be seen that the ELM synchronization technique leads to efficient suppression of the cold edge emission and C II impurity lines, which is an indicator of matching plasma properties in the ELM synchronized passive and active time windows. However, when the closest passive frame (possibly, in a different phase with respect to the ELM cycle) is used for the background subtraction, there is a residual emission from the plasma edge (highlighted in green) and carbon (highlighted in blue). 5.4. Analysis and experimental techniques 75 5.4.2 Inclusion of fast-ion Dαemission The active FIDA emission [139,158] is due to CX reactions of fast-ions with the neutral beam. In standard conditions, the FIDA contribution to the main ion spectra at the plasma edge is several orders of magnitude lower than the thermal contribution. However, the FIDA contribution can be important in scenarios with strong off-axis heating and/or low densities, which lead to high fast-ion content and a significant FIDA contribution. In these cases, the FIDA emission should be taken into consideration for the analysis of the main ion properties. Figure 5.11 illustrates a case with high FIDA emission, which corresponds to a QH-mode development scenario with a central electron density of 4 ·1019 m−3,NBI power of 4 MW and ECRH power of 0.75 MW. 652 654 656 658 660 Wavelength [nm] 1015 1016 1017 1018 Spect. Radiance [ph/s/sr/m 2 /nm] #39318 t = 5.29s CMR8-01 R = 2.062 m FIDASIM Th. CX DCX Halo Full Half Third BES FIDA Exp. data Figure 5.11: Active main ion spectrum and synthetic contributions as simulated by the fidasim code for a high FIDA case. (a) 0.85 0.90 0.95 1.00 pol 0.6 0.8 1.0 1.2 1.4 1.6 T [keV] PECRH = 750 kW PNBI = 3.6 MW ped . top *, i = 0.28 Low H-Mode #39318 t = 4.17 s With FIDA Without FIDA (b) 0.85 0.90 0.95 1.00 pol 80 100 120 140 160 180 v [km/s] PECRH = 750 kW PNBI = 3.6 MW ped . top *, i = 0.28 Low H-Mode #39318 t = 4.17 s With FIDA Without FIDA Figure 5.12: Impact of including (red) and excluding (blue) the FIDA contribution for the evaluation of the main ion (a) temperature and (b) toroidal rotation profiles for a low density and strong off-axis heating plasma. The impact of including the FIDA contribution in the analysis of the main ion CXRS data is illustrated in Figures 5.12(a,b). Excluding FIDA from the analysis leads to an overestimation of the main ion temperature, in agreement with previous work at DIII-D [17], and a higher toroidal rotation. The correction is more important for the temperature (up to 100 eV) compared to the toroidal rotation (below the uncertainty) and is more significant towards the pedestal top compared to the steep gradient region. 76 Chapter 5. Interpretation of the edge main ion spectra This is consistent with the fact that the FIDA contribution is more important where the fast-ion density is higher. In fact, the FIDA emission is generally more important for the analysis of core main ion CXRS data, where it has to be included for its interpretation [151,157]. This is an extreme case with low density and high NBI power, and still the correction is minimal in the steep gradient region. 5.4.3 Experimental determination of main ion poloidal rotation In addition to the direct measurement of the main ion temperature and toroidal rotation, the edge main ion diagnostic offers the capability to resolve the main ion poloidal rotation experimentally. While the direct measurement of the edge main ion poloidal rotation (vθ,D) is not available, this diagnostic enables its determination from measurements only, if an independent measurement of the radial electric field (Er) is provided. The combination of the TDand vϕ,D measurements from the edge main ion diagnostic with an Erprofile enables the determination of the main ion poloidal velocity via the radial force balance equation. The measurements of temperature and brightness can be used to determine the diamagnetic contribution and vϕ,D is used to determine the v × Bcontribution from the toroidal flow to Er. The main ion poloidal rotation (vθ,D) can be extracted as: vθ,D =∇pD ZDenD +vϕ,DBθ−ErB−1 ϕ,(5.15) where the Er,exp profile can be determined from impurity CXRS measurements. The magnetic field components from the equilibrium reconstruction also need to be known. Note that the assumption of ∇nD/nD∼ ∇ID/IDhas been made for the validation case discussed in Chapter 6. The direct measurement of the main ion poloidal rotation via c is beyond the scope of this work. This measurement is challenging and requires the inclusion of the poloidal rotation impact on the synthetic spectra in fidasim. The edge main ion poloidal rotation is expected to be small (see Section 2.6), which poses a challenge for its experimental diagnostic, as a small Doppler shift is expected. In addition, the thermal and beam emissions are superposed when the plasma is observed poloidally, due to the small poloidal velocity component of the beam neutrals. In its current implementation, fidasim does not take into account the poloidal velocity for determining the velocity of the markers (and consequently the Doppler shift of the synthetic emission is not affected by it). The application of a forward modelling framework (similar to the one described in Subsection 5.2) to poloidal velocity measurements would require the implementation of the effects of the poloidal velocity on the spectra in fidasim via Equation (5.9). 5.5 Summary This chapter exposes the analysis and modelling tools required for a reliable interpretation of the main ion spectra. The next chapter presents the main ion measurements carried out at the ASDEX Upgrade tokamak in different confinement and collisionality regimes. The measurements are compared to impurity ion properties, electrons and neoclassical transport theory predictions. 77 Chapter 6 Edge main ion temperature and toroidal rotation measurements and comparison to neoclassical theory The first measurements of main ion temperature and toroidal rotation at the plasma edge in the full tungsten ASDEX Upgrade tokamak are presented in this chapter. The main ion temperature is compared to the electron and impurity temperature, while the main ion toroidal rotation is compared to the impurity toroidal rotation and the neoclassical main ion toroidal rotation. The main ion toroidal rotation measurements serve as a test-bed for neoclassical transport theory. The edge main ion properties are studied in different collisionality (ν∗) regimes, as the coupling between the plasma species depends on plasma collisionality. The role of collisionality in H-mode plasmas is assessed by scanning the total input power to the plasma. The impact of the heating scheme on the plasma species temperatures is investigated by independently varying the power deposition to the electrons and to the ions. The collisionality scan is expanded by considering other confinement regimes. In particular, low ν∗(I-mode and QH- mode) and high ν∗(L-mode) ELM-free regimes are studied. Note that the impurity measurements presented in this chapter are performed on B5+, and the pedestal top and steep gradient region refer to ρpol = 0.95 and ρpol = 0.97 radial locations, respectively. 6.1 Impact of the heating scheme on main ion measurements 6.1.1 Experimental methodology The impact of collisionality on the main ion temperature has been studied by scanning the total ion and electron input power. In total, four H-mode experiments (Bϕ=−2.5 T) with different levels of NBI (PNBI ) and ECRH (PECRH) power have been performed at AUG. In all discharges, NBI sources Q3 and Q8 are diagnostic beams and at least one gyrotron is switched on to avoid impurity accumulation. The discharges were performed close to boronization to ensure good impurity CXRS signal. They feature Zeff between 1.4 and 1.5 as determined from Bremsstrahlung measurements. Relevant parameters are summarized in Table 6.1. An overview of the discharges1is given in Figures 6.1(a-f), which shows (a) PECRH, (b) the line integrated edge density (¯n), (c) PNBI , (d) the plasma fuelling (Dtot), (e) the outer radial plasma position (Raus) and (f) the ELM frequency (fELM ). 1Each experiment (or discharge) is identified with a unique number (#discharge number). 78 Chapter 6. Edge main ion measurements and comparison to neoclassical theory Figure 6.1: Time traces of the (a) ECRH power, (b) line integrated edge density, (c) NBI power, (d) gas fuelling, (e) outer plasma position and (f) divertor current (ELM monitor) for plasma discharges #38539 (black), #38540 (red), #38587 (blue) and #39000 (magenta). The divertor current is only shown for #38587 for clarity. Discharges #38539, #38540 and #38587 are divided in three phases (highlighted with dashed lines and in different shades of gray). There is a step-wise increase of the NBI power in each phase, while the ECRH power is constant throughout the discharge2. One additional full power NBI source (2.5 MW) is included in each step. In these discharges, NBI sources Q8 and Q3 are alternated for beam power compensation, as discussed in Subsection 5.4.1. The beam modulation gives rise to the oscillation of PNBI that can be seen in Figure 6.1(c). The additional beams included in each power step are indicated in Table 6.1. The ECRH heating scan is carried out by changing PECRH from one discharge to another. The minimum (maximum) PECRH is 0.7 (3.8) MW, corresponding to 1 (5) gyrotrons. In discharge #39000, PNBI is constant (one source) and PECRH is changed. This discharge provides two intermediate ECRH heating cases. Here, beam compensation of NBI source Q8 is done with NBI source Q6, and the impurity measurements are taken during steady phases with NBI source Q3 only. As shown in Figure 6.1(e) the plasma is radially swept to ensure good diagnostic coverage of the edge region (see Subsection 3.1.3). The total power, and stored energy, changes throughout the discharges (Ptot varies from 3.5 to 11 MW). A low ELM frequency is targeted to facilitate ELM synchronization of the data (see Subsection 3.1.3). However, the increase of input power unavoidably leads to an increase of the ELM repetition time [55]. This can be seen in Figure 6.1(f): as the input power increases, the ELM frequency increases. The radiated power (Prad) also changes in steps and proportionally to the stored energy (Prad varies from 1.5 to 3.5 MW). In these discharges, the Pfirsch-Schl¨uter collisionality limit is at ν∗∼7.0 (ν∗= 6.7−7.4), and the banana limit is at ν∗= 1 (see Subsection 2.3.2). The plasma line integrated density (¯n) is fairly constant across all plasma discharges, as shown in Figure 6.1(b). In #38587, the plasma current (Ip) was increased to Ip= 1.0 2Note that discharge #38539 terminates early due to an impurity event at the beginning of the third phase. 