arXiv subjects

D. R. Hatch

Publications and source records attributed to D. R. Hatch.

18 recordsLinked to original sources

arXiv2026

Modeling Temperature Profiles in the Pedestal of NSTX with Reduced Models

This paper describes new modeling capabilities for predicting H-mode pedestal profiles in spherical tokamaks. Temperature profiles for NSTX discharges 132543 and 132588 are modeled by coupling the \textsc{astra} transport solver with neoclassical transport and gyrokinetic-based reduced models for electron temperature gradient (ETG) and kinetic ballooning mode (KBM) instabilities. A quasi-linear surrogate model for ion-scale transport is developed using linear \textsc{gene} simulations, requiring only a single free parameter calibrated to one discharge. Time-evolving the temperatures with fixed density yields good agreement with experiments for both discharges. Systematic analysis of the transport mechanisms reveals that neoclassical transport is huge across the entire pedestal region for the ion channel. ETG turbulence is large in the plasma edge and low density gradient region, contributing substantially to the electron channel. However, KBM/MHD-like modes also drive significant transport in both the ion and electron thermal channels, making them essential for accurate pedestal modeling. Further refinements, including explicit $E \times B$ shear suppression and scaled ETG transport, produce quantitative but not qualitative improvements. This work lays the foundation for predictive modeling of future devices.

physics.plasm-ph↗

arXiv2025

Turbulent Transport-Limited Pedestals in Tokamaks

H-mode operation of tokamak fusion plasmas free of dangerous Type 1 edge-localized-modes (ELMs) requires a non-ELM mechanism for saturating the edge pedestal growth. One possible mechanism is turbulent transport. We introduce a transport threshold model to find pedestal width-height scalings for turbulent transport-limited pedestals. The model is applied to electron heat transport resulting from electron-temperature-gradient (ETG) turbulence. The width-height scalings are highly sensitive to the relative contribution of density and temperature to the pedestal pressure. Pressure that builds up mainly through temperature is more likely to be transport-limited, and hence ELM-free. A relative radial inward shift of the temperature to density pedestal location is also more likely to transport-limit the pedestal. A second constraint such as flow shear is required to saturate pedestal growth. We also calculate width-height transport scalings resulting from particle and heat transport arising from ETG and kinetic-ballooning-mode turbulence. Comparisons are performed for ELMy and ELM-free experiments in MAST-U, NSTX, and DIII-D. This is a first step towards a pedestal width-height scaling for transport-limited ELM-free pedestals.

physics.plasm-ph↗

arXiv2025

Direct Comparison of Gyrokinetic and Fluid Scrape-Off Layer Simulations

Typically, fluid simulations are used for tokamak divertor design. However, fluid models are only valid if the SOL is highly collisional, an assumption that is valid in many present day experiments but is questionable in the high-power scenarios envisioned for burning plasmas and fusion pilot plants. This paper reports on comparisons between fluid and kinetic simulations of the scrape off layer (SOL) for parameters and geometry representative of the Spherical Tokamak for Energy Production (STEP) fusion pilot plant. The SOLPS-ITER (fluid) and Gkeyll (gyrokinetic) codes are operated in a two-dimensional (2D) axisymmetric mode, which replaces turbulence with ad-hoc diffusivities. In kinetic simulations, we observe that the ions in the upstream SOL experience significant mirror trapping. This substantially increases the upstream temperature and has important implications for impurity dynamics. We show that the mirror force, which is excluded in SOLPS's form of fluid equations, enhances the electrostatic potential drop along the field line in the SOL. We also show that the assumption of equal main ion and impurity temperatures, which is made in commonly used fluid codes, is invalid. The combination of these effects results in superior confinement of impurities to the divertor region in kinetic simulations, consistent with our earlier predictions. This effect can be dramatic, reducing the midplane impurity density by orders of magnitude. These results indicate that in reactor-like regimes the tolerable downstream impurity densities may be higher than would be predicted by fluid simulations, allowing for higher radiated power while avoiding unacceptable core contamination. Our results highlight the importance of kinetic simulations for divertor design and optimization for fusion pilot plants.

physics.plasm-ph↗

arXiv2024

The effect of separatrix density and PFC material on H-mode confinement in the ITPA global H-mode database

