Ion heat transport dynamics during edge localized mode cycles at ASDEX Upgrade

Ion heat transport dynamics during edge localized mode cycles at ASDEX Upgrade E. Viezzer1,2, M. Cavedon3, E. Fable3, F. M. Laggner4,5, R. M. McDermott3, J. Galdon-Quiroga1,2, M. G. Dunne3, A. Kappatou3, C. Angioni3, P. Cano-Megias1,2, D. J. Cruz-Zabala1,2, R. Dux3, T. P¨utterich3, F. Ryter3, E. Wolfrum3, the ASDEX Upgrade Team and the EUROfusion MST1 Team‡ 1 Dept. of Atomic, Molecular and Nuclear Physics, University of Seville, Avda. Reina Mercedes, 41012 Seville, Spain 2 Centro Nacional de Aceleradores CNA (Universidad de Sevilla, Junta de Andalucia, CSIC), Avda. Thomas A. Edison 7, 41092 Seville, Spain 3 Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany 4 Institute of Applied Physics, TU Wien, Fusion@ ¨ OAW, Wiedner Hauptstr. 8-10, 1040 Vienna, Austria 5 Dept. of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey, United States E-mail: [email protected] October 2017 Abstract. The edge ion heat transport is analyzed in ASDEX Upgrade (AUG) by combining a comprehensive set of pedestal measurements with both interpretive and predictive modelling. The experimentally determined ion heat diffusivities, χi, are compared with neoclassical theory and the impact of edge localized modes (ELMs) on the edge ion heat transport level is studied in detail. Pedestal matching experiments in deuterium and hydrogen plasmas show that the inter-ELM pedestal χiremains close to the neoclassical value. The additional power needed in hydrogen to get similar pedestal temperatures as in deuterium plasmas mostly affects the electron heat channel, i.e. the electron heat diffusivity increases while the ion heat diffusivity stays at the same level within the uncertainties. Sub-ms measurements of the edge ion temperature allows us to extend the analysis to the entire ELM cycle. During the ELM crash, the ion heat transport is increased by an order of magnitude. The perturbed heat flux increases first at the separatrix, i.e. first the separatrix ion temperature increases, leading to a flatter ion temperature gradient, followed by a decrease of the whole pedestal profile. The ion heat transport returns to its pre-ELM neoclassical level 3–4 ms after the ELM crash. ‡See the author list of H. Meyer et al., Nucl. Fusion 57 102014 (2017). Ion heat transport dynamics during an ELM cycle at ASDEX Upgrade 2 1. Introduction Heat transport plays a key role in understanding fusion plasmas. At the transition from L- to H-mode, an edge transport barrier (ETB) for particles and heat is formed and a region with strongly reduced turbulent transport is established. The pedestal with its very strong gradients and proximity to open field lines, requires a different physics treatment than the plasma core. It is widely believed that the shear in the E×B velocity is fundamental for edge turbulence suppression and the formation of the ETB, thus, leading to the transition into H-mode [1]. Comprehensive heat transport studies of the plasma core have been carried out in the past [2, 3, 4]. In this region, the ion thermal transport is usually governed by long wavelength turbulence, such as ITG modes [5, 6]. The pedestal, with its small spatial width (typically 1.5–2 cm at ASDEX Upgrade, AUG) and fast temporal changes due to ELMs, is more challenging to analyze. Therefore, comparatively little work has been done in this region. At AUG substantial effort has been put into upgrading the diagnostics at the plasma edge to resolve the fast dynamics and the steep gradients of the pedestal. The unique edge diagnostic suite now available at AUG allows us to measure the edge plasma profiles on a sub-ms to ms timescale with a spatial resolution of better than 5 mm [7]. Previous AUG experiments indicated that the pre-ELM pedestal ion heat diffusion is close to the neoclassical level, at both low and high collisionality [8, 9]. The electron heat diffusivity is also at the ion neoclassical heat diffusion level, but remains significantly above the electron neoclassical heat diffusivity, consistent with observations at JT-60U [10]. Similarly, a transport analysis of a high-Teelectron cyclotron heated plasma in LHD showed that while the measured