6.1. Impact of the heating scheme on main ion measurements 79 Bϕ[T] Ip[MA] q95 PECRH [MW]ν∗,i,PS limit Extra NBI sources #38539 -2.5 0.8 5.3 0.7 7.4 Q5 #38540 -2.5 0.8 5.2 3.8 7.4 Q5, Q6 #38587 -2.5 1.0 4.3 2.3 7.0 Q2, Q6 #39000 -2.5 0.8 5.4 1.5; 3.0 6.7 N/A Table 6.1: Relevant parameters for the H-mode discharges. MA in comparison to #38539 (Ip= 0.8 MA) which leads to higher densities (n) due to the increased Greenwald limit [135]. (a) 0.0 0.2 0.4 0.6 0.8 1.0 pol 0 1 2 3 4 5 PECRH [W/cm 3 ] t = 2.55 s #38539 #38540 #38587 #39000 (b) 0.0 0.2 0.4 0.6 0.8 1.0 pol 10 3 10 2 10 1 100 PNBI [W/cm 3 ] t = 2.55 s #38539 #38540 #38587 #39000 To ions To electrons Figure 6.2: (a) ECRH power deposition (b) NBI power to ions (solid) and electrons (dashed). The ECRH and NBI power deposition have been simulated with the transport code transp [172,173] and are shown in Figures 6.2(a,b). The ECRH power is deposited only on the electrons and in the core (except for some PECRH deposition at the edge for the maximum PECRH heating case #38540). The NBI power is split between the ions and the electrons depending on the local density and temperature (see Subsection 2.3.2). Note that the NBI power deposition per particle is higher for impurities than for main ions, as shown in Figure 2.5. Validation case The validation of the main ion measurements is addressed in a medium collisionality low ELM frequency (fELM = 60 Hz) experiment. The pedestal top ion collisionality (νped. top ∗,i ) is 1.5, which corresponds to the plateau-regime. For the validation of the main ion temperature, the measurement is compared against independent measurements of impurity and electron temperature. The main ion (TD), the impurity (Tz) and the electron temperature (Te) profiles are shown in red, gray and blue in Figure 6.3(a), respectively. The profiles are in good agreement within the experimental uncertainties, which indicates that all species are in thermal equilibrium. This is consistent with the local equilibration times being short compared to the transport time scale (τzD,τze,τeD << τtr), as shown in Figure 2.4(b) for this specific case. As discussed in Subsection 2.3.2, this implies that energy will be exchanged via collisions between the different species at a faster rate than particles are 80 Chapter 6. Edge main ion measurements and comparison to neoclassical theory transported, and therefore, the plasma species are in thermal equilibrium, which results in TD=Te=Tz. (a) 0.85 0.90 0.95 1.00 pol 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 T [keV] PECRH = 0.7 MW PNBI = 2.5 MW ped . top *, i = 1.52 #38539 t = 2.43 s T e T z T D (b) 0.85 0.90 0.95 1.00 pol 0 10 20 30 40 50 60 v [km/s] PECRH = 0.7 MW PNBI = 2.5 MW ped . top *, i = 1.52 #38539 t = 2.43 s v z vD , NEOART v D Figure 6.3: (a) Experimental main ion (red), impurity (gray) and electron (blue) temperatures in the plateau regime (νped. top ∗,i = 1.5). (b) Experimental main ion (red) and impurity toroidal rotation (gray) together with the neoclassical prediction for the main ion toroidal rotation as calculated with the neoart code (black). The main ion toroidal rotation (vϕ,D, in red) is compared to the impurity toroidal rotation (vϕ,z, in gray) and to the neoclassical estimate of the main ion toroidal rotation (vϕ,D,neoart). As explained in Chapter 2, the toroidal rotation, and consequently the radial electric field (Er), are free parameters in neoclassical transport theory. Therefore, the neoclassical calculation is based on an input, i.e., the measured impurity toroidal rotation profile (vϕ,z) or the measured Erprofile. Unless specified otherwise, the vϕ,D,neoart profiles presented in this chapter rely on knowledge of vϕ,z and the expressions presented in Section 2.6. The comparison is shown in Figure 6.3(b). The experimental vϕ,D is consistent with neoclassical theory from ρpol = 0.85 to ρpol = 0.98, and features a rather flat shape and no pronounced dip in the steep gradient region. By applying the neoclassical correction to vϕ,z, a good prediction of the minimum of vϕ,D is recovered, which is 20 km/s higher than vϕ,z. This means that the difference between vϕ,D and vϕ,z is at the neoclassical level, and the dip feature of vϕ,z is due to the temperature gradient (see Equation (2.51)). Towards the separatrix, the ion pressure gradient length (Lpi=pi/∇pi) becomes larger than the ion Larmour radius (rL,i). This region is indicated in gray (note that the radial coverage of this region varies from one case to another depending on the pressure gradient at the specific plasma conditions). Since rL,i > Lpi, the local neoclassical description may not be sufficient in this region. Indeed, a discrepancy between the measurement and the neoclassical prediction for ρpol >0.985 is observed, which may be related to neoclassical ordering breaking down. In addition, the experimental main ion poloidal rotation is compared to neoclassical theory following the methodology described in Subsection 5.4.3. The radial electric field (Er) has been evaluated using impurity CXRS measurements. The experimentally determined Erprofile and the contributions to it are shown in Figure 6.4(a). The different terms represent the contributions to the radial force balance equation for the impurities (see Equation (2.37)). For impurities, the dominant term is vθ,zBϕ. Figure 6.4(b) shows the Erprofile (in black), as determined from impurities, and the experimentally determined pressure gradient term (in green) and vϕ,DBθ(in red) for the main ions. In the main ion radial force balance, the pressure gradient term is the 6.1. Impact of the heating scheme on main ion measurements 81 (a) 0.95 0.96 0.97 0.98 0.99 1.00 pol 60 50 40 30 20 10 0 10 20 30 Er [kV/m] #38539 t = 2.2s Impurity - B 5 + Er v B v B p / n / Z (b) 0.95 0.96 0.97 0.98 0.99 1.00 pol 60 40 20 0 20 Er [kV/m] #38539 t = 2.2 s Main ions Er v B v B p / n (c) 0.95 0.96 0.97 0.98 0.99 1.00 pol 10 5 0 5 10 15 v , D [km/s] ion diamagnetic #38539 t = 2.2 s Main ions Experimental NEOART ±5 mm Figure 6.4: (a) Experimentally determined contributions to the radial electric field (Er) and edge Erprofile for boron impurity ion. (b) Contributions to the radial force balance for main ions. The vθBϕterm is extracted using Equation (5.15). (c) Experimentally determined vθ,D (blue) compared to neoclassical vθ,D (solid black). The uncertainty due to radial profile alignment is illustrated by the black dashed profiles. dominant contribution [35,36,82]. The vθ,DBϕterm (in blue) is not directly determined from measurements, but extracted from the combination of the impurity (which give the Erprofile) and main ion measurements. Note that for the impurities, the diamagnetic term is small in comparison with the main ions, as it depends on Z−1. The vϕBθis small and of the same order of magnitude for the two species. Figure 6.4(c) shows the vθ,D profile derived from the measurements and the neoclassical main ion poloidal rotation calculated with the neoart code, which depends on the temperature and pressure gradients (see Subsection 2.6.3). The vθ,D is small (<5 km/s) from the pedestal top to ρpol ∼0.99. The dashed black profiles illustrate the sensitivity to a ±5 mm shift of the temperature profile (illustrative of the radial uncertainties of the measurements). Within this experimental uncertainty, vθ,D is in good agreement in sign and magnitude with neoclassical theory, as shown by previous studies at AUG [35,82, 84]. As the separatrix is approached, the main ion poloidal rotation reaches values up to 10 km/s. Close to the separatrix, the direction of the main ion poloidal rotation is consistent with the neoclassical expectation (positive, i.e., in the ion diamagnetic drift direction). However, the absolute magnitude is well above the neoclassical prediction. In this region (for ρpol >0.99 indicated in gray, neoclassical ordering breaks down due to rL,i > Lpi), local calculations may not be appropriate and extended neoclassical effects may be necessary to correctly describe the measurement [174]. 6.1.2 Scan of electron heating The impact of the input PECRH on the profiles is examined in this subsection. A total of 5 cases are considered at fixed NBI input power of 2.5 MW. The ECRH power is scanned from 0.7 to 3.8 MW, resulting in νped. top ∗,i that varies from 1.0 to 1.52, covering from the banana limit to the plateau collisionality regimes. The maximum electron heating case (PECRH = 3.8 MW) is at the banana collisionality limit at the pedestal top (νped. top ∗,i = 1.0). The profiles are shown in Figures 6.5(a,b). In this case, the three species are in thermal equilibrium in the steep gradient region (Te=TD=Tz). As the pedestal top is approached, TDand Tzdecouple. Interestingly, TDclosely follows Te. This is an unexpected observation, as the main ions and impurities are expected to be collisionally coupled and in closer thermal equilibrium due to a stronger and faster ion thermal equilibration time compared to electrons [9]. 88 Chapter 6. Edge main ion measurements and comparison to neoclassical theory (a) 0.85 0.90 0.95 1.00 pol 0 10 20 30 40 50 60 70 v [km/s] PECRH = 0.8 MW PNBI = 1.2 MW ped . top *, i = 1.42 L-mode #40223 t = 2.70 s v z vD , NEOART v D (b) 0.85 0.90 0.95 1.00 pol 0 10 20 30 40 50 60 70 v [km/s] PECRH = 1.2 MW PNBI = 1.2 MW ped . top *, i = 0.56 I-mode #40223 t = 4.80 s v z vD , NEOART v D (c) 0.85 0.90 0.95 1.00 pol 0 50 100 150 200 250 v [km/s] PECRH = 750 kW PNBI = 3.6 MW ped . top *, i = 0.16 QH-mode #39318 t = 5.29 s v z vD , NEOART v D Figure 6.13: Experimental main ion (red) and impurity toroidal rotation (gray) together with the neoclassical prediction for the main ion toroidal rotation as calculated with the neoart code (black) for an (a) L-mode and (b) I-mode plasma and (c) QH-mode phase. similar mechanisms. As in the L-mode case, vϕ,D is much larger than the neoclassical prediction, and the expected well feature is not recovered. 6.2.3 QH-mode As described in Subsection 2.7.4, the QH-mode scenario is typically established at low density, low collisionality and high input torque. The case presented here corresponds to an USN plasma with PNBI = 4 MW and PECRH = 0.55 MW. The temperature and toroidal rotation profiles are shown in Figures 6.12(c) and 6.13(c), respectively. For the interpretation of the main ion spectra in this low density scenario with strong off-axis heating, the FIDA contribution is not negligible, and has been taken into account in the analysis (see Subsection 5.4.2). In this case, TD> Tz> Tefor the whole edge region. Here, electrons and ions are not expected to be in thermal equilibrium, as the local transport and thermal equilibration time scales between main ions and electrons, and impurities and electrons are comparable. However, thermal equilibration between main ions and impurities would be expected. Interestingly, the gradients are similar (∇TD∼ ∇Tz). These measurements show similarities with DIII-D QH-mode plasmas. The low collisionality and high edge ion temperatures in DIII-D QH mode plasmas, often lead to both TDand Tzmuch higher than Tein the pedestal and around the separatrix [181]. Sometimes, TD> Tzis observed in the steep gradient region (see Figure 8 in [182]). This observation is in agreement with simulations for the QH-mode pedestal, which show, along with strong anisotropies in the parallel and perpendicular temperature, TD|| > Tz|| at the very edge, presumably because of the larger orbits for deuterium ions [183]. However, this hypothesis is insufficient to explain TD> Tzreported here, which affects the pedestal top temperatures. The main ion toroidal rotation features a monotonic decaying profile in this case, in agreement with the observations for the low ECRH high NBI H-mode plasmas. Neoclassical theory in this case fails to describe the measurement, and predicts a hilllike feature in the steep gradient region and rotations of up to 200 km/s when the experimental vϕ,z profile is used for the estimation of the neoclassical vϕ,D, as shown in Figure 6.13(c). Alternatively, vϕ,D has been evaluated using the neoart code combined with the experimental Erprofile. In this case, Erhas been determined from impurity CXRS measurements and an Erwell down to -90 kV/m has been recovered. If the experimental Eris used for the calculation of vϕ,D,neoart, a strong dip of -150 km/s is recovered in the steep gradient region, in strong disagreement with the measurement. 6.3. Main ion separatrix temperature measurements using a gas puff system 89 In this case, despite the presence of a strong Erwell (which is widely believed to strongly reduce turbulence and bring transport closer to neoclassical levels), vϕ,D is not satisfactorily described by neoclassical transport theory. 6.3 Main ion separatrix temperature measurements using a gas puff system This work has been focused on the exploitation of beam induced CX reactions with the main ions. In addition, the use of a gas puff system as a source for neutral donors for main ion CXRS measurements has been investigated in the framework of this thesis. Figure 6.14 shows a comparison of impurity and main ion measurements. The main ion measurements correspond to D beam based measurements (red), and D2(green) and He (magenta) gas puff based measurements of the Dα(n= 3 →2) and Dγ (n= 5 →2) lines. The gas puff spectra are simpler to fit, as the BES contribution is not present. The difference in the injection energy (in the order of the keV for the NBI system and at room temperature for the gas puff system) and plasma species determine how the neutral sources interact with the plasma and are attenuated. Therefore, the different methods may be better suited to diagnose different radial regions, and provide complementary information on the main ion profiles. The use of main ion gas puff measurements is a very promising technique that deserves to be studied in the future. (D - He GP) α (D - D GP) γ2 Figure 6.14: Main ion temperature using beam-based (red) and He (magenta) and D2(green) gas-puff based measurements compared to beam-based impurity (gray) and electron (blue) temperature. 