Performance prediction applying different reduced turbulence models to the SMART tokamak

PAPER • OPEN ACCESS Performance prediction applying different reduced turbulence models to the SMART tokamak To cite this article: D.J. Cruz-Zabala et al 2024 Nucl. Fusion 64 126071 View the article online for updates and enhancements. You may also like Transport and confinement physics: Chapter 2 of the special issue: on the path to tokamak burning plasma operation M. Yoshida, R.M. McDermott, C. Angioni et al. - Experimental research on the TCV tokamak B.P. Duval, A. Abdolmaleki, M. Agostini et al. - Model-predictive kinetic control with datadriven models on EAST D. Moreau, S. Wang, J.P. Qian et al. - This content was downloaded from IP address 193.147.173.203 on 04/04/2025 at 08:27 International Atomic Energy Agency Nuclear Fusion Nucl. Fusion 64 (2024) 126071 (11pp) https://doi.org/10.1088/1741-4326/ad8a70 Performance prediction applying different reduced turbulence models to the SMART tokamak D.J. Cruz-Zabala1,∗, M. Podest` a2,a, F. Poli2,b, S.M. Kaye2, M. Garcia-Munoz1, E. Viezzer1and J.W. Berkery2 1University of Seville, Seville, Spain 2Princeton Plasma Physics Laboratory, Princeton, NJ, United States of America E-mail: [email protected] Received 7 June 2024, revised 15 October 2024 Accepted for publication 23 October 2024 Published 7 November 2024 Abstract The SMall Aspect Ratio Tokamak (SMART) is currently being commissioned at the University of Seville and will be able to compare the performance of positive and negative triangularity plasmas at low aspect ratio. Predictive simulations have been performed for different machine scenarios and heating schemes using the TRANSP code. The objectives of these simulations are to predict the parameters expected in positive triangularity plasmas, to guide diagnostic development, and to validate transport models. Several reduced turbulence models have been used to predict electron and ion temperatures for the operational phase 2. All models provide similar results from approximately mid-radius to the separatrix but important discrepancies are found in the core region. These positive triangularity results are compared with experiments from a similar size machine like GLOBUS-M2. The multi-mode model (MMM) shows the best agreement. Simulations with different boundary conditions have been performed and no strong differences have been observed between them. The impact of neutral beam injection (NBI) on the predicted profiles has also been addressed. Rotation reduces turbulence levels so higher temperatures are achieved when included in the simulations. Studying the different contributions to the thermal diffusivities, it is observed that electron temperature gradient (ETG) turbulence dominates at the plasma core while micro-tearing modes (MTM) dominate at the edge in the electron channel. In the ion channel, the neoclassical contribution is dominant at the core and at the very edge while the Weiland component, which includes ion temperature gradient mode (ITG), trapped electron mode (TEM), kinetic ballooning mode (KBM), peeling mode (PM) and collisionless and collision dominated magnetohydrodynamic (MHD) modes governs the mid-radius region. For phase 3, two plasmas with different electron densities have been studied. The case with lower density matches well a specific discharge of GLOBUS-M2. The higher density plasma shows high performance with βN≈3.8. aCurrently employed by EPFL, SPC, Lausanne, Switzerland. bCurrently employed by ITER Organization, St. Paul Lez Durance Cedex, France. ∗Author to whom any correspondence should be addressed. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. 1741-4326/24/126071+11$33.00 Printed in the UK 1 © 2024 The Author(s). Published by IOP Publishing Ltd on behalf of the IAEA Nucl. Fusion 64 (2024) 126071 D.J. Cruz-Zabala et al Keywords: spherical tokamak, turbulence, prediction, profiles (Some figures may appear in colour only in the online journal) 1. Introduction Most of reactor relevant tokamaks which are currently under construction, like ITER [1] or SPARC [2], are aiming for a high confinement (H-mode) regime with tolerable plasma-wall interaction as a baseline scenario. However, the scenario for future fusion power plants like DEMO is still under discussion. Edge Localized Modes (ELMs) [3,4] are a major concern for the integrity of future fusion power plants and will have to be avoided or mitigated. In the search of ELM-free scenarios, negative triangularity (NT) plasmas emerge as a promising candidate [5]. Plasmas in NT have demonstrated to have similar performance to positive triangularity (PT) H-mode plasmas without ELMs [6]. NT brings some other advantages over standard PT plasmas, such as lower turbulent transport and a larger area