Recent data, added to the ITPA global H-mode database [1] for ASDEX-U [2] and JET-ILW, reveals that the separatrix density $n_{sep}$ has a correlation with the H20 factor (Confinement time relative to the ITPA20-IL scaling)[1]. These trends are analyzed in detail. They are not a result of proximity to the density limit. The normalized $n_{sepN} = n_{sep} / \bar{n}$ is introduced, motivated by theory ($\bar{n}$ is the average density). The trends in $n_{sepN}$ can be understood in terms of the two main mechanisms of pedestal characteristics -- MHD stability and recently developed theories of gyrokinetic transport. Careful analysis shows these mechanisms can be distinguished in the data. The most dramatic improvement in confinement time arises primarily from reductions in pedestal transport. A new definition of density peaking that includes core peaking is found to best explain H20 when advanced H-modes are included: $n_{sepN0} = n_{sep}/n(0)$, the inverse of the total density peaking from the separatrix to the axis. The highest H-factors are reached by the confluence of relatively low normalized $n_{sepN0}$ plus high Shafranov shift or poloidal beta. The importance of these two variables is also theoretically predicted from recent analysis of the gyrokinetic system, where a constraint can limit the access of ITG/TEM modes to free energy in equilibrium gradients. The Plasma Facing Component (PFC) material also shows a strong influence in the data. This is likely due to the importance of $n(0)/n_{sep}$ to attaining high H20, in conjunction with the known tendency for tungsten (W) to accumulate with density peaking and low transport. Preliminary results indicate that $n_{sepN0}$ might also be important with core ITBs.

physics.plasm-ph↗

arXiv2024

Stability and Transport of Gyrokinetic Critical Pedestals

A gyrokinetic threshold model for pedestal width-height scaling prediction is applied to multiple devices and to a shaping and aspect-ratio scan giving $Δ_{\mathrm{ped}} = 0.92 A^{1.04} κ^{-1.24} 0.38^δ β_{θ,\mathrm{ped}}^{1.05}$ for pedestal width $Δ_{\mathrm{ped}}$, aspect-ratio $A$, elongation $κ$, triangularity $δ$, and normalized pedestal height $β_{θ,\mathrm{ped}}$. We also find a width-transport scaling $Δ_{\mathrm{ped} } = 0.028 \left(q_e/Γ_e - 1.7 \right)^{1.5} \sim η_e ^{1.5}$ where $q_e$ and $Γ_e$ are turbulent electron heat and particle fluxes and $η_e = \nabla \ln T_e / \nabla \ln n_e$ for electron temperature $T_e$ and density $n_e$. Pedestals close to those limited by kinetic-ballooning-modes (KBMs) have modified turbulent transport properties compared to strongly driven KBMs. The role of flow shear is studied as a width-height scaling constraint and pedestal saturation mechanism for a standard and wide pedestal discharge.

physics.plasm-ph↗

arXiv2023

The free energy balance equation applied to gyrokinetic instabilities, the effect of the charge flux constraint, and application to simplified kinetic models

The free energy balance equation for gyrokinetic fluctuations is derived and applied to instabilities. An additional term due to electromagnetic sources is included. This can provide a simpler way to compute the free energy balance in practical applications, and is also conceptually clarifying. The free energy balance, by itself, is not sufficient to determine an eigenfrequency. The preceding results are derived in general geometry. The charge flux constraint in gyrokinetics can provide a necessary additional relation, and the combination of these two can be equivalent to a dispersion relation. The charge flux constraint can prevent the appearance of an unstable eigenmode even though the free energy balance would allow strongly growing fluctuations. The application of these concepts to simplified kinetic models in simplified geometry is also indicated.

physics.plasm-ph↗

arXiv2023

Modeling electron temperature profiles in the pedestal with simple formulas for ETG transport

This paper reports on the refinement (building on Ref.~\cite{hatch_22}) and application of simple formulas for electron heat transport from electron temperature gradient (ETG) driven turbulence in the pedestal. The formulas are improved by (1) improving the parameterization for certain key parameters and (2) carefully accounting for the impact of geometry and shaping in the underlying gyrokinetic simulation database. Comparisons with nonlinear gyrokinetic simulations of ETG transport in the MAST pedestal demonstrate the model's applicability to spherical tokamaks in addition to standard aspect ratio tokamaks. We identify bounds for model applicability: the model is accurate in the steep gradient region, where the ETG turbulence is largely slab-like, but accuracy decreases as the temperature gradient becomes weaker in the pedestal top and the instabilities become increasingly toroidal in nature. We use the formula to model the electron temperature profile in the pedestal for four experimental scenarios while extensively varying input parameters to represent uncertainties. In all cases, the predicted electron temperature pedestal exhibits extreme sensitivity to separatrix temperature and density, which has implications for core-edge integration. The model reproduces the electron temperature profile for high $η_e = L_{ne}/L_{Te}$ scenarios but not for low $η_e$ scenarios in which microtearing modes have been identified. We develop a proof-of-concept model for MTM transport and explore the relative roles of ETG and MTM in setting the electron temperature profile. We propose that pedestal scenarios predicted for future devices should be tested for compatibility with ETG transport.

