Gyrokinetic particle simulation of nonlinear evolution of mirror instability
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Peter Porazik↗
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Results for “nonlinear gyrokinetics”
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A novel approach to radially global gyrokinetic simulation using the flux-tube code stella
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70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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. Here our simulations show that long-wavelength ETG turbulence does not transport heat efficiently, and significantly decreases overall ETG transport—in our case by ~40%—through multiscale interactions.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Reduction or Enhancement of Stellarator Turbulence by Impurities
A systematic study of the impact of impurities on the turbulent heat fluxes is presented for the stellarator Wendelstein 7-X (W7-X) and, for comparison, the Large Helical Device and ITER. By means of nonlinear multispecies gyrokinetic simulations, it is shown that impurities, depending on the sign of their density gradient, can significantly enhance or reduce turbulent ion heat losses. For the relevant scenario of turbulence reduction, an optimal impurity concentration that minimizes the ion heat diffusivity emerges as a universal feature. This result demonstrates the potential of impurities for controlling turbulence and accessing enhanced confinement regimes in fusion plasmas and, in particular, in W7-X. Published by the American Physical Society 2024
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Feasibility Study: High-k Temperature (HiT) Fluctuation Diagnostic
The objective of the proposed research was to explore the feasibility of making measurements of high-k (electron-scale, ETG-relevant) electron temperature fluctuations in the core plasma of tokamaks and stellarators. We found that soft X-ray imaging combined with our novel pseudolocal tomographic algorithm enables local measurements of low-k (ion-scale, ITG/TEM and KBM/MTM relevant) electron temperature fluctuations in spherical tokamaks. The design parameters needed to consider deploying this new diagnostic are presented, and predictions for what the diagnostic would measure in L-mode and H-mode plasmas at NSTX-U, a high performance spherical tokamak in the USA, suggest that the new diagnostic can be used to study turbulence and transport over a wide range of plasma parameters, such as collisionality and plasma beta.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Importance of $\delta B_{\|}$ on ETG stability, turbulence, and transport in NSTX
This study employs electron-scale gyrokinetic simulations to investigate the electron temperature gradient (ETG) driven instabilities, turbulence, and transport in the pedestal region of the National Spherical Torus Experiment, comparing non-lithiated (narrow pedestal) and lithiated (wide pedestal) scenarios. Our findings reveal that, in the non-lithiated case, a branch of strongly unstable ETG modes exhibiting finite parallel magnetic field fluctuations ($\delta B_{\parallel} \neq 0$) emerges at the pedestal top and upper density pedestal region. This branch is uncovered only when $\delta B_{\parallel}$ is retained in the simulations and is associated with substantial electrostatic electron heat flux. This region of strong ETG transport corresponds to the only region in the plasma where the pressure gradient is far below the critical gradient for kinetic ballooning modes. We investigated the origin of this finite $\delta B_{\parallel}$ ETG branch by analyzing the gyrokinetic field equations. Nonlinear saturation is also analyzed and contrasted for simulations with and without $\delta B_{\parallel}$. In contrast with the nonlithiated case, ETG modes in the lithiated case produce substantial transport in the steep gradient region, but are negligible at the pedestal top.
ETG↗
Electron temperature gradient instability and transport analysis in NSTX and NSTX-U plasmas
Extensive linear and nonlinear simulations to study electron temperature gradient (ETG) stability and thermal transport in National Spherical Torus Experiment (NSTX) and NSTX-U plasmas were performed using the fully electromagnetic gyrokinetic code CGYRO. Linear simulations were performed to determine ETG thresholds in different discharges, showing that ETG modes in spherical tokamaks can present different scalings compared to conventional aspect-ratio tokamaks. Nonlinear gyrokinetic simulations were conducted for selected cases to calculate electron thermal transport and compare to experimental values. Results are also compared with those of ETG modes in the multi-mode model and the Trapped-Gyro-Landau-Fluid reduced model codes, to better understand their applicability in spherical tokamaks.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
ETG turbulent transport in the Mega Ampere Spherical Tokamak (MAST) pedestal
The results of a gyrokinetic analysis of turbulent transport driven by the electron temperature gradient (ETG) in the MAST pedestal are presented. Local nonlinear simulations from the gyrokinetic code, GENE, show that heat flux produced by ETG turbulence is 10%–30% of the total applied heating power in the upper pedestal and pedestal top during both the pre-edge-localized mode (ELM) (80%–99% inter-ELM period) and post-ELM (0%–20%) periods. Increasing strongly with the ETG, the ETG transport appears to be stiff. Considering radiation losses, ion thermal transport, and the strong sensitivity of the transport to the ETG, we propose that ETG transport is a plausible mechanism mediating the inter-ELM temperature profile on MAST. Cognizant of the possibility that sharp variations in the pedestal profiles may violate the local approximation, we conducted global nonlinear simulations; the results are in good agreement with local simulations except near the pedestal top, where extended radial structures and high transport levels (far beyond experimental) develop in the local simulations. We quantify and parameterize the discrepancy between local and global simulations by calculating the ratio of the radial correlation length to a length scale representative of the profile curvature. When this ratio is sufficiently small, local and global simulations agree as expected.
