Data for "Kinetic-Ballooning-Limited Pedestals in Spherical Tokamak Plasmas"
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Parisi, Jason↗
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Density pedestal prediction model for tokamak plasmas
Abstract A model for the pedestal density prediction based on neutral penetration combined with pedestal transport is presented. The model is tested against a pedestal database of JET-ILW Type I ELMy H-modes showing good agreement over a wide range of parameters both in standalone modelling (using the experimental temperature profile) and in full Europed modelling that predicts both density and temperature pedestals simultaneously. The model is further tested for ASDEX Upgrade and MAST-U Type I ELMy H-modes and both are found to agree with the same model parameters as for JET-ILW. The JET-ILW experiment where the isotope of the main ion is varied in a D/T scan at constant gas rate and constant β N is successfully modelled as long as the separatrix density ( n e,sep ) and pedestal transport coefficient ratio ( D / χ ) are varied in accordance with the experimentally observed variation of n e,sep and the isotope dependence of D / χ found in gyrokinetic simulations. The predictions are found to be sensitive to n e,sep which is why the model is combined with an n e,sep model to predict the pedestal for the STEP fusion reactor.
Physics↗
Simple, general, realistic, robust, analytic tokamak equilibria. Part 2. Pedestals and flow
Part 1 described a wide range of analytic tokamak equilibria modelling smooth limiter surfaces, double- and single-null divertor surfaces, arbitrary aspect ratio, elongation, triangularity and beta. Part 2 generalizes the analysis to further include edge pedestals and toroidal flow. Specifically, edge pedestals are allowed in the pressure, pressure gradient and toroidal current density. Also, an edge-localized contribution to the bootstrap current is treated. In terms of flow, analytic solutions are obtained for two cases: a $\gamma = 2$ adiabatic and a $\gamma = \infty $ incompressible energy conservation relation.
Physics↗
Core-Pedestal Plasma Configurations in Advanced Tokamaks
Here, several configurations for the core and pedestal plasma are examined for a predefined tokamak design by implementing multiple heating/current drive (H/CD) sources to achieve an optimum configuration of high fusion power in a noninductive operation while maintaining an ideally magnetohydrodynamic (MHD) stable core plasma using the IPS-FASTRAN framework. IPS-FASTRAN is a component-based lightweight coupled simulation framework that is used to simulate magnetically confined plasma by integrating a set of high-fidelity codes to construct the plasma equilibrium (EFIT, TOQ, and CHEASE), calculate the turbulent heat and particle transport fluxes (TGLF), model various H/CD systems (TORIC, TORAY, GENRAY, and NUBEAM), model the pedestal pressure and width (EPED), and estimate the ideal MHD stability (DCON). The TGLF core transport model and EPED pedestal model are used to self-consistently predict plasma profiles consistent with ideal MHD stability and H/CD (and bootstrap) current sources. In order to evaluate the achievable and sustainable plasma beta, varying configurations are produced ranging from the no-wall stability to with-wall stability regimes, simultaneously subject to the self-consistent TGLF, EPED, and H/CD source profile predictions that optimize configuration performance. The pedestal density, plasma current, and total injected power are scanned to explore their impact on the target plasma configuration, fusion power, and confinement quality. A set of fully noninductive scenarios are achieved by employing ion-cyclotron, neutral beam injection, helicon, and lower-hybrid H/CDs to provide a broad profile for the total current drive in the core region for a predefined tokamak design. These noninductive scenarios are characterized by high fusion gain (Q ~ 4) and power (P fus ~ 600 MW), optimum confinement quality (H 98 ~ 1.1), and high bootstrap current fraction (f BS ~ 0.7) for Greenwald fraction below unity. The broad current profile configurations identified are stable to low-n kink modes either because the normalized pressure β N is below the no-wall limit or a wall is present.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
The role of ion-scale micro-turbulence in pedestal width of the DIII-D wide-pedestal QH mode
The low-edge rotation, intrinsically ELM-free, and improved confinement wide-pedestal quiescent H-mode (QH-mode), discovered in DIII-D tokamak, has pedestal widths exceeding the EPED-kinetic-ballooning mode (KBM) model scaling typically by at least 25%. Ion-scale ($k_yp_s$ < 1) microturbulence and its role in setting the pedestal structure is investigated using the radially local δ$f$ gyrokinetic code CGYRO. The electromagnetic trapped electron mode (TEM) is unstable at the pedestal top, while plasma beta (β$_e$) is ∼60% below the KBM onset threshold and the electron temperature gradient mode is found to be unstable in the peak gradient region. Nonlinear simulation reveals that the ion-scale turbulence could produce electron energy flux consistent with the flux inferred from power balance at the pedestal top, with a reasonable variation of the local shearing rate; and the local neoclassical transport from NEO is dominant over the simulated