electron heat flux exceeds the neoclassical values by an order of magnitude, the measured ion heat flux is comparable to the neoclassical prediction [11]. In this paper, we compare the experimentally determined ion heat diffusivity at the plasma edge to neoclassical predictions calculated with the NEOART code [12]. The analysis of the ion heat transport presented in [8] was done in D. Here, we extend the analysis also to hydrogen plasmas and directly compare the pedestal heat transport in H and D via pedestal matching experiments. The isotope effect describes the change in confinement observed in plasmas with different main ion species. Deuterium plasmas show improved confinement compared to hydrogen [13, 14], contrary to the predictions of the gyro-Bohm scaling. Previous analysis focusing on the L-H transition showed that, for similar ion temperature gradients, the edge ion heat flux at the H-mode transition is about twice as high in H than in D [15]. Moreover, a comparison in the H-mode phase showed that in hydrogen the total heating power has to be more than doubled and the applied gas puff increased by an order of magnitude to match the D pedestal parameters [16]. This suggests that H plasmas typically feature lower electron density gradients, owing to the increased particle transport, while the total heat flux across the pedestal is twice that in D [17, 16, 18]. As more gas and power are required in H to match the D temperature and density pedestals, the total heat and particle fluxes in H Ion heat transport dynamics during an ELM cycle at ASDEX Upgrade 3 are also larger, implying higher heat and particle diffusivities. In this work we further explore the differences in the pedestal heat transport between D and H plasmas. In addition, we have also extended our analysis to the entire ELM cycle, in both deuterium and helium plasmas, utilizing the new edge CXRS spectrometer [19]. Previous AUG studies on the electron dynamics during the ELM cycle showed that the electron density and temperature pedestals have different recovery times [20]. Recently, it was found that the re-establishment of the pedestal top electron pressure after the ELM crash is correlated with the onset of high frequency magnetic fluctuations [21, 22]. The instabilities driving these fluctuations may limit the pedestal gradients prior to the crash. In this work, we add to the picture by measuring in detail the evolution of the ion heat transport during the ELM cycle. This paper is structured as follows: Section 2 briefly describes the experimental setup. Section 3 presents the analysis methods used in this work. A comparison of the heat fluxes and the ion heat transport coefficients obtained in hydrogen and deuterium pedestal matching experiments is discussed in section 4. Section 5 extends the ion heat transport analysis to the entire ELM cycle, which allows us to study the dynamics of the heat transport before and after the ELM crash. A summary of the presented work is given in section 6. 2. Diagnostic setup The experiments presented in this paper were performed in the AUG tokamak. AUG is equipped with a high spatial and temporal resolution edge diagnostic suite. The comprehensive set of charge exchange recombination spectroscopy (CXRS) diagnostics [23, 24], which provides measurements of the ion temperature, flow velocity and impurity density, is essential for the present work. The edge system was recently upgraded to increase the number of lines of sight (LOS), from 8 in both the toroidal and poloidal directions to 31 and 22, respectively [19]. The edge LOS can be divided between the different spectrometers of the edge CXRS suite. The upgraded CXRS diagnostic now enables fully resolved radial profiles without the necessity of a radial plasma sweep. The standard edge CXRS systems have a temporal resolution of 2.3 ms and image 24 toroidal LOS and 13 poloidal LOS using two Czerny-Turner like spectrometers [23]. A subset of the 53 edge lines of sight (up to max. 9 LOS) can be connected to a newly designed spectrometer [19] that can be operated with 50 µs integration times. In order to guarantee a high signal-to-noise ratio at such high time resolution, impurity seeding is required. For