to distribute the heat flux due to their larger X-point radii. Because of the reduced heat flux requirements, NT might also be a promising scenario for fusion power plants based on spherical tokamaks (STs) [7–9]. STs are tokamaks with an aspect ratio (ratio between major and minor radius) less than approximately two. These devices are more compact than conventional tokamaks (CTs), thus potentially reducing the overall cost of a fusion power plant based on STs because of the reduced volume. Due to their low aspect ratio and higher normalized beta (βN), STs can achieve high fusion power according to [7,9]: Pfus ∝β2 NB4 t A2q2 95 (1) where Pfus is the fusion power, Btis the toroidal magnetic field, Ais the aspect ratio and q95 is the safety factor at 95%of the poloidal flux surface. Furthermore, STs have shown to be more stable than CTs and can naturally carry higher currents due to their inherent strong elongation. The SMall Aspect Ratio Tokamak (SMART) [10–12] is a new ST being currently commissioned at the University of Seville that aims to combine the benefits of NT plasmas and low aspect ratio. It will be able to operate in NT and PT, which will enable the comparison between both triangularities. This work presents the results of predictive simulations using different reduced turbulence models for PT plasmas in SMART. Comparison with other machines will help us to understand which model is the most suitable for predicting ion and electron temperatures in this device. Ohmic and NBI heated plasmas are studied and the role of rotation and boundary conditions are addressed. After an introduction to SMART in section 2, the procedure followed to design the scenarios is described in section 3. The results of the predictive simulations are shown in section 4and conclusions are given in section 5. Figure 1. Sketch of the SMART tokamak. Toroidal field coils, poloidal field coils and central solenoid are shown in red. Three pairs of poloidal field coils are inside the vessel protected with coil casings. Reprinted from [13], Copyright (2023), with permission from Elsevier. 2. The SMART project Figure 1shows a sketch of the SMART tokamak [13]. The vessel dimensions are 1.6 m (diameter) ×1.6 m (height). In the center, a solenoid of 30 cm diameter is wrapped around 12 toroidal field coils. 8 poloidal field coils are responsible for the shaping capabilities. The main objective of the SMART tokamak is the evaluation of the synergy between STs and NT. The operation of SMART will be divided into three phases. In the first one, only Ohmic heated plasmas will be studied. In the second one, neutral beam injection (NBI) heating will be implemented [14,15] together with increased plasma current, magnetic field and pulse duration. Phase 3 will have increased auxiliary heating, plasma current, pulse duration, and magnetic field. The main parameters of the three operational phases are summarized in table 1. In order to address important aspects such as expected plasma performance and stability, diagnostic development, machine limits, etc, predictive simulations have to be performed. 3. Strategy for target scenario design The scenario design starts by choosing a set of basic parameters like Bt,Ip(plasma current), R(major radius), a(minor 2 Nucl. Fusion 64 (2024) 126071 D.J. Cruz-Zabala et al Table 1. Parameters for the three different operational phases of SMART. Parameters Phase 1 Phase 2 Phase 3 Ip(kA) 100 200–500 >500 Bt(T) 0.1 0.4 1.0 τpulse (s) 0.15 0.5 >1.0 PNBI (MW) — ⩽1 1 R(m) 0.40–0.60 a(m) 0.20–0.33 A1.46–3.00 κ < 3.0 δ−0.6–0.6 Figure 2. Examples of different equilibria that can be achieved at SMART. Positive and negative triangularity in lower single null, upper single null and double null configuration can be explored at SMART. radius), κ(elongation), δ(triangularity) and using a simple 0D model to give a first indication about the consistency of this combination of parameters by checking that q95 >3 [16,17], which will ensure that the operational point is far away from disruptions. Then, in order to predict the density and temperature profiles, ASTRA [18] simulations have been performed prescribing H-mode like diffusivity profiles extracted from the gyrobohm model [19] and adjusted to be similar to the values from GLOBUS, a machine with similar size and aspect ratio [20]. These preliminary profiles together with coil and vessel geometries are provided to the FIESTA code [21] as input. FIESTA is a free boundary equilibrium solver that provides the plasma equilibrium together with the coil and vessel currents that produce such equilibrium. Figure 2shows some examples of the different plasma geometries that SMART will be able to achieve obtained with FIESTA. FIESTA only uses volume averaged density and temperatures as input, which