turbulent transport in the ion energy flux channel. The simulated ion-scale turbulence produces much lower electron energy flux than inferred from experiment in the pedestal peak gradient region. A correction to the EPED-KBM pedestal width scaling is obtained based on the two-dimensional scan of pedestal top plasma beta (β$_e$) and normalized electron density and temperature scale lengths,${a}$/${L_n}_e$, ${a}$/${L_T}_n$using CGYRO linear simulations. Mode transitions among TEM, micro-tearing mode, ion-temperature gradient mode and KBM, are observed in the 2D scan at the pedestal top. A fixed normalized growth rate for these drift-type modes is taken to determine the pedestal width scaling, which shows good consistency with the QH experimental database on pedestal heights and widths. The onset of KBM instabilities and the local E × B shear suppression criterion set the lower and upper limit for the pedestal width of standard QH-mode, wide-pedestal QH-mode and type-I ELMy H mode. A potentially higher and wider pedestal is expected from the new scaling of pedestal width. This work presents an improved understanding of the ion-scale micro-turbulence of wide-pedestal QH-mode and sheds light on a promising scenario for future reactors, including ITER and beyond.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Flexible, integrated modeling of tokamak stability, transport, equilibrium, and pedestal physics
The STEP (Stability, Transport, Equilibrium, and Pedestal) integrated-modeling tool has been developed in OMFIT to predict stable, tokamak equilibria self-consistently with core-transport and pedestal calculations. STEP couples theory-based codes to integrate a variety of physics, including magnetohydrodynamic stability, transport, equilibrium, pedestal formation, and current-drive, heating, and fueling. The input/output of each code is interfaced with a centralized ITER-Integrated Modelling & Analysis Suite data structure, allowing codes to be run in any order and enabling open-loop, feedback, and optimization workflows. This paradigm simplifies the integration of new codes, making STEP highly extensible. STEP has been verified against a published benchmark of six different integrated models. Core-pedestal calculations with STEP have been successfully validated against individual DIII-D H-mode discharges and across more than 500 discharges of the H98,y2 database, with a mean error in confinement time from experiment less than 19%. STEP has also reproduced results in less conventional DIII-D scenarios, including negative-central-shear and negative-triangularity plasmas. Predictive STEP modeling has been used to assess performance in several tokamak reactors. Simulations of a high-field, large-aspect-ratio reactor show significantly lower fusion power than predicted by a zero-dimensional study, demonstrating the limitations of scaling-law extrapolations. STEP predictions have found promising scenarios for an EXhaust and Confinement Integration Tokamak Experiment, including a high-pressure, 80%-bootstrap-fraction plasma. ITER modeling with STEP has shown that pellet fueling enhances fusion gain in both the baseline and advanced-inductive scenarios. Finally, STEP predictions for the SPARC baseline scenario are in good agreement with published results from the physics basis.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
New understanding of inter-ELM pedestal turbulence, transport, and gradient behavior in the DIII-D tokamak
New observations of pedestal localized turbulence in the inter-ELM period of H-mode plasmas in DIII-D show that ion temperature gradient mode scale (ITG-scale) density fluctuation (ñ) increases immediately after each ELM crash and is quickly suppressed during the increase in local E × B shear. This excitation and subsequent suppression of ITG-scale ñ can explain the previously reported anomalous ion heat flux, Qi during the ELM (Viezzer et al 2017 Nucl. Fusion 57 022020). Shorter wavelength trapped electron mode scale (TEM-scale) ñ starts to increase at a critical pedestal temperature gradient (∇Te,ped) and saturates as local E × B shear, ${T}_{\mathrm{i}}^{\mathrm{C}\mathrm{6}+}/{T}_{\mathrm{e}}$ ratio, and ∇Te,ped saturate. This TEM-scale ñ, which has the potential to cause electron (and also ion) heat transport, is consistent with driving an anomalous electron heat flux Qe, where Qe is estimated between ELMs using experimental profiles and power balance. Both ITG- and TEM-scale ñ amplitude variations with background Ti/Te and ∇ne,ped are found to be consistent with theoretical predictions of these measured density fluctuations being ITG and TEM instabilities respectively. Furthermore, these new and unique observations on the nature of turbulence and their potential contributions to electron and ion heat fluxes at different ELM periods (i.e. collapse, recovery, and saturation phases of pedestal gradients) can significantly test and improve our pedestal predictive capabilities for ITER and other future fusion devices.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Broadening of the Divertor Heat Flux Profile in High Confinement Tokamak Fusion Plasmas with Edge Pedestals Limited by Turbulence in DIII-D