6.4 Discussion The observations discussed in the previous sections are summarized in Figures 6.15(a,b). Figure 6.15(a) shows the difference between TDand Te(circles) and TDand Tz(squares) at the pedestal top (ρpol = 0.95) as a function of the pedestal top ion collisionality. The different confinement regimes are highlighted by the color code. At medium to high collisionality (varying ν∗,i from 1 to 10) the electrons and main ions are in thermal equilibrium within the experimental uncertainties. In the intermediate collisionality range, TDis more strongly coupled to Tethan to Tz, and the difference between the ion 90 Chapter 6. Edge main ion measurements and comparison to neoclassical theory species is scattered around 150 eV. This is a robust observation and a common trend for all the confinement regimes. In the low to medium collisionality range (ν∗,i from 0.1 to 1.1), a few cases satisfy Tz≈TD. These cases correspond to PNBI >2·PECRH . In strongly NBI heated plasmas (low collisionality H-mode and QH-mode), the three species decouple, such that TD> Tz> Te. The decoupling between electrons and ions is expected for the QH-mode case, however, the decoupling between the ion species is not fully understood. The mismatch between impurity and main ion data cannot be explained by the uncertainties in the spatial resolution and radial profile alignment. In the steep gradient region (ρpol = 0.97), the equilibration of the main ion temperature with the impurity temperature is better, but not always perfect. (a) 10 1100101 ped . top *, i 0.2 0.0 0.2 0.4 0.6 0.8 T [keV] pol = 0.95 T D - T e T D - T z (b) 10 1100101 ped . top *, i 50 40 30 20 10 0 10 20 v exp - v neo [km/s] v , D at pol = 0.97 H L I QH USN L low H Figure 6.15: (a) Difference between main ion and electron (circles) and main ion and impurity (squares) temperature as a function of the pedestal top collisionality in the pedestal top (ρpol = 0.95). (b) Difference between the experimental and the neoclassical prediction for the main ion toroidal rotation in the steep gradient region (ρpol = 0.97) as a function of pedestal top collisionality. The color legend indicates the confinement regime. In the following, a discussion of the possible reasons for the discrepancy between the impurity and main ion temperatures is presented:  Turbulent equipartition Classical (collisional) equipartition is in general, down-gradient (i.e. counteracting the gradient, see Equation (2.11)) and driving the plasma to a thermal equilibration. In contrast, turbulence equipartition can lead to fluxes without gradients in the thermodynamic variables, and even up-gradient fluxes [177]. The relaxation to turbulence equipartition can lead therefore to non-uniform profiles, and may explain the experimental difference between the main ion and impurity temperature. To address this hypothesis, the nature of ion heat transport must be investigated by detailed interpretative modelling of the temperature measurements, simultaneously considering the main ion and impurity species to consistently evaluate the main ion-impurity heat exchange term, and their heat exchange term with electrons.  Heat transport The underlying reason for the temperature difference may originate due to heat transport mechanisms. The diagnostic beams for main ion and impurity CXRS measurements (NBI source Q3 for impurities and NBI source Q8 for main ions) are both radial and on-axis, but feature different injection energies, which leads 6.4. Discussion 91 to different power deposition profiles. For a higher voltage beam (beam injection energy), more power is deposited on the electrons at the edge (see Figure 2.4). In this scenario, a stronger coupling between electrons and main ions could lead to higher main ion temperatures compared to impurities. The estimate of the ion heat flux using NBI source Q3 and Q8 is shown in Figure 6.6(b), and no sizeable difference is expected from the two beam phases within errorbars.  Hydrogen contribution to the spectra Deuterium plasmas are not 100% pure and there is always a residual contribution of H. In D plasmas at AUG, the hydrogen concentration in discharges during the campaign can safely be assumed to be 3-6% [184]. Because of the small energy difference for the electronic transition (and therefore radiation frequency and wavelength), the deuterium and hydrogen Balmer αspectral lines are at 656.1 and 656.28 nm, respectively and are superposed in the main ion spectra. A contribution from the hydrogen emission can potentially corrupt the interpretation of the deuterium measurements, as it leads to an apparent broadening of the spectral line, which is not associated with TD. For the toroidal rotation, neglecting the H contribution leads to an underprediction of vϕ,D. The impact of a H contribution to the D spectra has been evaluated using the fidasim code. The impact of H contents up to 15% leads to an overestimation of the deuterium temperature below 50 eV at the pedestal top (the correction is reduced towards the separatrix). For the typical H concentrations at AUG, the correction is of the order of 20-30 eV for the temperature and below 5 km/s for the toroidal rotation, and this effect is insufficient to explain the temperature discrepancy between main ions and impurities.  Banana orbit width effect Particles in banana orbits experience large radial excursions, and may locally distort the distribution function (i.e., lead to a hotter apparent temperature than the local temperature). This effect may be important at low collisionality, as banana particles dominate transport. A more relevant impact of this effect could be expected in the steep gradient region, where the local temperature scale length is large, while the effect would be reduced at the pedestal top. However, the discrepancy between the main ion and impurity temperature is observed at the pedestal top, where the gradients are flatter. For this reason, the banana orbit width effect is likely not the explanation for the discrepancy at the pedestal top.  Scrape-off layer boundary condition If the temperature at the separatrix differs from one ion species to another, the gradient stiffness would lead to different main ion and impurity pedestal top temperatures. From a theoretical point of view, edge fluid codes (such as solps [185]) do not typically distinguish between ion temperatures to reduce the number of variables, due to the lack of experimental constrains up to now. The hypothesis of having different TDand Tzat the separatrix due to SOL/divertor physics effects (such as interaction with the wall) [186], could be tested with a Monte Carlo code, such as divimp [187]. The main ion temperature and toroidal rotation measurements presented in this chapter are the first in a full metal environment. The experimental observations differ from the edge main ion measurements at the carbon-wall DIII-D tokamak, where impurity and main ions are generally in thermal equilibrium, or impurities are hotter than the main ions [17,188]. The hotter impurity temperatures observed at DIII-D in comparison to the main ions could be explained in terms of impurity particle transport, orbit 92 Chapter 6. Edge main ion measurements and comparison to neoclassical theory width effects and/or main ion cooling [17,189,190]. If high-ionized charged state impurities from the core are transported outwards (to the pedestal) [189,190], the CXRS measurements would effectively diagnose the temperature of impurity ions that carry a higher temperature than those living in the pedestal. Alternatively, the interaction with cold deuterium at the plasma edge may pose a heat loss mechanism for the main ions but not for the impurities [17]. The differences may also arise due to a different interaction of the edge plasma with a carbon or metal wall. The difference between the experimental and the neoclassical prediction based on the impurity measurements for the main ion toroidal rotation in the steep gradient region (ρpol = 0.97) as a function of collisionality is shown in Figure 6.15(b). In H-mode plasmas, neoclassical theory can correctly describe the measurement within errorbars. For L-mode and I-mode plasmas, neoclassical theory cannot fully describe the measurement and other effects may need to be taken into account to correctly describe, and predict, the main ion toroidal rotation. This may be related to the presence of turbulent transport mechanisms in the steep gradient region in these regimes, which do not feature the strong flow shear driven by Er(or pressure gradient) in H-mode plasmas, which strongly reduces turbulence. In the QH-mode plasma, the main ion toroidal rotation is likewise not well described by neoclassical theory. In the pedestal top (ρpol = 0.95), the main ion toroidal rotation in H-mode is not always at the neoclassical level (it is mostly 10 km/s faster). These new measurements reveal that the impurity temperature may not be representative of the main ion temperature at the pedestal top, depending on the collisionality and on the heating scheme, and main ions may be more strongly coupled to electrons. These are state-of-the-art measurements and detailed modelling is required for a deep understanding of the implications that these experimental observations have on the current knowledge of heat transport at the plasma edge. 6.5 Summary The first deuterium main ion measurements of temperature and toroidal rotation in a full metal wall tokamak device have been presented in this chapter. The measurements expand over an ion pedestal top collisionality range of ν∗= 0.1−10 and a variety of confinement regimes, including H-mode, L-mode, I-mode and QH-mode. The main ion temperature has been compared to impurity and electron temperature. Surprisingly, the impurity ion temperature does not always provide a good approximation for the main ion temperature (even at collisionalities for which thermal equilibration is expected). The thermal coupling between main and impurity ions is a complex function of collisionality and heating scheme, and may be related to turbulent equipartition mechanisms. The main ion toroidal rotation in H-mode plasmas is in remarkably good agreement with the neoclassical transport theory prediction in the steep gradient region and is consistent with previous works [82,84]. The main ion pedestal top toroidal rotation is not always captured by neoclassics, being generally faster than the neoclassical expectation. Close to the separatrix, neoclassical theory does not appropriately capture the main ion toroidal rotation, possibly due to neoclassical ordering breakdown. The characterization of the plasma properties is fundamental for understanding plasma transport and enables reliable projections towards future fusion devices. Importantly, the main ion properties determine the fusion power that can be produced in next step devices, and conditions their performance. In the next chapter, the integration of the European DEMO tokamak with a power conversion system is investigated. 6.5. Summary 93 In particular, the thermodynamic efficiency of the integration is optimized, which is also a crucial parameter for the success of future fusion devices. 95 Chapter 7 Power cycles for future fusion reactors The integration of the power conversion system and a fusion reactor is optimized in this chapter. A framework that couples the Engineering Equation Solver (ees) [191] with the process system code [102,103] has been developed to assess the thermodynamic and economic performance of fusion power plants. For the fusion reactor, the DEMO Baseline 2018 is taken as the reference design. Its integration with a portfolio of Rankine and Brayton cycles is investigated, with a special focus on the impact that the use of different working fluids for the power conversion system has on the fusion power plant performance. The power cycle layouts have been made consistent with the boundary conditions imposed by the DEMO Baseline 2018. The implications of the boundary conditions and assumptions made for the study are discussed. Note that parts of this chapter have been published in the article [192], of which the thesis author is second author. 