physics.plasm-ph↗

arXiv2022

Gyrokinetic Simulations Compared with Magnetic Fluctuations Diagnosed with a Faraday-Effect Radial Interferometer-Polarimeter in the DIII-D pedestal

Experimental data on electromagnetic fluctuations in DIII-D, made available by the Faraday-effect Radial Interferometer-Polarimeter (RIP) diagnostic, is examined in comparison with detailed gyrokinetic simulations using Gyrokinetic Electromagnetic Numerical Experiment (GENE). The diagnostic has the unique capability of making internal measurements of fluctuating magnetic fields $\frac{\int n_e δB_r dR}{\int n_e dR}$. Local linear simulations identify microtearing modes (MTMs) over a substantial range of toroidal mode numbers (peaking at $n=15$) with frequencies in good agreement with the experimental data. Local nonlinear simulations reinforce this result by producing a magnetic frequency spectrum in good agreement with that diagnosed by RIP. Simulated heat fluxes are in the range of experimental expectations. However, magnetic fluctuation amplitudes are substantially lower than the experimental expectations. Possible sources of this discrepancy are discussed, notably the fact that the diagnostics are localized at the mid-plane -- the poloidal location where the simulations predict the fluctuation amplitudes to be smallest. Despite some discrepancies, several connections between simulations and experiments, combined with general criteria discriminating between potential pedestal instabilities, strongly point to MTMs as the source of the observed magnetic fluctuations.

physics.plasm-ph↗

arXiv2022

Three-Dimensional Inhomogeneity of Electron-Temperature-Gradient Turbulence in the Edge of Tokamak Plasmas

Nonlinear multiscale gyrokinetic simulations of a Joint European Torus edge pedestal are used to show that electron-temperature-gradient (ETG) turbulence has a rich three-dimensional structure, varying strongly according to the local magnetic-field configuration. In the plane normal to the magnetic field, the steep pedestal electron temperature gradient gives rise to anisotropic turbulence with a radial (normal) wavelength much shorter than in the binormal direction. In the parallel direction, the location and parallel extent of the turbulence are determined by the variation in the magnetic drifts and finite-Larmor-radius (FLR) effects. The magnetic drift and FLR topographies have a perpendicular-wavelength dependence, which permits turbulence intensity maxima near the flux-surface top and bottom at longer binormal scales, but constrains turbulence to the outboard midplane at shorter electron-gyroradius binormal scales. Our simulations show that long-wavelength ETG turbulence does not transport heat efficiently, and significantly decreases overall ETG transport -- in our case by $\sim$40 \% -- through multiscale interactions.

physics.plasm-ph↗

arXiv2021

A Learned Closure Method Applied to Phase Mixing in a Turbulent Gradient-Driven Gyrokinetic System in Simple Geometry

We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system - temperature gradient driven turbulence in an unsheared slab. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition (SVD). Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with other closures schemes over a broad range of the relevant 2D parameter space (collisionality and gradient drive). We find that the turbulent kinetic system produces phase mixing rates much lower than the linear expectations, which the LMM closure is capable of capturing. We also compare radial heat fluxes. A Hammett-Perkins closure, generalized to include collisional effects, is quite successful throughout the parameter space, producing ~14% Root-Mean-Square (RMS) error. The LMM closure is also very effective: when trained at three (two) points (in a 35 point parameter grid), the LMM closure produces 9% (12%) RMS errors. The LMM procedure can be readily generalized to other closure problems.