Multimachine empirical scaling predicts an extremely narrow heat exhaust layer in future high magnetic field tokamaks, producing high power densities that require mitigation. Here, in the experiments presented, the width of this exhaust layer is nearly doubled using actuators to increase turbulent transport in the plasma edge. This is achieved in low collisionality, high confinement edge pedestals with their gradients limited by turbulent transport instead of large-scale, coherent instabilities. The exhaust heat flux profile width and divertor leg diffusive spreading both double as a high frequency band of turbulent fluctuations propagating in the electron diamagnetic direction doubles in amplitude. The results are quantitatively reproduced in electromagnetic XGC particle-in-cell simulations which show the heat flux carried by electrons emerges to broaden the heat flux profile, directly supported by Langmuir probe measurements.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Grassy ELM regime at low pedestal collisionality in high-power tokamak plasma
Spontaneous mitigation of giant ELMs and appearance of grassy ELMs have been observed repeatedly at low pedestal collisionality (${\nu }_{\mathrm{e},\mathrm{p}\mathrm{e}\mathrm{d}}^{{\ast}}\sim 0.15$) in the high-power (P inj > 13 MW) hybrid scenario in DIII-D. Higher β p and higher q 95 appear to be beneficial to achieving the grassy ELM regime. The grassy ELM H-mode plasma shows high energy confinement performance (H 98y2 up to over 1.5) under the conditions of high neutral beam torque and high core rotation. The pedestal width appears to exceed the EPED1.0 model prediction by more than 50%. Pedestal stability analysis performed with the ELITE code indicates that the stability against low-n kink/peeling modes is improved with increased auxiliary heating power and the operational point in the grassy ELM regime is located near the ballooning boundary. The pedestal stability characteristics during the grassy ELM crashes have been investigated in comparison with the giant ELM crashes based on plasma profiles experimentally measured with high resolution and accuracy. It has been found that the underlying mechanism for the observed small-amplitude ELM crashes is mainly the expansion of the ballooning stability boundary induced by an initial radially localized collapse in the pedestal, which helps to stop the growth of instabilities and further collapse of the pedestal. The effect of electron density pedestal on mitigating edge localized instabilities has been analyzed by numerical simulation, suggesting that the electron density pedestal characterized by high n e,sep /n e,ped and low density gradient helps to stabilize peeling-ballooning modes because of a low pressure pedestal gradient and to lower the ballooning boundary mainly because of a low ion diamagnetic frequency in the pedestal region, thus triggering ballooning instabilities and producing the intrinsic grassy ELMs. Numerical simulation of the Chinese fusion engineering test reactor (CFETR) with the SOLPS code indicates that the separatrix density might be insensitive to the electron diffusivity in the pedestal region and increase with the power flowing from the core region to the edge region. Furthermore, pedestal stability analysis suggests that the flat density pedestal with high separatrix density obtained in the high-power plasma in CFETR would make the operational point close to the ballooning boundary, which is considered to help destabilize ballooning instabilities and facilitate the access to the grassy ELM regime.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Direct measurement of the electron turbulence-broadening edge transport barrier to facilitate core–edge integration in tokamak fusion plasmas
Abstract The integration of a high-performance core and a dissipative divertor, or the so-called ‘core–edge integration,’ has been widely identified as a critical gap in the design of future fusion reactors. In this letter, we report, for the first time, direct experimental evidence of electron turbulence at the DIII-D H-mode pedestal that correlates with the broadening of the pedestal and thus facilitates core–edge integration. In agreement with gyrokinetic simulations, this electron turbulence is enhanced by high η e ( η e = L n / L T e , where L n is the density scale length and L T e is the electron temperature scale length), which is due to a strong shift between the density and temperature pedestal profiles associated with a closed divertor. The modeled turbulence drives significant heat transport with a lower pressure gradient that may broaden the pedestal to a greater degree than the empirical and theoretically predicted pedestal width scalings. Such a wide pedestal, coupled with a closed divertor, enables us to achieve a good core–edge scenario that integrates a high-temperature low-collisionality pedestal (pedestal top temperature T e,ped > 0.8 keV and a pedestal top collisionality ν * ped < 1) under detached divertor conditions. This paves a new path toward solving the core–edge integration issue in future fusion reactors.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Reduction of blob-filament radial propagation by parallel variation of flows: Analysis of a gyrokinetic simulation