7.1 Workflow for the integration of a fusion reactor and power conversion system The evaluation of thermal and economic parameters for a future fusion power plant (FPP) requires the combination of plasma physics and engineering models, that can simulate the performance of the fusion reactor and of the power conversion system (PCS). In this work, the process system code [102,103] and Engineering Equation Solver (ees) [191] have been integrated to calculate the electricity production, efficiency and levelized cost of electricity (LCOE) (see Subsection 7.4.4 for its definition). The process system code combines simplified plasma physics [102], engineering and economic models [103] that enable the assessment of the engineering and economic viability of a hypothetical fusion power station. A more detailed description of process is given in Subsection 3.2.4.ees is a numeric solver that can resolve systems of nonlinear coupled equations. It contains libraries with the thermodynamic properties of fluids, providing an excellent environment for the development of PCS models. The workflow followed in this study is illustrated in Figure 7.1. In this framework, process is used to provide the boundary conditions for the PCS optimization. process calculates the thermal power available in the different heat sources (i.e., the power available in the first wall, blanket, divertor and shield) and the reactor consumption. The boundary conditions for the fusion reactor, namely the temperature and thermal power of the different heat sources and the reactor consumption, are taken from the EUDEMO Baseline 2018 [15] and are summarized in Table 7.1. These boundary conditions are provided to ees for the optimization of the power cycle. A portfolio of PCS layouts are simulated with ees, and the cycle electric efficiency and electrical power output are 96 Chapter 7. Power cycles for future fusion reactors PROCESS systems code - Thermal power - Reactor self-consumption - Economic parameters Engineering Equation Solver ηpower cycle, Pnet,elec Cost of Electricity Figure 7.1: Framework of the study, integrating the process system code and ees for the assessment of a fusion power plant viability. Power [MW] Temperature [ ° C] Blanket 2254.0 500 Divertor 389.5 150 Shield 1.5 150 Consumption 491.8 - Table 7.1: Boundary conditions for the DEMO Baseline 2018 scenario. evaluated. These parameters can be further combined with the costs estimations from process to determine economic indicators such as the LCOE. 7.2 Considerations for power cycles for future fusion power plants The design of the reactor heat extraction system and PCS for a future FPP can benefit from the knowledge and developments of existing power cycles, and especially from current and future fission nuclear power plant (NPP) technologies. However, some challenges are intrinsic to the fusion power plant operation, and an analogy to fission NPPs is not trivial. The main challenges and distinct characteristics of a FPP are its pulsed operation and the need to integrate different heat sources at possibly different temperatures. Other important considerations are the implications of the PCS being framed in a nuclear environment with fast neutrons, the high reactor self-consumption power and the uncertainties in the final design of FPP. These considerations are discussed in the next subsections. 7.2.1 Pulsed operation As outlined in Subsection 3.2.2, the European DEMO Baseline 2018 (DEMO1 class) is based on the tokamak reactor1and, therefore, assumes intermittent operation. The pulsed operation of DEMO creates significant challenges for the primary heat transfer system and PCS. The cyclic operation of the reactor jeopardizes the PCS components integrity and lifetime, and the power cycle efficiency due to partial loads. A thermal 1A tokamak reactor type uses, amongst others, inductive heating and current drive. Although tokamak continuous operation may be possible if current drive can be solely provided by non-inductive means [12], a tokamak reactor type generally implies that the plant operation is pulsed. 7.2. Considerations for power cycles for future fusion power plants 97 (a) Divertor Shield Blanket Thermal Energy Storage Power Conversion System Water Helium Pelec Paux V1 V2 V3 V4 V1 V2 V3 V4 (b)                   Figure 7.2: (a) Integration of the power conversion cycle, thermal energy storage and reactor heat sources. (b) Thermal energy as a function of time during a full cycle. energy storage can be employed to mitigate the impact of the cyclic operation [102,116, 193]. In this work, a thermal energy storage (TES) is included in the PCS modelling to guarantee reasonable components lifetime and reliable power production [192]. The TES is loaded during pulse time (tpulse) and emptied during dwell (tdwell) and ramp (tramp, time for the transition from dwell to pulse and vice versa) times. The power flow is sketched in Figure 7.2(a). During the dwell and ramp time, the power flows from the TES to the PCS following the solid lines and valves V3 and V4 are closed. During pulse time, valves V1, V2, V3 and V4 are opened, such that the power flows directly from the reactor heat sources to the PCS and TES. The thermal power (Q) is split proportionally between the PCS and the TES during pulse time: Qk=Qk,PCS +Qk,TES.(7.1) Here, the subindex krefers to the power source (blanket, divertor and shield). This leads to an energy distribution between the PCS (Ek,PCS) and TES (Ek,TES) of: Ek,PCS =Qktpulse tpulse ttotal ,(7.2) Ek,TES =Qktpulse tstop ttotal ,(7.3) where tstop =tdwell + 2tramp. During dwell time, the TES unloads to feed the PCS: Ek,TES→P CS =Ek,T ES ηT ES =Qktpulse tstop ttotal ηTES,(7.4) where ηTES is the adiabatic efficiency of the TES and is assumed to be 95% [194]. The power input to the PCS during pulse (Qk,pulse) and dwell (Qk,dwell) time are therefore: Qk,pulse =EPCS tpulse =Qktpulse tpulse ttotal 1 tpulse =Qk tpulse ttotal ,(7.5) Qk,dwell =ETES ηT ES tstop =Qktpulse tstop ttotal ηTES tstop =Qk tpulse ttotal ηTES =Qk,pulse ηT ES.(7.6) 104 Chapter 7. Power cycles for future fusion reactors (a)       pLPT            pMPT  TRH  pHPT     cycle (b) Figure 7.6: (a) Efficiency of the plant as a function of the low and medium turbine pressures for the C1 layout shown in Figure 7.4(a). (b) The h-s diagram for the supercritical (red) and subcritical (blue) cycles. pLPT are shown in Figure 7.6(a). The vertical line indicates the condition of xLP T = 0.90, and limits the possible operation space to a pLPT <52 bar. The maximum cycle performance is achieved for pMP T = 96 bar and pLPT = 51 bar, which gives ηcycle = 38.5%. The h-s diagrams for the supercritical (red) and subcritical (blue) layouts are shown in Figure 7.6(b). The parameters for layout C1 considering a pLP T = 52 bar and pMP T = 96 bar are shown in Table 7.2. Figure 7.7(a) illustrates the impact of increasing the HPT and LPT inlet pressures on the cycle electric efficiency for a fixed ∆TPH = 30 ° C for the C2 layout. The increase of either of them leads to a higher ηcycle. The dashed black line indicates the condition of xLPT = 0.90. The maximum cycle performance is limited by this factor, and restricts the operational space to lower pressures. At pLP T = 12.25 bar, ηcycle improves from 38.8% to 39.4% when increasing pHP T from 180 to 300 bar, as shown in Figure 7.7(a). For a fixed pLP T = 10.8 bar, ηcycle has a similar dependence on ∆TRH compared to pLPT , as both are related, and also limited by the moisture fraction at the LPT outlet. In order to overcome this limitation, a second reheating stage (before the LPT inlet) is included. Figure 7.7(b) shows the impact of adding a reheating stage before the LPT inlet. The thermal power in the blanket is split and also used for the reheating. The area to the left of the dashed line does not satisfy xLP T >90% (would require stronger reheating to guarantee the cycle integrity). Since adding a second reheating stage penalizes the overall efficiency of the cycle, the minimum reheating for a given operating pressure should be pursued. In Table 7.2, the parameters for layout C2 considering a ∆TPH = 30 ° C, pTB = 12.3 bar and ∆TRH = 5 ° C are shown. Alternatively, an interesting possibility for boosting the efficiency of the reactorpower cycle integration is the use of the low-temperature heat sources (divertor and shield) for cogeneration, as will be discussed in Chapter 8. The integration of Rankine cycles with a FPP would benefit from the experience and know-how of the technology. For a successful integration, the feasibility of tritium recovery needs to be demonstrated. In addition, superheated and supercritical water cycles need licensing for sodium-water reactions. In a fusion power plant, chemical safety regarding the alkali lithium-water reaction also needs to be guaranteed. 7.4. Working fluids for the integration 105 (a)      pLPT         pHPT  TRH      cycle (b)       TRH , LPT         pHPT  TRH  pLPT     cycle Figure 7.7: Efficiency of the cycle as a function of (a) the inlet pressure for the high and low-pressure turbines and (b) the pressure at the HPT inlet and the reheating before the LPT for the supercritical cycle based on the C2 layout shown in Figure 7.5(a). 7.4.2 Integration with the supercritical CO2cycle Although the advantages of the use of carbon dioxide (sCO2) as working fluid for a PCS in conditions above its critical point (73.77 bar, 31 ° C) have been acknowledged since the 1950s [203,204], supercritical CO2(sCO2) is still a non-commercial technology. In the last years, sCO2is gaining the interest in the scientific and technological community, as well as nuclear and solar industries, because of its thermodynamic properties within the temperature ranges of interest for both applications. The use of sCO2framed in 4th generation nuclear facilities has been highlighted [205]. The use of sCO2for a FPP has been studied for different blanket models, such as Helium-Cooled Pebble Bed (HCPB) [192,206] and dual-coolant models [207–209]. Supercritical CO2is a good candidate for integration with a fusion reactor because of its high efficiency at the temperature ranges considered in the DEMO Baseline 2018 (see Figure 7.3(b)) and low coolant interaction with tritium. Supercritical CO2offers high recuperation potential and reduced compressor work compared to the helium Brayton cycle, as the fluid works close to the critical point in the compression phase, resulting in reduced compressibility. In this thesis, the carbon dioxide properties are evaluated from the equation of state proposed by Span and Wagner (applicable for T < 1100 K and p < 800 MPa) [210]. The maximum pressure for all layouts is 280 bar to comply with the sCO2technology standards [206]. In this subsection, the results published in [192] are discussed. A portfolio of 14 layouts has been simulated to explore the configuration that yields the best performance for the integration of a sCO2cycle with a HCPB DEMO reactor [192,211]. These layouts are split between more conservative (DEMO1) and advanced (DEMO2) scenarios [99,116]. In the DEMO1 scenario, the blanket temperature is limited to 500 ° C, while in the DEMO2 scenario, temperatures up to 800 ° C are considered feasible due to the use of advanced structural materials, e.g., SiC composites [212,213]. Interestingly, the compatibility and good performance of sCO2cycles using SiC pipes has recently been proved [125]. The integration of the fusion reactor with a sCO2PCS is illustrated in Figure 7.8(a). The cycles include a double recuperator and may include a secondary compressor. The basic layout is illustrated in black. The optimization of the PCS has been assessed by changing the configuration in which the different elements are integrated. Three 106 Chapter 7. Power cycles for future fusion reactors (a) (b) Figure 7.8: (a) Schematic representation of the sCO2power cycle layouts. The numbering corresponds to the layout HLC-LDS. The fluid properties in these points are shown in Table 7.6. (b) Cycle and plant efficiency for the DEMO1 and DEMO2 (SS) layouts. variations are proposed for the positioning of the elements on the low-pressure branch of the cycle. These elements are the High Temperature Recuperator (HTR),Low Temperature Recuperator (LTR) and the secondary compressor (SC). In addition, three alternatives are proposed for the high-pressure branch of the cycle, which refer to the order in which the divertor, shield and LTR are placed. This leads to a total of nine combinations which are labelled as:  Depending on the divertor and shield heat sources positioning in the high-pressure branch: –LDS (LTR-Divertor-Shield): the fluid goes first through the LTR, then the divertor and shield HX. The divertor and shield positioning is indicated in a red circle. –DSL (Divertor-Shield-LTR): the fluid goes first through the divertor and shield HX, then the LTR. The divertor and shield positioning is indicated in a blue circle. –No-DS: the divertor and shield heat sources are discarded, eliminating their temperature constraint.  