physics.plasm-ph↗

arXiv2020

Microtearing modes as the source of magnetic fluctuations in the JET pedestal

We report on a detailed study of magnetic fluctuations in the JET pedestal, employing basic theoretical considerations, gyrokinetic simulations, and experimental fluctuation data, to establish the physical basis for their origin, role, and distinctive characteristics. We demonstrate quantitative agreement between gyrokinetic simulations of microtearing modes (MTMs) and two magnetic frequency bands with corresponding toroidal mode numbers n=4 and 8. Such disparate fluctuation scales, with substantial gaps between toroidal mode numbers, are commonly observed in pedestal fluctuations. Here we provide a clear explanation, namely the alignment of the relevant rational surfaces (and not others) with the peak in the omega star profile, which is localized in the steep gradient region of the pedestal. We demonstrate that a global treatment is required to capture this effect. Nonlinear simulations suggest that the MTM fluctuations produce experimentally-relevant transport levels and saturate by relaxing the background electron temperature gradient, slightly downshifting the fluctuation frequencies from the linear predictions. Scans in collisionality are compared with simple MTM dispersion relations. At the experimental points considered, MTM growth rates can either increase or decrease with collision frequency depending on the parameters thus defying any simple characterization of collisionality dependence.

physics.plasm-ph↗

arXiv2020

Gyrokinetics investigations of an I-mode pedestal on Alcator C-Mod

Naturally stable to ELMs, and with widths larger than EPED predictions, the I-modes are an excellent laboratory for investigating the role of drift micro-instabilities in pedestals since I-mode pedestal are not "limited" by MHD instabilities. We present here a study based on gyrokinetic simulations (using GENE) to model fluctuations and heat transport in the I-mode pedestals in C-Mod. We find the Weakly Coherent Mode observed on C-Mod I-mode to be an electrostatic Ion Temperature Gradient/Impurity density gradient (ITG/Impurity) driven mode. The ITG/Impurity mode match frequency and the impurity confinement time observed on the I-mode. Nonlinear ETG simulations, can match experimental heat flux with profile adjustment well within experimental error bars. Simulations, varying impurity level (Zeff) and temperature and density profiles (within experimental error bars), are used to probe the sensitivity of fluctuations and transport.

physics.plasm-ph↗

arXiv2019

Gyrokinetic analysis and simulation of pedestals, to identify the culprits for energy losses using fingerprints

Fusion performance in tokamaks hinges critically on the efficacy of the Edge Transport Barrier (ETB) at suppressing energy losses. The new concept of fingerprints is introduced to identify the instabilities that cause the transport losses in the ETB of many of today's experiments, from widely posited candidates. Analysis of the Gyrokinetic-Maxwell equations, and gyrokinetic simulations of experiments, find that each mode type produces characteristic ratios of transport in the various channels: density, heat and impurities. This, together with experimental observations of transport in some channel, or, of the relative size of the driving sources of channels, can identify or determine the dominant modes causing energy transport. In multiple ELMy H-mode cases that are examined, these fingerprints indicate that MHD-like modes are apparently not the dominant agent of energy transport; rather, this role is played by Micro-Tearing Modes (MTM) and Electron Temperature Gradient (ETG) modes, and in addition, possibly Ion Temperature Gradient (ITG)/Trapped Electron Modes (ITG/TEM) on JET. MHD-like modes may dominate the electron particle losses. Fluctuation frequency can also be an important means of identification, and is often closely related to the transport fingerprint. The analytical arguments unify and explain previously disparate experimental observations on multiple devices, including DIII-D, JET and ASDEX-U, and detailed simulations of two DIII-D ETBs also demonstrate and corroborate this.

physics.plasm-ph↗

arXiv2019

Direct Gyrokinetic Comparison of Pedestal Transport in JET with Carbon and ITER-Like Walls

This paper compares the gyrokinetic instabilities and transport in two representative JET pedestals, one (pulse 78697) from the JET configuration with a carbon wall (C) and another (pulse 92432) from after the installation of JET's ITER-like Wall (ILW). The discharges were selected for a comparison of JET-ILW and JET-C discharges with good confinement at high current (3 MA, corresponding also to low $ρ_*$) and retain the distinguishing features of JET-C and JET-ILW, notably, decreased pedestal top temperature for JET-ILW. A comparison of the profiles and heating power reveals a stark qualitative difference between the discharges: the JET-ILW pulse (92432) requires twice the heating power, at a gas rate of $1.9 \times 10^{22}e/s$, to sustain roughly half the temperature gradient of the JET-C pulse (78697), operated at zero gas rate. This points to heat transport as a central component of the dynamics limiting the JET-ILW pedestal and reinforces the following emerging JET-ILW pedestal transport paradigm, which is proposed for further examination by both theory and experiment. ILW conditions modify the density pedestal in ways that decrease the normalized pedestal density gradient $a/L_n$, often via an outward shift of the density pedestal. This is attributable to some combination of direct metal wall effects and the need for increased fueling to mitigate tungsten contamination. The modification to the density profile increases $η= L_n/L_T$ , thereby producing more robust ion temperature gradient (ITG) and electron temperature gradient driven instability. The decreased pedestal gradients for JET-ILW (92432) also result in a strongly reduced $E \times B$ shear rate, further enhancing the ion scale turbulence. Collectively, these effects limit the pedestal temperature and demand more heating power to achieve good pedestal performance.