Data from the XGC1 gyrokinetic simulation is analyzed to understand the three-dimensional spatial structure and the radial propagation of blob-filaments generated by quasisteady turbulence in the tokamak edge pedestal and scrape-off layer plasma. Spontaneous toroidal flows vary in the poloidal direction and shear the filaments within a flux surface resulting in a structure that varies in the parallel direction. Here, this parallel structure allows the curvature and grad-B induced polarization charge density to be shorted out via parallel electron motion. As a result, it is found that the blob-filament radial velocity is significantly reduced from estimates which neglect parallel electron kinetics, broadly consistent with experimental observations. Conditions for when this charge shorting effect tends to dominate blob dynamics are derived and compared with the simulation.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Edge-localized mode mitigation enabled by active control of pedestal density gradient with new EAST tokamak divertor
Mitigation of large edge-localized modes (ELMs) has been achieved by actively reducing the pedestal density gradient with the EAST new right-angled lower divertor through changing the strike point position from the vertical target to the horizontal target. A series of dedicated experiments in the 2021–2024 EAST campaigns demonstrate that this ELM control solution is highly reproducible in a broad parameter space of edge safety factor q 95 = 4.7–7.1, heating power P total = 2.3–5 MW, and pedestal collisionality $ν_{e,ped}^{*}$ = 1–6, under both favorable and unfavorable magnetic configurations. Higher plasma density could facilitate the achievement of this ELM control solution. Statistical results indicate that the ELM mitigation effect can be observed at relatively larger Greenwald density fraction of f GW > 0.47. In addition, this ELM mitigation effect can be achieved with both lithium-coated and boronized metal walls. The pedestal density gradient is systematically lower in the horizontal target case than that of the vertical target case when the ELM mitigation effect can be observed. SOLPS-ITER simulation results indicate that the pedestal fueling from divertor recycling is significantly lower in the horizontal target case. This could contribute to the formation of a flattened pedestal density profile with small ELMs.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
The role of ETG modes in JET–ILW pedestals with varying levels of power and fuelling
Abstract We present the results of GENE gyrokinetic calculations based on a series of JET–ITER-like-wall (ILW) type I ELMy H-mode discharges operating with similar experimental inputs but at different levels of power and gas fuelling. We show that turbulence due to electron-temperature-gradient (ETGs) modes produces a significant amount of heat flux in four JET–ILW discharges, and, when combined with neoclassical simulations, is able to reproduce the experimental heat flux for the two low gas pulses. The simulations plausibly reproduce the high-gas heat fluxes as well, although power balance analysis is complicated by short ELM cycles. By independently varying the normalised temperature gradients ( ω T e ) and normalised density gradients ( ω n e ) around their experimental values, we demonstrate that it is the ratio of these two quantities η e = ω T e / ω n e that determines the location of the peak in the ETG growth rate and heat flux spectra. The heat flux increases rapidly as η e increases above the experimental point, suggesting that ETGs limit the temperature gradient in these pulses. When quantities are normalised using the minor radius, only increases in ω T e produce appreciable increases in the ETG growth rates, as well as the largest increases in turbulent heat flux which follow scalings similar to that of critical balance theory. However, when the heat flux is normalised to the electron gyro-Bohm heat flux using the temperature gradient scale length L T e , it follows a linear trend in correspondence with previous work by different authors.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Comparison of MHD stability properties between QH-mode and ELMy H-mode plasmas by considering plasma rotation and ion diamagnetic drift effects
Magnetohydrodynamic (MHD) stability at tokamak edge pedestal in a quiescent H-mode (QH-mode) and type-I ELMy H-mode plasmas in DIII-D experiment was analyzed by considering plasma rotation and ion diamagnetic drift effects. QH-mode plasma is marginally stable to kink/peeling mode (K/PM), but ELMy H-mode one is almost unstable to peeling-ballooning mode (PBM). It was identified that there are three physics features responsible for the difference in the MHD stability properties between QH-mode plasma and ELMy H-mode one. These are the distance of pedestal foot from the last closed flux surface (LCFS), the amount of the ion diamagnetic drift frequency at pedestal, and impact of coupled rotation and ion diamagnetic drift effects. These features were confirmed through the numerical experiments that the stability properties of the QH-mode plasma can be changed to that of the ELMy H-mode one by shifting the plasma profiles inward in the radial direction and halving the ion diamagnetic drift frequency. The reasons of the change in the stability properties are thought as that K/PM is stabilized due to the inward shift of the bootstrap current profile, and PBM is destabilized due to the reduction of the coupled rotation and ion diamagnetic drift stabilizing effect. Importance of these features was validated through numerical experiments with experimental data of other QH-mode plasmas in DIII-D. All the results show that MHD stability properties of QH-mode plasma can be obtained in case that pedestal foot is close to LCFS, ion diamagnetic drift frequency is large due to high ion temperature, and strong rotation shear exists near pedestal.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Transport-driven toroidal rotation with general viscosity profile