the discharges presented in section 5, nine LOS were measured with the fast edge CXRS spectrometer. The upgraded diagnostic now allows us to analyze the behaviour of the impurity density, temperature, flow and Erprofiles during fast transient events, such as the L-H transition [25] and ELM cycles [26]. Information on the electron temperature and density profiles is also needed for a complete heat transport analysis. The electron temperature, Te, profiles are measured via the electron cyclotron emission [27] and the Thomson scattering diagnostic [28], Ion heat transport dynamics during an ELM cycle at ASDEX Upgrade 4 which also provides information on the electron density, ne. Additional information on neis provided by the Lithium beam [29] and interferometry system [30]. The measurements from all of these diagnostics are combined within the integrated data analysis algorithm based on Bayesian probability theory [31] to produce a consistent set of neand Teprofiles on a unified time base. For all discharges the radial profile alignment technique [32], which is based on the twopoint model [33] and which localizes the profiles with respect to the separatrix position, was applied to the measured profiles. This procedure allows us to reduce the radial uncertainties due to the magnetic equilibrium down to 2–3 mm [34]. 3. Analysis of energy transport The ion and electron heat fluxes, Qiand Qe, are determined by the radial component of the energy balance equation for the main ions and electrons. The heat fluxes are obtained by volume integrating the energy sources and losses for a particular channel, Qj=RPjdV (jbeing ions or electrons). For the ions we include neutral beam injection (NBI), the electron to ion heat flux, and the power that is lost via atomic processes including charge exchange with background neutrals, ionization, and recombination, i.e. Pi=PNBI i+Pei +Patomic i. For the electrons, additional terms such as the absorbed ECRH power, the ohmic power, and radiation cooling play a role, i.e. Pe=PNBI e+ PECRH e+Poh -Prad -Pei -Patomic e. The heat diffusivity, χj(ρ) = −Qj nj ∂Tj ∂ρ , is determined by the heat flux Qj, the particle density njand the radial temperature gradient. In this study, Qiand Qeare provided by time-dependent power balance analysis using the ASTRA code [35]. Here, ne,Te,Ti, the effective charge (Zeff ), and Prad are used as inputs. In addition, the auxiliary power to the ions and electrons, the plasma current, toroidal magnetic field and loop voltage are provided. The minor and major radius, the elongation and triangularity, and the shape of the separatrix determined by a 2D magnetic equilibrium reconstruction are used. ASTRA reconstructs the equilibrium with this prescribed boundary condition and a 3-moment approach [35]. Note that the temporal variation in the plasma energy is taken into account in the evaluation of the heat flux and the heat diffusivity. ASTRA can be run in an interpretive or in a predictive way. Using the interpretive approach, the heat diffusivities are determined from Qiand Qeand the experimental input profiles. The necessary transport is inferred by adjusting the heat diffusivities to match the evolution of the measured profiles. In the predictive approach, the heat fluxes are calculated from the energy sources, and the heat diffusivities are prescribed in space and time. The heat transport equations are then solved iteratively for Te and Ti.The ability of the chosen model (the prescribed diffusivities) to reproduce the profile dynamics can be tested by comparing the evolution of the modelled and measured profiles. When running ASTRA predictively, it is not possible for any single set of diffusivities to reproduce both the ELM and inter-ELM phases, due to the highly anomalous heat fluxes during the crash. Therefore, for all predictive runs shown in this Ion heat transport dynamics during an ELM cycle at ASDEX Upgrade 5 0.80 0.85 0.90 0.95 1.0 ρpol 0 0.5 1.0 1.5 T [keV] T #31393 (H) i T #31619 (D) i T #31619 (D), [2.0, 2.11]s e T #31393 (H), [4.1, 4.35]s e Figure 1. Electron and ion temperature profiles for deuterium and hydrogen. work the heat diffusivities during the ELM crash are artificially increased to reproduce the behaviour during the ELM crash and the correct starting conditions for the post- ELM evolution. For the ELM crash itself, non-linear MHD modelling is required to understand and reproduce the observed high anomalous heat transport. 