physics.plasm-ph↗

arXiv2017

Plasma turbulence in the equatorial electrojet: A two-dimensional Hamiltonian fluid model

A nonlinear unified fluid model that describes the Equatorial Electrojet, including the Farley-Buneman and gradient-drift plasma instabilities, is defined and shown to be a noncanonical Hamiltonian system. Two geometric constants of motion for the model are obtained and shown to be Casimir invariants. A reformulation of the model shows the roles of the density-gradient scale-length ($L_n$) and the cross-field drift-velocity (${\upsilon}_E$) in controlling the dynamics of unstable modes in the growing, transition, and saturation phases of a simulation.

physics.plasm-ph↗

arXiv2017

Flow Shear Suppression of Pedestal Turbulence--A First Principles Theoretical Framework

A combined analytic and computational gyrokinetic approach is developed to address the question of the scaling of pedestal turbulent transport with arbitrary levels of $E \times B$ shear. Due to strong gradients and shaping in the pedestal, the instabilities of interest are not curvature-driven like the core instabilities. By extensive numerical (gyrokinetic) simulations, it is demonstrated that pedestal modes respond to shear suppression very much like the predictions of a basic analytic decorrelation theory. The quantitative agreement between the two provides us with a new dependable, first principles (physics based) theoretical framework to predict the efficacy of shear suppression in burning plasmas that lie in a low-shear regime not accessed by present experiments.

physics.plasm-ph↗

arXiv2016

Multiscale Equatorial Electrojet Turbulence: Energy Conservation, Coupling, and Cascades in a Baseline 2-D Fluid Model

Progress in understanding the coupling between plasma instabilities in the equatorial electrojet based on a unified fluid model is reported. A deeper understanding of the linear and nonlinear evolution and the coupling of the gradient-drift and Farley-Buneman instabilities is achieved by studying the effect of different combinations of the density-gradient scale-lengths (Ln) and cross-field (E?B) drifts on the plasma turbulence. Mechanisms and channels of energy transfer are illucidated for these multiscale instabilities. Energy for the unified model is examined, including the injected, conservative redistribution (between fields and scales), and ultimate dissipation. Various physical mechanisms involved in the energetics are categorized as sources, sinks, nonlinear transfer, and coupling to show that the system satisfies the fundamental law of energy Oonservation. The physics of the nonlinear transfer terms is studied to identify their roles in producing energy cascades { the transference of energy from the dominant unstable wavenumbers and driving irregularities of different scale-lengths. The theory of two-step energy cascading to generate the 3-meter plasma irregularities in the equatorial electrojet is verified. In addition, the nonlinearity of the system allows the possibility for a reverse energy cascading, responsible for generating large-scale plasma structures at the top of the electrojet.

physics.plasm-ph↗

arXiv2014

Electromagnetic stabilization of tokamak microturbulence in a high-$β$ regime

The impact of electromagnetic stabilization and flow shear stabilization on ITG turbulence is investigated. Analysis of a low-$β$ JET L-mode discharge illustrates the relation between ITG stabilization, and proximity to the electromagnetic instability threshold. This threshold is reduced by suprathermal pressure gradients, highlighting the effectiveness of fast ions in ITG stabilization. Extensive linear and nonlinear gyrokinetic simulations are then carried out for the high-$β$ JET hybrid discharge 75225, at two separate locations at inner and outer radii. It is found that at the inner radius, nonlinear electromagnetic stabilization is dominant, and is critical for achieving simulated heat fluxes in agreement with the experiment. The enhancement of this effect by suprathermal pressure also remains significant. It is also found that flow shear stabilization is not effective at the inner radii. However, at outer radii the situation is reversed. Electromagnetic stabilization is negligible while the flow shear stabilization is significant. These results constitute the high-$β$ generalization of comparable observations found at low-$β$ at JET. This is encouraging for the extrapolation of electromagnetic ITG stabilization to future devices. An estimation of the impact of this effect on the ITER hybrid scenario leads to a 20% fusion power improvement.

physics.plasm-ph↗