ETG↗
Metriplectic foundations of gyrokinetic Vlasov–Maxwell–Landau theory
Here, this Letter reports on a metriplectic formulation of a collisional, nonlinear full-f electromagnetic gyrokinetic theory compliant with energy conservation and monotonic entropy production. In an axisymmetric background magnetic field, the toroidal angular momentum is also conserved. Notably, a new collisional current, contributing to the gyrokinetic Maxwell–Ampère equation and the gyrokinetic charge conservation law, is discovered.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Comparison of Saturation Rules Used for Gyrokinetic Quasilinear Transport Modeling
Theory-based transport modeling has been widely successful and is built on the foundations of quasilinear theory. Specifically, the quasilinear expression of the flux can be used in combination with a saturation rule for the toroidal mode amplitude. Most transport models follow this approach. Saturation rules are heuristic and difficult to rigorously derive. We compare three common saturation rules using a fairly accurate quasilinear expression for the fluxes computed using local linear gyrokinetic simulation. We take plasma parameters from experimental H-mode profiles and magnetic equilibrium and include electrons, deuterium, and carbon species. We find that the various saturation rules provide qualitatively similar behavior. This may help to explain why the different theory-based transport models can all predict core tokamak profiles reasonably well. Comparisons with nonlinear local and global gyrokinetic simulations are discussed.
Parker, Scott E. (ORCID:000000030942630X)↗
ETG turbulence in a tokamak pedestal
This paper explores the fundamental characteristics of electron-temperature-gradient (ETG)-driven turbulence in the tokamak pedestal. The extreme gradients in the pedestal produce linear instabilities and nonlinear turbulence that are distinct from the corresponding ETG phenomenology in the core plasma. The linear system exhibits multiple (greater than ten) unstable eigenmodes at each perpendicular wave vector, representing different toroidal and slab branches of the ETG instability. Proper orthogonal decomposition of the nonlinear fluctuations reveals no clear one-to-one correspondence between the linear and nonlinear modes for most wave vectors. Moreover, nonlinear frequencies deviate strongly from those of the linear instabilities, with spectra peaking at positive frequencies, which is opposite the sign of the ETG instability. The picture that emerges is one in which the linear properties are preserved only in a narrow range of k-space. Outside this range, nonlinear processes produce strong deviations from both the linear frequencies and eigenmode structures. This is interpreted in the context of critical balance, which enforces alignment between the parallel scales and fluctuation frequencies. We also investigate the nonlinear saturation processes. We observe a direct energy cascade from the injection scale to smaller scales in both perpendicular directions. However, in the bi-normal direction, there is also nonlocal inverse energy transfer to larger scales. Neither streamers nor zonal flows dominate the saturation.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Nonlinear saturation of reverse shear Alfvén eigenmodes induced by kinetic electrons
A strong nonlinear saturation mechanism of the reverse shear Alfvén eigenmode (RSAE) induced by thermal electrons is observed in gyrokinetic $\delta$$f$ particle-in-cell simulation. This nonlinear effect occurs at moderate mode amplitude, $\delta$$B$ ⟂ /$B$ < 10 -3 , and is associated with the electron parallel streaming along the perturbed magnetic field lines, the term v $\|$ $\frac{δΒ_{⟂}}{B}$ ∙ ∇$\delta$$f$, in the electron drift-kinetic equation. In the case of an n = 4 RSAE, where n is the toroidal mode number, this magnetic fluttering nonlinearity leads to strong mode coupling and broadening of the saturation spectrum. The nonlinear components, which are highly damped through the interaction between thermal electrons and the parallel electric field, modifies the RSAE mode structure and suppresses energetic particle drive significantly. The split-weight scheme (Chen and Parker 2007 J. Comput. Phys. 220 839–55) is used to simulate kinetic electrons.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Global gyro-kinetic ion temperature gradient and trapped electron mode turbulence modelling in X -point geometry in negative and positive triangularity
Comparative modelling of ion temperature gradient (ITG)/trapped electron mode (TEM) turbulence in negative (NT) and positive (PT) triangularity plasma shapes was done using the nonlinear global full-f gyrokinetic particle code JOREK-GK in the realistic X-point tokamak geometry including the Scrape Off Layer (SOL) for TCV and DIII-D parameters. A comparison of JOREK-GK code with the gyrokinetic codes GS2 and GENE was done using NT/PT triangularity TCV L-modes parameters showing good agreement between codes in linear growth rates and clear beneficial effect of NT as compared to PT. Global non-linear modelling of the ITG/TEM saturated turbulence for realistic DIII-D NT pulses was done and compared with numerically constructed PT equilibrium with the same plasma profiles. Existence of longer correlation length of density fluctuations in PT compared to NT was demonstrated. Stronger and more sheared zonal flows are generated via Reynolds stress in NT compared to PT. These factors are stabilizing for TEM/ITG turbulence in NT and lead to smaller heat fluxes and heat conductivities in NT compared to PT configuration. Weak dependence of plasma confinement on collisionality and plasma rotation was found in modelling of DIII-D NT shots similar to the experiment. The confinement scaling with normalized ion gyro-radius ρ* was estimated both for NT and PT. Bohm-like scaling was obtained in both configurations, however with better confinement for NT compared to PT which could be favourable factor for reactor size machines.