Depending on the secondary compressor positioning in the low-pressure branch: –HLC (HTR-LTR-Secondary compressor): the fluid goes first through the HTR, then the LTR and finally the SC. The mass in the cold LTR side is lower than that in the hot LTR side. This integration is shown in magenta. –HCL (HTR-Secondary compressor-LTR): the fluid goes first through the HTR, then the SC and finally the LTR. The mass in both LTR sides is the same. This configuration is shown in green. –No-SC: there is no secondary compressor. This configuration explores the effect of eliminating the extra consumption of the secondary compressor on the efficiency of the cycle. The position of the divertor and shield heat sources is indicated with the red and blue DIV-SHD circles for the LDS and DSL configuration, respectively, while the secondary compressor position is indicated in magenta and green in the HLC and HCL 7.4. Working fluids for the integration 107 configuration, respectively. Another important consideration for the study of sCO2 cycles is the evaluation of the LTR performance. Because of the important changes in heat capacity (cp) close to the critical point (in the LTR low pressure branch) [204], the minimum temperature difference between the cold and hot temperature streams may be located inside the recuperator. This effect is accentuated in configurations with a secondary compressor, as they lead to unbalanced mass flows in the recuperator (since mLTR, low pressure > mLTR, high pressure). The temperature profile through the recuperator needs to be analysed to ensure a minimal temperature difference between the two streams. This is typically satisfied if enough temperature difference in the inlets is ensured (4 ° C sufficed in this work). Figure 7.8(b) shows the cycle and plant efficiencies for the 14 layouts, which include the 9 configurations, and modifications to them, that are discussed in the following paragraphs. The HLC-LDS configuration is the one yielding the highest efficiency among these nine combinations, which gives a maximum cycle electric efficiency of 38.4%. For this cycle, more optimistic scenarios in which the temperature constraint on the heat sources has been relaxed up to 800 ° C are evaluated. These scenarios include the HT label (for high temperature) and are representative of a future reactors for which potential developments in structural materials have been made. The HT scenarios bridge the gap between the DEMO1 and DEMO2, which assumes important advancements in both plasma physics (continuous operation) and engineering. The HT1 and HT2 scenarios consider longer pulses, with tpulse of 4 and 6 h and tdwell of 20 and 10 min, respectively. These scenarios study the improvement of efficiency when approaching steady state operation. Finally, the more optimistic steady-state DEMO2 scenario is also investigated for the HLC-LDS layout (SS-HLC-LDS). In this case, the TES is removed and softer constraints on the temperature are assumed. The impact of adding a second turbine with intermediate reheater (the blanket power is split between the two heat exchangers) is evaluated in SS-HLC-LDS-2T. The study is completed by adding a case in which advancement in the physics understanding is assumed (steady-state operation is possible), but not in the material limits (the blanket temperature limit of 500 ° C is maintained). This configuration is labelled SS-HLC.LDS-2T (500 ° C). For all low-pressure branch arrangements, the LDS configurations are the optimal ones. The fact that LDS configurations give better efficiencies than DSL configurations implies that the cycle performance greatly benefits from exploiting the recuperation potential (i.e., it is beneficial to prioritize the extraction of heat from the hot LTR branch over the use of the divertor and shield heat sources). Additionally, the better efficiencies of LDS against NDS highlights that the inclusion of the divertor and shield benefits the efficiency, despite the constraint on the temperature they impose. The pulsed high-temperature scenarios can increase the efficiency by over 16%, while the DEMO2 layouts significantly improve the efficiency almost by 18%, up to ηcycle = 56.2%. This result highlights that the PCS efficiency would benefit more from a relaxation of the temperature limits, rather than by extending the pulse duration. 7.4.3 Integration with the helium Brayton cycle The helium Brayton cycle has been considered because of its good thermal conductivity and stability under high neutron fluxes. The use of helium Brayton cycles for the HCPB [199] and dual and self-coolant blanket models [124,207] has been previously studied. The cycle layout discussed here is based on [199] and adapted to integrate the divertor and shield heat sources before the recuperator HX (RHX), as shown in Figure 7.9. The maximum pressure is 80 bar [207,214,215]. 108 Chapter 7. Power cycles for future fusion reactors TC3 IC1 C1 C2 BNK-HX DIV-HX RHX DH-HX PC IC2 10 1 2 3 4 5 678 9 11 12 Figure 7.9: Helium Brayton cycle for the DEMO Baseline 2018 fusion nuclear power. Schematic representation of the cycle. The helium is expanded in the turbine (T) and is directed to the recuperator heat exchanger (RHX) at its outlet. In pure electric operation, the helium by-passes the district heating heat exchanger (DH-HX) and heat is dissipated in the precooler (PC). The helium is compressed in three stages (C1, C2 and C3). The intercoolers (IC1 and IC2) are interleaved between the compression stages to reduce the compression work. The helium is firstly heated in the divertor heat exchanger (DIV-HX), then in the RHX and finally in the blanket heat exchanger (BNK-HX). Two intercooling phases (IC1 and IC2) are included to reduce the compression work and improve the cycle electric efficiency. An identical compression ratio (ρci) has been considered for each compressor, calculated as ρci =n qrc/Pj(1 −∆plcj) where ρcis the total compressor pressure ratio, and ∆plcj is the pressure loss in each intercooler [215]. The efficiency of the turbine and compressor are 93% and 89%, respectively. The pressure drops in the components are 0.8 bar in the high pressure side of the RHX, 0.5 bar in the low pressure side of the RHX and 0.4 bar in the precooler and intercooler [216]. The pressure drop in the heat sources has been neglected [216]. The conditions at the outlet of the hot and cold sides of the RHX are calculated considering a recuperator efficiency (Equation 7.9) of 95% [199] and energy conservation (Equation 7.10): ηRHX =T2−T12 T2−T11 ,(7.9) h2−h3=h12 −h11,(7.10) where Tand hare the helium temperature and enthalpy in the points indicated in Figure 7.9. (a)      c         cycle (b) -9 -8 -7 -6 -5 -4 -250 250 750 1250 1750 2250 2750 1 2 34 5 6 7 8 9 10 11 12 Figure 7.10: (a) Cycle efficiency (ηcycle) for the helium Brayton cycle as a function of the total compression ratio (ρc). (b) The h-s diagram of the reference cycle. 7.4. Working fluids for the integration 109 The helium Brayton cycle is characterized by a large compression work that strongly conditions the efficiency of the cycle. The pressure ratio needs to be optimized to maximize the cycle electric efficiency. Figure 7.10(a) shows the cycle electric efficiency as a function of the compression ratio (ρc). A maximum cycle electric efficiency of 28.7% is achieved for a compression ratio of 1.735, including the impact of a TES. The maximum efficiency of the system is 35% if the use of a TES is neglected. This result is in line with previous works [199], which indicate a cycle electric efficiency of 34.7% in the absence of a TES for a compression ratio of 2.3. These efficiencies are low compared to the Rankine and Brayton cycles. Higher efficiencies will naturally be achieved at higher temperature (as shown in Figure 7.3(b)) in advanced blanket concepts, e.g., efficiencies above 40% can be achieved for self-cooled and dual-coolant breeding blanket models [124]. The h-s diagram for the selected compression ratio is shown in Figure 7.10(b). Given the maximum pressure and temperature of the cycle, once the compression ratio is selected (in this case, the one that maximizes ηcycle), the conditions at the turbine outlet are fixed (T2, p2). The conditions at the divertor inlet are also fixed for a given ambient temperature (Tamb =T7=T9= 30 ° C) and ρc. The temperature at the divertor outlet is 85 ° C, well below the 150 ° C limit, and its integration is possible. 7.4.4 Economic assessment The economic performance of the different layouts is evaluated in terms of the LCOE. This economic indicator is defined as: LCOE =CCa+PxV Cx·fa·fx Etotal ,(7.11) where CCais the capital costs annuity, VC are the variable costs, fais the amortization factor, fxis the levelization factor and Etotal is the annual electric energy production. This is a usual indicator within the energy sector to compare the economic feasibility of different technologies. Annualization of capital costs The capital cost annuities (CCa) are calculated from the total capital investment (TCI) according to: CCa=T CI ·fa=TCI ·i(i+ 1)n (1 + i)n−1,(7.12) where fais the amortization factor, ithe discount rate, and nthe total number of years.The annual costs or annuities, related to both variable and capital costs, are calculated within process. Dividing those by the annual electricity production gives rise to the Cost of Electricity (COE). These values are shown in Table 7.4. Levelization of variable costs The evaluation of the LCOE in comparison to the COE requires, in addition of the normalization (or calculation of annuities), the levelization of costs. The levelization of costs is applied to the variable costs (expenditures over an n-year period, such as fuel or operation and maintenance costs). The constant-escalation levelization factor (CELF) is used for the calculation of the levelized value. The levelization factor depends on both the effective annual cost-of- money rate (or discount rate, i) and the nominal escalation rate (rn) [217]. The CELF 110 Chapter 7. Power cycles for future fusion reactors is defined as: CELF =fx·fa,(7.13) where fx=k(1 −kn) 1−k,(7.14) and k=1 + rn (1 + i).