4. Characterization of the pre-ELM ion heat transport in the edge pedestal - comparison between D and H plasmas Pedestal matching experiments in deuterium and hydrogen plasmas were carried out in AUG to study and compare the pedestal structure and stability [16]. Dedicated transport analyses with ASTRA have been performed to analyze the heat fluxes. Figure 1 shows the electron and ion temperature profiles at the plasma edge for both deuterium (Tein black crosses, Tiin red squares) and hydrogen (Tein blue triangles, Tiin magenta circles) plasmas. The experiments were performed at a toroidal magnetic field, Bt, on-axis of -2.5 T, plasma current, Ip, of 1 MA and an average triangularity of 0.22 (average being the mean of the upper and lower triangularity).To match the density and temperature pedestals, different gas puffs and NBI heating powers were applied [16]. In D, an NBI heating power of 2.5 MW and a D puff of 1.5×1021 s−1were applied, whereas in H, the NBI heating power was increased to 6 MW and the gas puff to 12.1×1021 s−1. In both cases, the ECRH heating was 1.1 MW. The ion collisionality, defined as the effective collision frequency normalized to the trapped particle bounce frequency [36], in the pedestal (at ρpol = 0.97) was 0.53 in H and 0.49 in D. As shown in figure 1, the edge profiles are very similar, though Tiin hydrogen is slightly higher. The heat transport coefficients are determined using power balance analysis with ASTRA. To this end, Ti,Teand neas well as the radiated power and the effective charge, Zeff , are used as inputs to the analysis. As described in section 3, the electron and ion heat fluxes are determined by the respective energy sources. Figure 2 shows (a) the fitted profiles of Tiand Te, (b) the ion and electron energy sources, Piand Pe, together with the heat exchange rate between electrons and ions, Pei, and (c) the resulting heat Ion heat transport dynamics during an ELM cycle at ASDEX Upgrade 6 Ti Te #31619, D #31393, H T [keV] 0.0 0.2 0.4 0.6 0.8 1.0 ρpol 0 1 2 3 4 5 T [keV] Pe Pi Pei #31619, D #31393, H -1 0 1 2 3 4 5 6 0.0 0.2 0.4 0.6 0.8 1.0 ρpol P [MW/m ] 3 0 1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0 Q [MW] ρpol Qe D Qi D #31619, D #31393, H Qi H Qe H (a) (b) (c) Figure 2. (a) Fitted Ti(red) and Te(black) profiles, (b) ion (red) and electron (black) energy sources and electron-ion heat exchange rate (blue), (c) surface-integrated heat fluxes of ions (red, magenta) and electrons (black, blue). Solid lines correspond to the deuterium discharge, while dashed lines to the hydrogen discharge. 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.0 0 1 2 3 4 5 6 ρpol χ[m /s] 2 #31393, H χi neo χe PB χi PB 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.0 0 1 2 3 4 5 6 ρpol χ[m /s] 2 #31619, D χi PB χe PB χi neo (a) (b) Figure 3. Edge ion heat diffusivities for (a) deuterium and (b) hydrogen. fluxes. Note that effects due to ELMs have been excluded. The profiles have been averaged over the time window [-4.5,-1.5] ms before the ELM onset. Due to the mass dependence of the electron-ion heat exchange rate, Pei in hydrogen is approximately a factor of 2 larger than in deuterium [37]. Figure 3 shows the corresponding heat transport coefficients determined via power balance, χP B iand χP B e. At the edge (ρpol >0.96), the ion heat transport is close to the neoclassical level for both D and H, consistent with previous observations in D [9, 8].Note that the much larger Qeneeded in H (see figure 2(c)) to maintain the same Temeans much higher transport in the electron channel. The electron heat diffusivity is higher by a factor of 2–3 in H compared to D, while the change in the ion heat transport is small (compare figure 3(a) and (b)). In H, the NBI effectively heats the electrons more and thus, the surface-integrated electron heat flux is increased. In order to maintain the same pedestal a higher heat flux in the electron channel is needed, suggesting that the turbulent