means that the output equilibrium is not kinetically constrained to the profiles obtained with ASTRA. Furthermore, the current density in FIESTA is evaluated using a linear model in which the current density is proportional to the poloidal magnetic flux on each flux surface and to the total beta poloidal. This was the initial strategy for scenario design at SMART [20]. SMART has recently been implemented in the TRANSP environment [22] to perform more advanced simulations [15]. In these studies, TRANSP was used to optimize the NBI parameters for phase 2. TRANSP solves the poloidal diffusion equation in order to evolve the current distribution and, hence, the poloidal magnetic field. Moreover, NUBEAM is a well-established code that calculates the neutral beam fast ion distribution and heating. TRANSP also supports different turbulence models such as TGLF [23], GLF23 [24], COPPI-TANG [25–27], RLW [28] and MMM [29] that can be used to predict plasma profiles accounting for different turbulence mechanisms and different numerical implementations of the underlying physics. The main objective of this work is to analyze the heat transport employing the aforementioned turbulence models. The procedure followed for designing SMART scenarios is summarized in figure 3. Note that no machine has explored NT in STs so far, so the accuracy of the predictions in this scenario cannot be trusted until experiments are performed, providing a basis for model validation. However, predictive simulations are a good benchmark of the different reduced turbulence 3 Nucl. Fusion 64 (2024) 126071 D.J. Cruz-Zabala et al Figure 3. Flow diagram showing the procedure followed for the scenario design. models for PT plasmas in SMART. Furthermore, PT results can be validated comparing to a similar size machine like GLOBUS-M2 [30]. 4. Predictive simulations based on TRANSP TRANSP can be run in interpretative or in predictive mode. In the interpretative mode, plasma profiles are inputs of the simulations and transport diffusivities are calculated. In predictive mode, transport diffusivities are calculated by a transport model and the kinetic profiles are obtained as output. The objective of the simulations presented here is to predict ion an electron temperatures during the flat-top phase. In a first step, TRANSP is run in interpretative mode with the objective of studying the current evolution solving the poloidal diffusion equation. For this particular study, a phase 2 plasma has been considered with Ip=200 kA and Bt=0.4 T. An artificial safety factor (q) profile with high central value (≈2) together with temperature and density profiles calculated with ASTRA for this specific case are used as initial condition in the simulation. Then, TRANSP evolves the equilibrium keeping the boundary fixed. As can be seen in figure 4, after ≈30 ms the equilibrium evolves to reach a stationary state and the central safety factor drops to ≈1. Note that this relaxation time is much less than the pulse duration (≈0.5 s in phase 2) which ensures a long enough stationary plasma. After reaching stationary state, TRANSP is switched to predictive mode and the temperature profiles are evolved following different Figure 4. Evolution of the equilibria from t=0 ms (FIESTA equilibrium) to t=30 ms (stationary equilibrium obtained with TRANSP). It can be seen in the bottom-left corner the evolution of the safety factor. turbulence models while the electron density is kept fixed. Ion and impurity densities are also fixed with an effective charge Zeff =2.3. There is no intrinsic mechanism that leads to an H- mode regime in TRANSP. To partially catch the characteristics of an H-mode, a pedestal is set in the electron density profile and is kept fixed during the entire simulation. Note that it is expected that the Ohmic heating will overcome the L-H power threshold in phases 2 and 3 of SMART [20], so operation in H-mode in PT is expected. 4.1. Temperature prediction using different turbulence models in Ohmic heated plasmas Figure 5shows the electron and ion temperatures obtained with TGLF [23], GLF23 [24], MMM [29], RLW [28] and COPPI-TANG [25–27] turbulence models. The electron density (ne) profile is shown in figure 6. This density corresponds to a Greenwald fraction ne Ip/(πa2)of ≈30%. As can be seen, all models predict similar values for the electron temperature in the range 0.5≲ρtor ≲1.0, where ρtor is the square root of the normalized toroidal flux. However, in the innermost region (ρtor ≲0.5) all methods provide very different temperatures, especially at the plasma center. Similar behavior is observed in the ion temperature but the range where all models agree is reduced to 0.7≲ρtor ≲1.0. Note that the separatrix temperatures have been set to 30 eV as a boundary condition. Most