(7.15) The nominal escalation rate (rn) is defined as: (1 + rn) = (1 + rr)(1 + ri),(7.16) here, riis the constant average inflation rate and rris the real escalation rate. rris independent and exclusive of inflation, and results from source depletion, increase in demand and technology developments. The economic parameters for the calculation of the LCOE are summarized in Table 7.3. The inflation rate riis representative of the European Union (EU27) and has been calculated with EUROSTAT data in the 2015-2020 period [218]. Likewise, the real escalation rate of the auxiliary heating (rr,aux) has been estimated through the cost increase of electricity in EU27 for the 2016-2020 period [218]. For the rest of the variable costs, a real escalation rate has been set to 0.0. This is a conservative approach as their cost will likely decrease as the technology develops [192]. Discount rate (i)0.0650 Inflation rate (ri)0.0113 Real escalation rate heating (rr,aux)-0.0022 Real escalation rate others (rr,other)0.0000 Life of the project [years] 40 Dollar inflation 0.9802 Table 7.3: Economic parameters for the analysis of the LCOE. Annual Cost [M $ ] COE [m $ /kWh] LCOE [ $ /MWh] Capital Investment 523.65 178.58 209.51 Operation & Maintenance 44.41 15.14 18.47 Decommissioning Fund 4.43 1.51 0.12 Total Fuel Cost 165.93 56.59 68.97 Blanket & first wall 125.40 42.76 52.14 Divertors 34.80 11.87 12.42 Auxiliary Heating 1.75 0.6 0.71 Actual Fuel 1.44 0.49 0.60 Waste Disposal 2.54 0.87 1.06 Total 1990 US dollars 738.42 251.82 297.07 Total 2020 US dollars 1462.22 498.65 588.25 Table 7.4: Breakdown of LCOE calculation for the DEMO Baseline 2018 scenario reported in Table 7.1 for 500 MW electricity production and availability factor of 75%. All values are in 1990 US dollars. The last row converts the cost to 2020 US dollars, taking into account inflation. Note that the capital cost and economic parameters are common parameters to all layouts, as they are established in the DEMO Baseline 2018, as discussed in Subsection 3.2.4. The variation of the LCOE between layouts responds to the differences in electricity production (i.e., due to the denominator of Equation (7.11)). As an example, the LCOE evaluation for the DEMO Baseline 2018 scenario reported in Table 7.1 is given 7.4. Working fluids for the integration 111 in Table 7.4. The COE calculation is directly provided by process, which assumes an amortization factor of fa= 0.065. Note that the costs refers to 1990 US dollars, as a 1990 cost model is implemented in process. The last row shows the conversion to 2020 US dollars taking into account US dollar inflation. Figure 7.11(a) shows the dependence between the LCOE and the net electric power output. It can be seen that electrical power outputs above 0.6 GW are required for the LCOE to drop below the 200 1990 US $/MWh. The electrical power outputs for the Rankine cycles A3 and B, the helium and the sCO2PCS are shown with vertical dashed lines. Their respective LCOEs are given by their intersection with the curves. Figure 7.11(b) shows the LCOE as a function of the plant efficiency (ηplant) and the recirculated power (Pconsumption), and highlights the importance of reducing the power consumption of the system independently of the cycle electric efficiency, i.e., the impact of improving the plant efficiency for the economic feasibility of a future FPP. The recirculated power constitutes an important efficiency limit for a FPP, and leads to negative power balance in cases where the electrical power output is on the order of a few hundreds of MW. For the DEMO Baseline 2018, based on a HCPB blanket, the primary heat pumps make up for half of the inner recirculated power. (a)        Pplant            fav        2 DEMO 1  2 DEMO 2 (b)      plant        Pconsumption             Figure 7.11: (a) Levelized cost of electricity as a function of the net electrical power output for an availability factor of 70% (black), 75% (red) and 80% (blue). The electrical power output for the DEMO Baseline for the different cycle technologies is indicated with the vertical dashed lines. (b) Levelized cost of electricity as a function of the cycle electric efficiency and recirculated power. The gray area indicates the region with negative LCOE (negative power balance), the white area a LCOE >1000 US $ /MW h and the white dashed lines the LCOE levels from 100 to 1000 in steps of 100 US $ /MW h. 7.4.5 Comparison of the different layouts The thermodynamic and economic indicators for the selected layouts are summarized in Table 7.5. For the temperature constraints considered for the DEMO Baseline 2018, the Rankine (both sub and supercritical) and sCO2cycles yield similar performance close to ηplant = 20%. The Rankine cycles benefit from a large experience of the technology, while sCO2cycle is still a technology to reach the market, but with a very strong impulse in current nuclear and solar programs in USA and Europe. For the integration with nuclear fusion, the choice of sCO2over water as working fluid for the PCS would be justified if tritium recovery is facilitated, as this is a critical point for the success of the plant operation. The efficiency of the helium cycle is substantially lower, 112 Chapter 7. Power cycles for future fusion reactors Rankine Rankine SC sCO2Helium ηelec,cycle [%] 38.4 39.0 38.5 27.9 ηelec,pulse [%] 28.0 28.8 28.0 20.5 ηelec,plant [%] 19.8 20.4 19.9 10.0 Pcycle [MW] 716.7 727.1 718.0 521.3 Pplant [MW] 369.5 379.9 371.0 174.1 COE [1990 $ /MWh] 282.0 274.3 280.8 598.4 LCOE [2020 $ /MWh] 658.7 640.7 656.0 1398.0 Table 7.5: Thermodynamic and economic performance of Rankine (layout B), supercritical Rankine (layout C2), supercritical CO2Brayton and helium Brayton cycles for fusion. below 10%, compared to all other possibilities and therefore would be disregarded in the DEMO Baseline 2018 temperature range. Sensitivity analyses have been performed to assess the impact of having a more flexible blanket temperature constraint (the temperature constraint in the divertor is maintained) on the cycle performance. Due to the temperature difference between the divertor and blanket, minimizing the power deposited in the divertor would maximize the cycle electric efficiency. Both the increase of the maximum temperature constraint and a reduction of the power deposited in the divertor are expected to improve the efficiency due to an increase in the average supply temperature. The power deposited to the divertor may be affected by plasma conditions (edge plasma profiles, radiation, confinement regime, etc., see Figure 7.3(a)). Therefore, the robustness of the results for the different PCS when varying the power split between the divertor and the blanket has been analysed. The results for a bi-dimensional scan in maximum temperature and power fraction to the divertor (αdiv) are shown in Figures 7.12(a-d). As expected, the efficiency increases when reducing the power into the divertor and increasing the maximum temperature for all layouts. The sharp decrease of efficiency for the Rankine cycle with mixer (layout C1) at high αdiv (indicated by the dashed white line) occurs when the temperature at the divertor outlet reaches the constraint of 150 ° C. Note that the y-axis and the color scale differ between the different plots. These results illustrate how the best PCS for integration with a FPP strongly depends on the temperature constraint. As soon as the temperature constraint is increased to 600 ° C, the advantage of a sCO2cycle over a Rankine cycle is evident. In the temperature range of 600-800 ° C, the sCO2would also be preferred against the helium Brayton cycle. If the blanket temperature can be up to 1000 ° C, the helium Brayton cycle would be chosen for the PCS, which can achieve efficiencies up to 54%. Figure 7.3(b) compares all the layouts for a power split between divertor and blanket (αdiv) of 14.8%, as in the DEMO Baseline 2018. The attainable efficiency for sCO2and helium at 800 and 1000 ° C, respectively, are comparable. However, if high temperatures (over 1000 ° C) are attainable, the use of helium may be preferred over sCO2due to helium chemical and radiological inertness. The use of helium and sCO2heat exchangers removes the need for steam generators, simplifying the control of tritium and minimizing the risk of other interactions (e.g. reactions between molten salts, used as coolant and/or for the TES used in this thesis, and steam). The fluid conditions for the Rankine, helium and sCO2cycles are indicated in Table 7.6. 7.4. Working fluids for the integration 113 (a)        div            cycle (b)        div              cycle (c)        div              cycle (d)        div         2       cycle Figure 7.12: PCS efficiency as a function of the maximum temperature and power fraction going to the divertor (constrained to 150 ° C) for the (a) Rankine cycle with mixer pre-heaters (layout A), (b) Rankine cycle with HX preheaters (layout B), (c) helium cycle, (d) sCO2cycle. Note that the temperature axis depend on the working fluid. The dashed white line in (b) indicates a divertor outlet temperature of 150 ° C. Rankine (layout B) Helium Supercritical CO2 p [bar] T [ ° C] m [kg/s] p [bar] T [ ° C] m [kg/s] p [bar] T [ ° C] m [kg/s] 1180.0 500.0 603.1 80.0 500.0 1971.0 86.2 361.0 6756.0 232.2 267.1 538.1 46.1 358.0 1971.0 85.8 155.1 6756.0 332.2 500.0 538.1 45.6 98.9 1971.0 85.4 62.9 6756.0 410.8 353.8 485.7 45.6 98.9 1971.0 85.4 62.9 6215.0 50.05 33.1 485.7 45.2 30.0 1971.0 85.0 30.0 6215.0 60.05 33.1 485.7 55.1 58.1 1971.0 282.0 58.4 6215.0 710.8 33.2 485.7 54.7 30.0 1971.0 281.6 126.0 6215.0 810.8 150.0 485.7 66.7 58.1 1971.0 281.2 149.6 6215.0 910.8 183.3 603.1 66.3 30.0 1971.0 280.8 149.7 6215.0 10 10.8 186.1 603.1 80.8 58.1 1971.0 280.8 151.1 6756.0 11 180.0 212.0 603.1 80.8 85.1 1971.0 280.4 314.0 6756.0 12 180.0 236.1 603.1 80.0 344.4 1971.0 280.0 500.0 6756.0 13 180.0 258.9 603.1 85.4 62.9 540.4 14 47.4 312.3 33.4 280.8 168.5 540.4 15 32.2 267.1 31.6 16 20.5 437.4 24.3 17 10.8 353.8 28.1 Table 7.6: Fluid conditions at the different points in the reference layouts indicated in Figures 7.5(a), 7.9 and 8.5(a). 120 Chapter 8. Boosting the efficiency by hybrid heat and electricity production         Tcond         3 rd  2 nd  DH elec elec , ref           Pelec / QDH Figure 8.3: Cogeneration heat and power production parameters for a fission nuclear power plant based on a Pressurised Water Reactor model. Electric (green line with triangles), total (red line with squares) and reference electric (dashed gray line) efficiency as a function of the condenser temperature. The ratio of electric power over heat is represented against the right y-axis in blue. The light and dark gray shaded regions indicate integration with a third and second generation district heating network, respectively. 1 2 3 4 5 6 7 8 9 10 11 p [bar] 69.0 11.0 11.0 11.0 0.05 0.05 11.0 82.8 11.0 69.0 69.0 T [ ° C]284.9 184.1 184.1 250.0 32.9 32.9 81.3 81.8 184.1 284.9 284.9 m [kg/s] 1391.0 1391.0 1279.0 1279.0 1078.0 1078.0 1078.0 1078.0 111.8 111.8 201.8 Table 8.1: Fluid properties at the different points of the fission power conversion system of Figure 8.2(a) in pure electric operation. that enable the practical use of this energy. For simplicity, it was assumed that the cycle only has to be modified at the LPT outlet level. A scan of Tcond was performed from Tcond,ref = 33 ° C up to 180 ° C, as indicated with the black arrow in Figure 8.2(b). When the condensation temperature increases over 70 or 100 ° C, it is possible to use the heat waste for feeding a third or second generation DHN, respectively. This comes at the cost of reduced electric output, as the steam is not being fully expanded, which results in a smaller enthalpy drop in the turbines. The impact of this scan on ηelec and ηDH is illustrated in Figure 8.3. Hybrid electricity and heat production boosts the efficiency of the system by approximately 20%, from a reference efficiency of ηelec = 34.2% to ηDH = 52.8% at 80 ° C. It can be seen that both efficiencies decrease as the condenser temperature increases, which indicates that the minimum condensation temperature/pressure that enables heat waste recovery should be pursued. 8.4 Combined heat and power production for future fusion reactors In this section, the hybrid generation of heat and electricity for a set of Rankine and Brayton cycles with the DEMO fusion reactor is presented. The layouts presented in Chapter 7are the starting point for this analysis. Therefore, the boundary conditions for the fusion reactor, namely the temperature and thermal power of the different heat sources and the reactor self-consumption, are taken from the European DEMO Baseline 2018. In all the layouts presented in this section, the heat dissipated to the environment is of the order of 1 GW, which is 37% of the total thermal power in the reactor of 2.6 GW. 8.4. Combined heat and power production for future fusion reactors 121 8.4.1 Rankine cycles The performance of the hybrid cycle has been assessed following the same method as for the fission NPP: by scanning the temperature at the condenser. For the study of the Rankine fusion integration, the subcritical layout shown in Figure 7.5(a) has been used, as it gave the best performance among the subcritical cases. Since the temperature constraint of the divertor and shield heat sources (150 ° C) is close to TDH, two options have been considered for the integration of the cycle with the DHN. The first option considers a back-pressure turbine (no steam is expanded under TDH) and the divertor and shield thermal power (Qdiv,shield) is transferred to the power cycle in the divertor-to-cycle heat exchanger (DIV-C-HX). Option 1 is illustrated in Figure 7.5(a) with a black dashed line. The second option considers the use of Qdiv,shield and condenser thermal power (Qwaste) for the DHN via the divertor-to-DH (DIV-DH-HX) and the DH heat exchangers (DH-HX), respectively, as illustrated in Figure 7.5(a) with a dashed blue line. In option 1, Qdiv,shield is preferentially used for electricity production. This implies that Qdiv,shield is used for electricity production when TDH ≤ 150 ° C. When TDH >150 ° C the temperature