Abstract Using the assumption of a weak normalized turbulent viscosity, usually valid in practice, the modulated-transport model (Stoltzfus-Dueck 2012 Phys. Plasmas 19 055908) is generalized to allow the turbulent transport coefficient to vary in an arbitrary way on radial and poloidal position. The new approach clarifies the physical interpretation of the earlier results and significantly simplifies the calculation, via a boundary-layer asymptotic method. Rigorous detailed appendices verify the result of the simple boundary-layer calculation, also demonstrating that it achieves the claimed order of accuracy and providing a concrete prediction for the strong plasma flows in the immediate vicinity of the last closed flux surface. The new formulas are used to predict plasma rotation at the core-edge boundary, in cases with and without externally applied torque. Dimensional formulas and extensive discussion are provided, to support experimental application of the new model.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
The impact of kinetic and global effects on ideal ballooning 2nd stable pedestals of conventional and low aspect-ratio tokamaks
The EPED model (Snyder et al 2011 Nucl. Fusion 51 103016) has had success in describing the pedestal structure of Type-I ELM and QH-mode plasmas in tokamaks, by combining kinetic ballooning mode (KBM) and peeling–ballooning (PB) constraints. Within EPED, the KBM constraint is often approximated by a technique using calculated ideal ballooning mode (IBM) thresholds, fit to a functional form designed to capture non-local effects. It has been noted that quantitative differences between local ideal MHD and gyro-kinetic (GK) ballooning stability can be larger at low aspect ratio. KBM critical pedestals are consistent with observations in initial studies on conventional and spherical tokamaks. In this work, the application of a reduced model for the calculation of the kinetic ballooning stability boundary is presented based on a novel and newly developed gyro-fluid system (GFS) code (Staebler et al 2023 Phys. Plasmas 30 102501). GFS is observed to capture KBMs in DIII-D as well as the NSTX pedestals, opening a route to integrating this model into EPED. Finally, high but finite $n$ global ballooning modes are observed to limit the access to the local 2nd stability and thus provide a transport mechanism that constrains the pedestal evolution with $β_{p,\textrm{ped}}$. The high $n$ global ballooning stability is approximated by its ideal MHD analog using ELITE. It is shown that nearly-local high $n$ modes with $k_yρ_s$ ~ $0.25 - 0.5$ can provide a proxy for the critical $β_{p,\textrm{ped}}$ when a 2nd stable access exists on DIII-D plasmas. The use of GFS and ELITE scaling in EPED provides improved agreement to EPED1 in an initial comparison with DIII-D pedestal data.
Anastopoulos Tzanis, Michail Savvas [Oak Ridge Nat↗
The role of isotope mass on neutral fueling and density pedestal structure in the DIII-D tokamak
Abstract Experimental measurements on DIII-D of hydrogen neutral penetration lengths ( λ n 0 ) on the high field side (HFS) are longer by a factor of 2 than for deuterium consistent with the thermal velocity ratio for neutrals at the same temperature ( v t h H / v t h D = 2 ) . This ratio is constant for both low and high pedestal electron density. At low pedestal density ( n e ∼ 4 × 10 19 m − 3 ) , the neutral penetration length is greater than the density pedestal width for both isotopes, and the additional 40% increase of neutral penetration in hydrogen widens the pedestal by the same amount. As the density pedestal height increases ( n e ∼ 6 × 10 19 m − 3 ) , the neutral penetration lengths drop below the density pedestal widths for both isotopes, and the increased penetration of hydrogen has no increased effect on the pedestal width compared to deuterium. Extrapolating to future reactor-relevant high electron density pedestals, the isotope-mass change in neutral fueling on the HFS from the deepest neutral penetration of hydrogen, to the shortest neutral penetration of tritium will be negligible (0.2–0.4 cm) in comparison to estimates of the density pedestal width (6–8.5 cm).
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Quasilinear modeling of heat flux from microtearing turbulence
Microtearing (MT) turbulence affects plasma confinement and profile evolution in many different magnetic-confinement scenarios, ranging from tokamak core plasmas to the H-mode pedestal and from spherical tokamaks to reversed-field pinches. Thus, an urgent need exists to design and test reduced models of MT turbulence and transport. Here, a heuristic quasilinear model is composed and verified by comparing its predictions against nonlinear MT simulations. It is found to yield good predictions of magnetic flutter transport as key parameters are varied: the collision frequency, the electron temperature gradient, and the normalized plasma pressure.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