electron heat transport is higher in H compared to D. Note that the neoclassical ion heat diffusivity depends on χneo i∝niρ2 i,pol/τi∝√m, where niis the ion density, ρi,pol the poloidal ion gyro-radius, τithe ion collisional time, and mthe mass. Therefore, the neoclassical χiin H is slightly smaller than in D (0.6 m2/s compared to 0.8 m2/s). This small difference is difficult to resolve in the experiment Ion heat transport dynamics during an ELM cycle at ASDEX Upgrade 7 due to the uncertainties. In both cases the neoclassical χiis within the experimental uncertainties. It is, however, interesting to note that in the pedestal region (ρpol >0.96), the experimental χidoes in fact show a decrease by 35% in H compared to D, consistent with the expectations from neoclassical theory. Note that the error bars given in figure 3 include uncertainties in the temperature and density profiles as well as uncertainties in the radiated power. In the following, we extend our analysis to the entire ELM cycle. These measurements were performed utilizing the new edge CXRS spectrometer [19] in a deuterium [26] and a helium plasma. 5. Evolution of ion heat transport during the ELM cycle 5.1. Investigations in deuterium The recent upgrade of the edge CXRS diagnostics [19] allows us to measure the dynamics of the ion temperature at AUG with an unprecendented time resolution down to 50 µs. A dedicated type-I ELMy H-mode discharge was performed to measure the evolution of the ion temperature, impurity density and flows, and the edge radial electric field [26]. Here, Ipwas 0.8 MA, Btwas -2.5 T, the average triangularity was 0.27, the core lineaveraged density was 6.9×1019 m−3, and the total input power was 5.8 MW (4.8 MW NBI, 1 MW ECRH). The ELM frequency was constant at around 85 Hz. For the analysis the data measured during the time window [3.5, 5.5] s are synchronized with respect to the onset of the ELMs. In this discharge helium seeding was applied to provide fast CXRS measurements. The measurements were taken on the He2+ spectral line (n= 4 →3, λ=468.571 nm) with a temporal resolution of 65 µs. Note that the ion temperature can be approximated by the measured impurity temperature as the energy equilibration time between main ions and impurities is short (several µs) compared to local transport time scales (∼1 ms) [34]. Comparison of the ion and electron profiles [26] shows that the ion temperature gradient recovers on a faster timescale than the electron temperature gradient. The maximum Ti gradient recovers to its pre-ELM values approximately 4 ms after the ELM onset, while the maximum Tegradient takes 7–8 ms [26]. The ion heat transport modelling workflow using ASTRA was applied to the entire ELM cycle to reveal the nature of the ion heat transport dynamics before the ELM crash and during the recovery phase. During an ELM, the plasma moves inward by 5–10 mm, which affects the measurements since different local radial positions are being probed after the ELM onset. This effect was taken into account by mapping the measurements onto the radial coordinate ρpol using a high-resolution magnetic equilibrium reconstruction (100 µs). Note that the same procedure was applied in the He discharge. In order to have concurrent measurements of Ti,Teand nefor the simulations, the data of the fast edge CXRS system was rebinned to 100 µs to match the time basis of the nemeasurements. As the full profile of Tiis needed for the simulations, the measurements of the fast edge CXRS system (CNR) were Ion heat transport dynamics during an ELM cycle at ASDEX Upgrade 8 0 1 2 3 χi PB/10 χi PB 2 [m /s] χi neo 0.0 0.2 0.4 0.6 0.8 T [keV] i t-t = -2 ms ELM t-t = +0.8 ms ELM t-t = +3 ms ELM t-t = +6 ms ELM #31529(a) (b) 0 1 2 3 4 Q [MW] i Q/10 i (c) 0.90 0.92 0.94 0.96 0.98 1.0 Figure 4. Profiles for four time points during the ELM cycle: (a) Ti, (b) χidetermined via power balance and χneo icalculated from neoclassical theory, (c) heat flux Qi. combined with the slower standard edge CXRS diagnostics (CMR and CPR, temporal resolution 2.3 ms), also measuring on He2+, and the core CXRS system (CER, set to 5 ms in this discharge) measuring on B5+ (n= 7 →6, λ= 494.467 nm).In figure 4, an example profile