at the DIV-C-HX inlet (T7) surpasses the temperature limit in the divertor and shield, and therefore this power cannot be used for electricity production. For this reason, Qdiv,shield is used for the DHN in option 1 when TDH >150 ° C. In option 2, Qdiv,shield is preferentially used for thermal power production (in practice, Qdiv,shield is used for the DHN at all temperatures in option 2). This means that both options are equivalent when TDH >150 ° C. (a)   Tcond            Pelec QDH Ptotal   (b)   Tcond         elec DH Pelec / QDH   Figure 8.4: Cogeneration heat and power production parameters for a Rankine cycle for the DEMO Baseline 2018 fusion nuclear power. (a) The electric power (Pelec), thermal power (QDH ) and total power (Ptotal) as a function of the condenser temperature (Tcond). (b) The electric (ηelec) and total (ηDH ) efficiency and the ratio of Pelec/QDH as a function of Tcond. The lines with markers show the results of option 1, while without markers show the results of option 2. The results of the hybrid integration are shown in Figures 8.4(a,b). Figure 8.4(a) shows the power (electric, thermal and total) and Figure 8.4(b) shows the efficiencies (electric, total and the electric-to-thermal power ratio). As for the fission case, ηDH is higher than ηelec,ref for all temperatures, and shows a difference of 16.3-18.2% at 80 ° C for options 1 and 2, respectively. Options 1 and 2 give equivalent results at high temperatures (above 150 ° C). This is because the heat of the divertor can be used for DH. At temperatures below 150 ° C, option 2 gives a higher ηDH, at the cost of a higher penalization of the electric production (step down in Pelec). This is because the 122 Chapter 8. Boosting the efficiency by hybrid heat and electricity production remaining heat from the divertor is used for electricity production in option 1 and for heat production in option 2. 8.4.2 sCO2cycles The cogeneration performance for a supercritical CO2(sCO2) layout is based on the HLC-LDS cycle shown in Figure 8.5(a), which presents the highest efficiency of the sCO2integrations with the DEMO1 reactor presented in Section 7.4.2 [192]. The cycle features a secondary compression, and the divertor and shield are integrated before the high-temperature recuperator. (a) TC2C1 BNK-HX HTR DH-HX PC LTR 11 1 23 4 5 7 9 8 13 10 6 12 DIV-HX (b) 3= h [kJ/kg] s [kJ/kgK] Figure 8.5: Supercritical CO2HLC-LDS cycle Brayton cycle with DH-HX for cogeneration. (a) Schematic representation of the cycle. (b) The h-s diagram of the reference cycle. The integration of the power cycle and the DHN has been done by adding a DH heat exchanger (DH-HX) before the pre-cooler. The performance of the cycle has been characterized by scanning the temperature at the inlet of the DH-HX (T3, which sets the DH supply temperature, Tin,DH ). In the reference case, T3=T4and Qwaste = 1098 MW, and the fluid temperature decreases from 60 to 30 ° C, as the waste heat is dissipated to the environment in the precooler (PC). The h-s diagram of the cycle is shown in Figure 8.5(b). The results of the performance analysis of the cycle in such an integration are presented in Figure 8.6.         Tin , DH          Pelec QDH Qwaste Ptotal        DH elec elec , ref Figure 8.6: Powers (left-axis) and efficiencies (right-axis) for the hybrid sCO2Brayton cycle as a function of Tin,DH . When Tin,DH increases, the mass fraction to the secondary compressor increases, resulting in lower Qwaste. This is because of the condition of a maximum temperature 8.4. Combined heat and power production for future fusion reactors 123 of 150 ° C at the divertor outlet. The reduction of Qwaste (shown in solid blue) saturates, and is limited to 600 MW within the explored temperature range. The improvement of ηDH is 3-4% (dashed red line with squares), much smaller compared to the efficiency improvement in Rankine cycles. While ηelec (dashed green line with triangles) decreases with Tin,DH (which is derived from the dependence of Pelec with Tin,DH ), it is interesting to note that ηDH maximizes for Tin,DH = [100,120] ° C, which gives the optimal operation conditions. 8.4.3 Helium cycles For the integration of the helium Brayton PCS with the DHN, the DH heat exchanger (DH-HX) is added between the recuperator and the precooler, as illustrated in Figure 7.9(a), following the same strategy as for the sCO2cycle integration. In the pure electric case, the temperature of the fluid decreases from 80 to 30 ° C as the heat is transferred to the environment in the precooler (PC). The performance of the cycle is studied by scanning the temperature at the inlet of the DH-HX (T3=Tin,DH). This temperature must be larger than the temperature at the divertor outlet, if the divertor heat is to be used for electricity generation, and penalizes the heat recovery at the turbine outlet. For each given DH-HX inlet temperature, the compression ratio (ρc) that maximizes the efficiency (ρc∈[1.5,2.6]) has been chosen. The results are shown in Figures 8.7(a,b). For this cycle, ηDH is higher than ηelec,ref for the full temperature range, although the maximum improvement in the efficiency is up to 2% at 100 ° C. This improvement is of the same order of magnitude as for the sCO2cycle. While this improvement may seem modest, it can be relevant when assessing the economic feasibility of the layout (see Section 8.5). As for the Rankine cycle, the efficiencies and the profits of a hybrid integration decrease with temperature. Figures 8.7(b) shows the compression ratio that optimizes the hybrid integration as a function of the supply DH temperature. (a)        Tin , DH           elec DH elec , ref Pelec / QDH        Pelec / QDH (b)       Tin , DH          c            Figure 8.7: (a) Cogeneration heat and power production parameters for a helium Brayton cycle for the DEMO Baseline 2018. The electric (ηelec, in green with triangles) and total (ηDH , in red with squares) efficiency (left y-axis) and the ratio of Pelec/QDH (in blue with circles, in the right y-axis) as a function of the DH supply temperature (Tin,DH ). The reference efficiency (ηelec,ref ) is shown in a dashed gray line (left y-axis). (b) Compression ratio (ρc, left-axis) maximizing the efficiency (right-axis) as a function of Tin,DH . 124 Chapter 8. Boosting the efficiency by hybrid heat and electricity production 8.5 Economic feasibility and emissions savings This section presents the economic analysis and the evaluation of greenhouse gases (GHG) emissions savings by hybrid production. The production (penalization on electricity production) and distribution costs (pumping) have been considered for the analysis. The pumping consumption refers to the power required for the DHN (i.e., for the distribution of pressurised supply (hot) and return (cold) water), and not to the primary coolant consumption, which is part of the recirculated power of the plant. The pumping cost has been estimated as a pressure loss due to friction, according to: ∆Ppump L=ρgQ∆H L=π 8fD v3ρ2gϕ ηpump .(8.2) The electric pumping power (Ppump) depends on the piping diameter (ϕ), the distance from the NPP to the DHN (L), the fluid velocity (v) and the efficiency of the pump (ηpump). Here, Qand Hare the flow rate and the pressure head, and ρ,gand fDare the mass density, gravity and friction factor. The later was estimated by the Darcy-Weissbach equation. The pump efficiency has been calculated by ηpump = 0.823(vπ/4ϕ2)0.046 [233] and v= 4QDH(hsupply −hreturn)−1(ρπϕ2)−1, where h is enthalpy. An excessive pumping consumption (friction) was avoided by constraining v < 1.2 m/s. In addition, a maximum distance (L < 100 km) and piping diameter (ϕ < 1.2 m) have been considered. The diameter has been limited to adhere to commercial piping. When needed, the number of pipes was increased. 8.5.1 Calculation of the levelized cost of hybrid production The Levelized Cost of Hybrid Production (LCHP) has been used as a figure of merit for the economic analysis. The LCHP is an indicator inspired by the LCOE, which considers the distribution (pumping) and production (penalization of electricity generation) costs and the production income (generation of heat). The LCHP is defined as: LCHP =CC ·CRF +PV CX·CELFX−EDH ·LCH Eelec +EDHηelec,ref ,(8.3) where CC is the capital cost, CRF is the cost recovery factor, VCxis the variable cost, CELFxis the constant escalation levelization factor, LCH is the levelized cost of heat, and Eelec and EDH are the electric and thermal DH energy produced in a year. The fusion power plant cost estimation has been assessed with the process system code [102,103]. For the economic analysis, the DEMO Baseline 2018 is taken as reference, and the net electric power (which takes into account the internal power consumption) and the electric power conversion system efficiency ηelec (shown in Table 7.1) are considered. The 1990 model has been used, which estimates capital and variable costs [102,103]. Note that here the cost of the power cycle island does not depend on the power cycle technology, despite the fact that Rankine and Brayton cycles would have different costs. In particular, the fact that sCO2power cycles are a technology in the demonstration phase could lead to a higher cost of the power island (note that the system compactness could counteract the cost increase). This approximation is considered adequate since, in a fusion reactor, the capital cost is dominated by the cost of the magnets and the fusion island. These are estimated to account for ∼44% and ∼30% of the cost, respectively, while the power cycle cost is ∼4% (see Figure 3.8(a)). For the estimation of the fission plant costs, a LCOE of 69.57 $ /MWh for a 1000 MW plant was assumed [234]. 8.5. Economic feasibility and emissions savings 125 (a)          TDH , supply         LCHP / LCHPref     2    (b)      Tsupply , DH             2    Figure 8.8: (a) The variation in the levelized cost of hybrid production (LCHP) with respect to the reference pure electric production (LCHPref ) as a function of the district heating supply temperature for the fission plant presented in Section 8.3 and for the fusion power plants presented in Section 8.3. (b) Primary energy savings (PES) indicator as a function of the district heating supply temperature. The LCHP has been normalized to the reference case (pure electric production). If the ratio is smaller than one, the hybrid plant would be more profitable than the electric plant from an economic point of view. Note that the direct comparison of absolute cost between fission and fusion power plants is not possible due to the lack of recent validation of the cost data for more modern fusion designs. These results refer to the relative cost normalized to the reference values in the pure electric case. Figure 8.8(a) summarizes the results of the economic analysis. For fusion power plants, the Rankine and sCO2integrations are interesting from the economic point of view for the full temperature range, while the helium hybrid cycle would not be profitable. The hybrid integration is interesting for the fission power plant from an economic perspective for a supply DH temperature below 90 ° C. Further economic profit could be derived from reducing GHG emissions due to their externalities pricing. Carbon pricing may become very important and can potentially reduce production costs due to GHG emissions. The GHG emission savings (derived from their reduction in the hybrid production scheme) are estimated as the product of the annual emission reduction (details on the calculation are presented in Subsection 8.5.2) by the CO2 prices. The total annual emissions reduction is of the order of 1-2 MtCO2/year, which results in total savings ∼10 M e /year and an improvement of the LCHP/LCHPref ratio of 2-5%. Although these estimations are subject to large uncertainties, because of the uncertainty in the future carbon prices, the economic savings resulting from the reduction in GHG emissions may be very important and increase the economic interest of all the cogeneration layouts. 