ITG↗
Implicit full-F simulations of neoclassical ion transport
The development of implicit time integration capabilities for axisymmetric full-F continuum simulations of ion neoclassical transport is reported. The approach involves the implicit treatment of the gyrokinetic Vlasov equation coupled to the nonlinear Fokker–Planck collision model in the long-wavelength limit approximation. To facilitate implicit simulations, advanced preconditioning of individual physics operators is developed, and a global multi-physics preconditioner is constructed by adopting an operator splitting methodology. The algorithm is implemented in the finite-volume code COGENT and is applied to study neoclassical transport properties for both the main ion species and the lithium impurity species in the closed-field-line region of the LTX- β tokamak. The implicit COGENT simulations elucidate the role of non-local transport effects, while demonstrating substantial speedup over the corresponding explicit approach.
Dorf, Mikhail [Lawrence Livermore National Laborat↗
Saturation of the kinetic ballooning instability due to the electron parallel nonlinearity
The electron parallel nonlinearity (EPN) is implemented in the gyrokinetic particle-in-cell turbulence code GEM [Y. Chen and S. E. Parker, J. Comp. Phys. 220, 839 (2007)]. Application to the Cyclone Base Case reveals a strong effect of EPN on the saturated heat transport above the kinetic ballooning mode (KBM) threshold. Evidence is provided to show that the strong effect is associated with the electron radial motion due to magnetic fluttering, which turns fine structures of the KBM eigenmode in radius into fine structures in velocity and increases the magnitude of the EPN term in the kinetic equation.
Gyrokinetic simulations↗
Examination of stiff ion temperature gradient mode physics in simulations of DIII-D H-mode transport
A systematic evaluation of gyrokinetic and gyrofluid model predictions of ion temperature gradient (ITG) stability and transport using parameters from DIII-D high confinement mode (H-mode) plasmas has been performed. The nonlinear CGYRO code is used to make the gyrokinetic predictions, and the quasilinear TGLF model for the corresponding gyrofluid predictions. The assessments are made at three radii (normalized toroidal flux ρtor = 0.4, 0.55, and 0.7) in three different plasma scenarios with varying levels of neutral beam heating and torque. For each of the nine cases (3 radii × 3 scenarios) considered, ITG turbulence is found to be the dominant long-wavelength instability and transport mechanism. The inclusions of both transverse magnetic fluctuations and dynamic fast beam ions are stabilizing for all cases considered, with strongest effects seen at ρor = 0.4 where the fast ion population and normalized plasma pressure β = 2μ0nT/B2 are highest. The further inclusion of parallel magnetic fluctuations does not have a meaningful impact on the ITG turbulence in these scenarios, but does destabilize (in combination with fast ions) new high-frequency instabilities at ρtor = 0.4 in the high power scenarios. In each case the linear and nonlinear ITG critical gradients are predicted to be lower than the measured ITG scale lengths and their associated uncertainties. Inclusion of equilibrium flow shear in the transport predictions generally leads to an upshift in effective critical gradient rather than a qualitative change in the predicted stiffness, with stronger responses typically seen in the gyrokinetic predictions than in the gyrofluid results. However, in most cases these upshifted gradients still remain below the measured values and their uncertainties. Although the predicted critical gradients are below the measured gradients, both models predicted flux-matching gradients consistent with measured values in six of the nine cases considered, with no clear systematic over- or underprediction. Thus, while the experimental ion temperature profiles do not appear to be closely pinned to the ITG critical gradient, both gyrokinetic and gyrofluid models are able to accurately match the measured gradients reasonably well in most cases.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Gyrokinetic Simulation of Tokamak Fusion Plasmas
The final technical report for project DE‐FG02‐08ER54954 “Gyrokinetic Simulation of Tokamak Fusion Plasmas”. This report covers the entire period of the sponsored project. This grant supported in part the salary, travel, and research supplies for the principal investigator Scott E. Parker, graduate research associate Stefan Tirkas, who is a Ph.D. graduate student in the Physics Department. Postdoctoral Scholar Dr. Neeraj Kumar is also collaborating on this project. The main goals of the project are to investigate the nonlinear saturation of electron scale turbulence using gyrokinetic theory and simulation and to investigate impurity transport in the edge pedestal region.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Collaborative Research: Particle Simulation of Collisionless Magnetic Reconnection Under Finite Guide Field (Final Technical Report)
The project investigated 3-D linear instabilities of Harris current sheet under a realistic ion-to-electron mass ratio and a finite guide field. The excitation and 3-D properties of lower hybrid drift instability (LHDI), along with two new instabilities were demonstrated. The report presents the nonlinear properties of current sheet instabilities by employing Gyrokinetic electron and Fully kinetic ion (GeFi) particle simulation code. The GeFi simulation results are compared with fully kinetic PIC simulations.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