measured during the analyzed time window is shown, highlighting the measurement regions of each diagnostic. Here, the measured data points correspond to a pre-ELM profile. Note, these data points do not correspond directly to any of the fitted Tiprofiles shown. The ELM synchronized measurements of the slower systems have been fitted for various time windows during the ELM cycle and mapped onto the 100 µs time basis by interpolating the profiles. Any impact of the ELMs on the pre- and post-ELM profiles was excluded. For the core system the ELM averaged profile is used due to the limited time resolution. At the overlap point between the slower and fast edge CXRS systems (highlighted in gray in figure 4), the gradients are not real as Ion heat transport dynamics during an ELM cycle at ASDEX Upgrade 9 the profiles are interpolated to generate one combined core and edge profile at the fast temporal resolution. The analysis below, therefore, focuses only on the radial region between 0.98 and 1.0. Figure 4 shows (a) the ion temperature profiles, (b) the ion heat diffusivities and (c) the surface-integrated ion heat flux Qifor four time points during the ELM cycle. Note that the χiand Qiprofiles highlighted in red are taken during the ELM crash (at time t-tELM = +0.8 ms) and have been divided by a factor of 10. The perturbation of Ticaused by the ELM induces large changes in the heat flux and in the heat diffusivity at the edge. Note that the NBI source stays constant throughout the analyzed time window. The ELM causes large changes in the transport which affect the heat and particle fluxes, leading to flatter temperature and density gradients. In figure 4(b) the neoclassical χi profile is highlighted by a dashed line. For clarity, only the profile of the first time point (pre-ELM) is shown. During the ELM cycle, the neoclassical χiat the edge increases by a factor of 2, however, as shown below, the neoclassical flux cannot account for the high ion heat flux observed during the ELM crash. In the core, turbulent transport dominates leading to a strong deviation of χifrom neoclassical theory, while in the edge transport barrier χiapproaches the neoclassical level (except for the time points during the ELM). Note that close to the separatrix, the ordering of standard neoclassical theory breaks down and cannot be applied to the region ρpol>0.997. Figure 5 shows the evolution of (a) Tiand (b) the ratio between the experimentally determined χP B iand the neoclassical χneo iduring the ELM cycle, as well as (c) the thermo-currents at the inner divertor used as an ELM monitoring signal. At the ELM onset, the separatrix Tiincreases [26], leading to a reduced gradient in the pedestal, similar to observations at DIII-D [38]. Shortly after the initial separatrix increase, the whole profile drops and then the Tipedestal starts to build up again. The pre-ELM profile is fully recovered 3–4 ms after the ELM crash, which is faster than the thermal energy confinement time (60 ms in this discharge). As shown before, the pre-ELM values of χiat the plasma edge are in agreement with neoclassical predictions while, during the crash, χiis increased due to anomalous transport caused by the ELM itself. Note that later in the ELM cycle (t-tELM >6 ms), χi at the very edge of the plasma is higher than the neoclassical calculation (see figure 5(b)), indicating that close to the separatrix anomalous transport may become important. It should also be noted that during the inter-ELM phase, the uncertainties of the separatrix Tiare large due to uncertainties in the equilibrium mapping and in the profile alignment (2–3 mm), and due to a low signal-to-noise ratio. Extending the CXRS measurements into the SOL and combining them with other SOL diagnostics capable of measuring Tiwould help to quantify χiat the separatrix and beyond. This is subject of ongoing work. The temperature profiles have also been modelled using ASTRA in a predictive way. As described in section 3, for the predictive approach, the χiand χeprofiles are prescribed and the heat transport equations are solved for Tiand Te. The χP B iprofile determined via power balance analysis is used for the plasma core, while at the edge (ρpol>0.98)