8.5.2 Savings in greenhouse gases emissions The GHG emission savings (∆εGHG) are estimated in this section. The NPP availability factor (fav) has been set to 75% for the estimations. This is in line with the expected availability of fusion power plants [235–237], while it is a rather conservative assumption based on fission NPP (which have availability factors typically above 80% [229]). The plants are considered to run in a pure electric mode 75% and in a hybrid mode (i.e., during winter months) 25% of the available time. Two contributions are considered: 1. A reduction due to clean generation of heat (∆εGHG,Q) in comparison to the reference case, in which the heat is generated by a natural gas boiler with an 126 Chapter 8. Boosting the efficiency by hybrid heat and electricity production efficiency (ηboiler) of 92%. ∆εGHG,Q will be negative. 2. An increase due to lower electricity production (∆εGHG,Pelec ). This is due to Pelec < Pelec,ref . In the reference case, the electricity deficit ( ∆Pelec =Pelec − Pelec,ref ) is provided by nuclear energy, i.e., without emissions. This electricity deficit has some GHG emissions associated, which depend on the electricity generation energy mix. The pump consumption as a function of the distance between the NPP and the DHN is discounted from the electricity production. Generally, ∆εGHG,Pelec will be positive. Therefore, ∆εGHG is calculated as: ∆εGHG =∆Peleccelec +QDHη−1 boilercNGthybridfav,(8.4) where thybrid is the annual time in hybrid operation (i.e., only during winter months). The emission factors for natural gas and electricity, celec = 0.275 kgCO2/kWh and cNG = 0.252 kgCO2/kWh, respectively, have been taken from [218]. The average carbon price in the electricity sector is assumed to be 6.36 e /tCO2[238]. Note that the emission factors correspond to the European average, while the absolute savings, and the dependence with heat rejection temperature, are determined by the specific generation scheme. For example, for countries with low electricity emission factors (those which already have transitioned to decarbonised electricity generation schemes, such as France) the savings increase with TDH.GHG savings are of the order of 1-1.8 MtCO2/year1for the reference PWR reactor presented in Section 8.3. These emissions correspond to those produced by 160000-260000 inhabitants in a year2. 8.5.3 Calculation of primary energy savings In this section, the Primary Energy Savings (PES) is evaluated. The PES complements the performance assessment of the layouts. This indicator enables a comparison of the performance of the different technologies, and is defined by the CHP EU directive as [239]: PES = 1−1 ηCHP,Q ηref,Q +ηCHP,Pelec ηref,Pelec  ·100,(8.5) Here, ηCHP,Q is the heat efficiency of the combined heat and power production, which is defined as the annual useful heat production divided by the fuel input (here, Qreactor) used to produce the sum of useful heat and electricity, and ηCHP,Pelec is the electrical efficiency of the cogeneration production, which is defined as the annual electricity production divided by the fuel input used to produce the sum of useful heat and electricity. The parameters are calculated as: ηCHP,Q =QDH(T)·0.25 ·fav ·ty Ereactor ,(8.6) ηCHP,Pelec =[0.25Pelec(T)+0.75Pelec,ref ]favty Ereactor ,(8.7) where tyis 8760 hours/year and Ereactor is calculated as Ereactor,fission =Qreactor ·fav ·ty for fission power plants and Ereactor,fusion =Qreactor ·fav ·ty·tpulse/tcycle for fusion power 1Depending on the electricity generation mix of the country, the European average would be in 1.4 MtCO2/year 2Given a carbon footprint of EU-27 equal to 6.8 tonnes of CO2per person in 2019 [218]. 8.5. Economic feasibility and emissions savings 127   Tsupply , DH        CHP / ref   CHP , Q / ref , Q CHP , Pelec / ref , Pelec   Tsupply , DH          CHP , Q / ref , Q CHP , Pelec / ref , Pelec   Tsupply , DH          2 CHP , Q / ref , Q CHP , Pelec / ref , Pelec   Tsupply , DH          CHP , Q / ref , Q CHP , Pelec / ref , Pelec   Tsupply , DH          CHP , Q / ref , Q CHP , Pelec / ref , Pelec Figure 8.9: Efficiency ratios for heat (solid red line) and electricity (blue dashed line) production as a function of the district heating supply temperature for fusion (a-d) and fission (e) layouts. plants. The tpulse/tcycle ratio is introduced to take into account that part of the fusion reactor energy is transferred to the thermal storage system during pulse time, so that it can be used for the power cycle while the fusion reactor is during dwell time. ηref,Q and ηref,Pelec refer to the efficiency reference value for separate heat and electricity production, respectively, and are taken from the Commission Delegated Regulation (EU) 2015/2402 Annex I [240]. For nuclear energy, ηref,Q = 92% and ηref,Pelec = 33%. In this regard, no distinction is made between fusion and fission power plants. The results of the calculation are presented in Figure 8.8(b). It can be seen that a positive PES is only recovered for fission NPPs, and it decays from 20 to 10% as the DH supply temperature increases from 40 to 180 ° C. For all fusion layouts, the PES indicator is negative, which in principle implies that the hybrid production operation has lower performance than the pure electric operation. This result may seem in contradiction with the ηDH > ηelec reported in the previous Section 8.4 and the economic profitability for the Rankine and sCO2layouts reported in Section 8.5. However, the reason behind this negative result for a FPP is due to the high recirculated power (the reactor self-consumption power is 491.8 MW, as shown in Table 7.1) considered in the conservative EU-DEMO Baseline 2018 assumptions, compared to the net electric power production (170-370 MW, as shown in Table 7.5). A high plant consumption power results in low ηCHP,Pelec /ηref,Pelec ratios for all layouts in comparison to a fission power plant, as illustrated in Figures 8.9(a-e). In this regard, the use of a sCO2integration would be best amongst the options for fusion. It can be seen that the ηCHP,Q/ηref,Q of the Rankine FPP is comparable to that of a fission NPP, which is consistent with the fact that both designs rely on the same power cycle technology. This indicates that, if the recirculated power in the FPP decreases (or Pelec increases for the same fusion power), a positive PES would also be recovered for the Rankine fusion layouts. In fact, if the recirculated power is reduced by 200 MW, a positive PES is recovered for the Rankine cycle for fusion NPP for TDH,in <130 ° C. For the helium and sCO2Brayton cycles, the ηCHP,Q/ηref,Q ratio is low at the temperature range required for modern DHN (∼100 ° C), which indicates that this type of technology is less appropriate for low-grade heat recovery applications, such as DH, compared to Rankine cycles. This is consistent with the fact that Brayton cycles have high regeneration potential, i.e., a large fraction of the heat at the turbine outlet is recovered within the cycle in the recuperator heat exchangers down to low temperatures. It is interesting to note that the ηCHP,Q/ηref,Q ratio increases with temperature and is comparable to the Rankine values for the sCO2cycle, suggesting hybrid production of electricity and high-grade heat may be interesting for the sCO2cycles. Note that the assumption of pure electric operation 75% of the time affects ηCHP,Q/ηref,Q << ηCHP,Pelec /ηref,Pelec . If the system works a bigger portion of the year in hybrid mode, ηCHP,Q/ηref,Q ∼ηCHP,Pelec /ηref,Pelec . 128 Chapter 8. Boosting the efficiency by hybrid heat and electricity production 8.6 Discussion Regarding the thermodynamic performance, the hybrid production scheme shows improvements in the efficiency for all the power conversion cycles. Cogeneration of heat and electricity resulted in an important increase of the efficiency close to 20% for Rankine cycles and up to 6% for Brayton cycles. In terms of economic feasibility, the hybrid generation decreases costs and seems profitable for Rankine and sCO2cycles. The production and distribution costs (i.e., penalization in the electricity production and pumping consumption of the DHN) have been considered for the economic viability assessment. The economic interest of the layouts may as well be conditioned by the environmental impact of the layouts. Potential pricing of the externalities of greenhouse gas emissions and an increase in fossil fuel prices would improve the competitiveness of the presented layouts, as these configurations result in a decrease in emissions. The primary energy savings indicator has been calculated for all layouts, and is found to be favorable for fission NPPs. The high fraction of recirculated power in the DEMO Baseline 2018 prevents that a positive primary energy savings indicator is recovered for the fusion layouts. However, a performance comparable to that of the fission reactor is expected if the recirculated fraction is lowered. It is important to highlight that all the layouts can be operated in hybrid and pure electric mode. In Rankine cycles, the fluid will pass through the district heating heat exchanger in case of hybrid production and through the condenser in case of pure electric production. In Brayton cycles, the fluid dissipates the low-temperature heat in the district heating heat exchanger and precooler in hybrid production. In pure electric production, the fluid by-passes the district heating heat exchanger and dissipates all the low-temperature heat to the environment in the precooler. These integrations imply that, besides having relative flexibility for electric or hybrid production, it would not become necessary to stop the operation of the plant in the event of a breakdown or maintenance of the district heating network since the plant could continue to operate exclusively in electric production, i.e., even when unexpected maintenance or shut-down of the DH system is required, the plant should be able to work in pure electric mode, and its availability shall not be penalized. This work shows opportunities for boosting the efficiency and for a broader potential of fusion energy applications and deployment in the energy market, besides its use for electricity supply, at a medium temperature range. The application of fusion energy could be extended to cooling production following a similar strategy to that presented here (e.g. via absorption chillers). This would increase the operating time in hybrid mode throughout the year and expand the technology applicability to regions where cooling demand is important. Alternatively, the low grade heat can be used for water desalination. This may be very important, as the growth of population, energy, and water consumption are strongly coupled. The multi-stage flash distillation technology uses low-grade heat with a maximum temperature of 120 ° C and is an interesting candidate. In more advanced technological and physical scenarios (where higher temperatures are attainable), fusion energy could be utilised for a broader range of applications [241], such as hydrogen production or industrial heat generation, to achieve and sustain decarbonization commitments and maximize fusion penetration in the energy market. Although the use of nuclear power for space heating is mostly disregarded, nuclear district heating has been a tried-and-tested technology in Europe (including Russia and Ukraine) [242,243], providing valuable empirical insights [244], and is currently being exploited [245,246]. In addition, the recent fast growth of the Chinese DHN has 8.7. Summary 129 led to the integration of China’s Haiyang NPP with a DHN in its surrounding area [247]. These recent developments are proof of the economic and environmental interest in these generation schemes for nuclear fission, in agreement with the results of the analysis presented in this chapter. It can be concluded that cogeneration based on nuclear fusion is expected to be an interesting strategy that can contribute to meet the space heating demand. 8.7 Summary The efficiency of cogeneration schemes of electricity and heat for fusion and fission reactors has been studied in this chapter. While the efficiency of all power conversion systems increases, the largest efficiency improvements (by 20%) are obtained for the Rankine layouts. The economic feasibility of the hybrid production has been evaluated by considering production and distribution cost, and is profitable for Rankine and supercritical CO2layouts. The economic savings that could derive from rising fossil fuels and emissions prices could lead to an increase of the interest on all layouts. The potential use of fusion reactors for the production of heat and electricity expands the opportunities for fusion in the energy market.