of the reduced models were developed to describe plasmas with conventional aspect ratios. Extensive research on the performance of reduced models predicting transport 4 Nucl. Fusion 64 (2024) 126071 D.J. Cruz-Zabala et al Figure 5. Electron temperature (a) and ion temperature (b) obtained with different turbulence models in an Ohmic plasma. Figure 6. Fixed density and toroidal rotation used in phase 2 simulations. Note that the toroidal rotation was neglected for the simulations shown in figures 5and 7. in STs was performed in [31], and it was concluded that the most successful models were MMM and RLW, with TGLF and GLF23 under-predicting the level of transport in the core. A recent comparison between TGLF and MMM, the two most recent models, showed good agreement predicting temperature profiles in high aspect ratio machines [32]. However, in NSTX-U, which is a low aspect ratio machine, MMM reproduces better the experimental results compared to TGLF [33,34]. Temperature predictions of NSTX plasmas with MMM consistently remain within 20%of the root mean square (RMS) deviation of the experimental data while TGLF temperature predictions result in RMS errors can be up to 50%. Note that these errors correspond to predictions over different radial ranges, being 0.0< ρtor <0.8 for MMM and 0.2< ρtor <0.7 for TGLF, which enhances even more the better performance of MMM predicting temperature profiles at low aspect ratio compared to TGLF. Note that MMM is the model including more turbulence drivers: electron temperature gradient mode (ETG), ion temperature gradient mode (ITG), microtearing mode (MTM), trapped electron mode (TEM), kinetic ballooning mode (KBM), drift resistive inertial ballooning mode (DRIBM), peeling mode (PM) and collisionless and collision dominated magnetohydrodynamic (MHD) modes. As seen in figure 5, the COPPI-TANG model provides similar results to TGLF/GLF23. 4.2. Impact of NBI and rotation on temperature profiles NBI is planned for phases 2 and 3 at SMART. Initially, up to 0.26 MW of power will be available and will be upgraded to 1 MW during phase 2. Studies were carried out to obtain an optimized (lowest shine-through and prompt losses) injection energy of 25 keV and a tangency radius of 0.44 m [15, 20]. These specifications have also been implemented in the TRANSP code. Figure 7shows the electron and ion temperatures obtained with the turbulence models mentioned above during a phase with 0.26 MW of NBI power. The COPPITANG model leads to the highest ion and electron temperature increase when NBI is introduced. The MMM model increases its prediction for the core electron temperature by ≈30%and by ≈65%for the core ion temperature when adding NBI heating. In general, the discrepancies between the different models have increased with the addition of NBI heating. With the purpose of understanding which model can lead to more accurate predictions in SMART, a comparison between the predictions of the different models and experimental results from a similar size machine like GLOBUS-M2 is considered. GLOBUS-M2 is a ST that operates in PT with R≈0.36 m, a≈0.24 m, A≈1.5 and κ≈2 [30]. These parameters are similar to SMART. In [30], time traces of ion and electron temperatures and electron density of a plasma with the same current and magnetic field as the phase 2 plasma of SMART considered (Ip=200 kA, Bt=0.4 T) are shown. It is observed that MMM provides the closest central temperatures to GLOBUS-M2 experimental values. However, the central ion temperature at GLOBUS-M2 does not increase with the addition of NBI heating, contrary to MMM predictions at SMART. Note that in the analysis presented here radiation has been neglected, while it can be up to 45%of the input power in GLOBUS-M2 [35]. 5 Nucl. Fusion 64 (2024) 126071 D.J. Cruz-Zabala et al Figure 7. Electron temperature (a) and ion temperature (b) obtained with different turbulence models in an NBI heated plasma. Figure 8. Ratio between predicted electron temperatures (a) and ion temperatures (b) including the rotation and without including it in the simulations. So far, plasma rotation has been neglected in the predictive simulations. However, NBI is a source of torque and, hence, a rotation driver. Plasma rotation can mitigate turbulence, reducing the transport [36–38]. It is expected that, when enabling rotation in the simulations the predicted temperatures will increase. The shape of the rotation profile from GLOBUS-M2 shown in [39] has been used to model the rotation at SMART. It reaches a maximum of ≈120 km s−1(≈200 krad s−1) in the inner region and it decreases towards the edge as can be seen in figure 6. The ratio between the predicted temperatures when enabling the rotation in TRANSP or disabling the rotation (profiles shown in figure 7) are shown in figure 8. All models predict an increase in both electron and ion temperatures. However, this increase is different between them, TGLF being the model predicting the highest impact of the rotation on the predicted temperatures. In fact, TGLF predicts a similar impact in ion and electron temperatures while the rest of the models predict a stronger impact in the ion temperature compared to the electron temperature. Focusing now on the MMM model, which according to the indications commented above seems to be the most suitable model for SMART, it predicts just a slight increase of around 5%–25% in the electron temperature and a stronger increase in the ion temperature of around 10%–85% depending on the radial position. In the following, only the MMM model is considered as it is the one that better predicts NSTX-U temperature profiles [33] and also shows the best agreement between predicted central temperatures at SMART and experimental central temperatures at GLOBUS-M2. 4.3. Role of boundary condition on the predicted profiles In TRANSP, important inputs for the predictive simulations are the temperatures at the boundary. In the cases considered here, the boundary has been considered to be at the separatrix position. The simulations shown above consider a fixed value of the electron and ion temperatures at the separatrix of 30 eV. In order to address the importance of these boundary conditions, a reduced Scrape of Layer (SOL) model implemented in TRANSP has been used [40]. This reduced SOL model calculates the temperatures and density in the SOL considering the recycling coefficients and power and particle fluxes. In the model, it is possible to disable the prediction of the electron density at the boundary and predict only the temperatures. Figure 9shows the electron and ion temperature profiles together with the temporal evolution of the temperatures just 6 Nucl. Fusion 64 (2024) 126071 D.J. Cruz-Zabala et al Figure 9. Impact of boundary condition on electron and ion temperatures. (a) Shows the electron temperature, (b) the ion temperature, (c) the electron temperature at ρtor =0.99 and (d) the ion temperature at ρtor =0.99. Profiles in (a) and (b) have been extracted at t=0.88 s. inside the separatrix, at ρtor =0.99, for four different simulations: using the SOL model with the electron density prediction at the boundary enabled and disabled and fixing the temperature at the boundary at 30 eV and 60 eV. Note that the predictive simulations are performed in the range of 0.6–1.0 s and the NBI is on from 0.7 to 0.9 s. The temperature profiles are extracted when the NBI is on. It can be seen that, at the core, all cases agree well with a maximum deviation of ≈10%. This maximum deviation is observed in the ion temperature using the SOL model disabling the prediction of the electron density at the boundary. The electron temperature at ρtor =0.99 predicted by the SOL model increases from ≈15 eV during the Ohmic phase to ≈19 eV during the NBI phase, while the ion temperature increases from ≈8 eV to ≈40 eV. In the cases with fixed boundary conditions, both electron and ion temperatures at ρtor =0.99 do not change much as they have to be consistent with their fixed values at ρtor =1.00. The electron density at ρtor =0.99 (not shown here) drops by ≈17%when the prediction of the electron density at the boundary is activated in the SOL model. 4.4. Identification of the dominant turbulence mechanism As commented in section 4.1, the MMM model simulates different instabilities: ETG, ITG, MTM, TEM, KBM, DRIBM, PM and MHD. Furthermore, it considers E×B flow shear stabilization [33]. The Weiland [41] part of the MMM model accounts for: ITG, TEM, KBM, PM and MHD. With the purpose of identifying the dominant transport mechanisms, the different contributions to the diffusivities in both the electron and the ion channels are shown in figures 10 and 11, respectively. In the electron channel, contributions to the diffusivities from the Weiland, ETG and MTM components have been considered while in the ion channel, the Weiland and neoclassical components are contemplated. The four cases studied in the previous section are shown for comparison. In the electrons (figure 10), ETG dominates at the plasma core while MTM dominate at the plasma edge. This behavior agrees with results obtained for NSTX [33,42]. The Weiland component plays a minor role. The case with the temperatures at the boundary fixed to 60 eV shows a stronger 7 Nucl. Fusion 64 (2024) 126071 D.J. Cruz-Zabala et al Figure 10. Contributions to the electron diffusivity. (a) Shows the Weiland component, (b) the ETG contribution and (c) the MTM contribution. Figure 11. Contributions to the ion diffusivity. (a) Shows the Weiland contribution and (b) the neoclassical component. 8