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At least 19 records

Intrinsic Toroidal Rotation Driven by Turbulent and Neoclassical Processes in Tokamak Plasmas from Global Gyrokinetic Simulations

Gyrokinetic tokamak plasmas can exhibit intrinsic toroidal rotation driven by the residual stress. While most studies have attributed the residual stress to the parallel-momentum flux from the turbulent E × B motion, the parallel-momentum flux from the drift-orbit motion (denoted $Π^D_\parallel$) and the E × B-momentum flux from the E × B motion (denoted $Π_{E×B}$) are often neglected. Here, we use the global total-f gyrokinetic code XGC to study the residual stress in the core and the edge of a DIII-D H-mode plasma. Numerical results show that both $Π^D_\parallel$ and $Π_{E×B}$ make up a significant portion of the residual stress. In particular, $Π^D_\parallel$ in the core is higher than the collisional neoclassical level in the presence of turbulence, while in the edge it represents an outflux of countercurrent momentum even without turbulence. Using a recently developed “orbit-flux” formulation, we show that the higher-than-neoclassical-level $Π^D_\parallel$ in the core is driven by turbulence, while the outflux of countercurrent momentum from the edge is mainly due to collisional ion orbit loss. In conclusion, these results suggest that $Π^D_\parallel$ and $Π_{E×B}$ can be important for the study of intrinsic toroidal rotation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A new synthetic correlation electron cyclotron emission diagnostic for validating nonlinear gyrokinetic simulations of electron temperature turbulence

To validate nonlinear gyrokinetic simulations of electron temperature turbulence, the experimental correlation electron cyclotron emission (CECE) measurements are to be compared using a synthetic CECE diagnostic, which generates modeled CECE measurement quantities by implementing realistic measurement parameters (e.g., spatial and wavenumber resolutions, radial location, etc.) to nonlinear gyrokinetic simulations. In this work, we calculate the radial and vertical spatial and wavenumber transfer functions, which are defined by the electron cyclotron emission emissivity radial profile and vertical probing antenna pattern, respectively. These transfer functions are applied to nonlinear gyrokinetic simulations of electron temperature turbulence using the continuum gyrokinetic code. A simultaneous comparison of the experimental electron temperature turbulence power spectrum and root-mean-square (RMS) level, as well as the radial correlation length with the new synthetic CECE diagnostic at a core location ρ ∼ 0.75 in an L-mode DIII-D tokamak plasma, is presented. Here, the preliminary result shows that the synthetic CECE output underestimates the RMS level by ∼42% and overestimates the radial correlation length by ∼40%.

Cyclotron radiation↗

Plasma edge and scrape-off layer turbulence in gyrokinetic simulations of negative triangularity plasmas

Gyrokinetic simulations in the long-wavelength or drift-kinetic limit are carried out of DIII-D inner-wall-limited (IWL) plasmas to investigate the effect of triangularity on edge and scrape-off layer (SOL) turbulence. The effect of neutral interactions and triangularity on plasma blobs is explored due to the impact blobs can have in setting the SOL width or introducing impurities through interactions with plasma-facing components. Seeded blob simulations with neutrals in shaped SOL scenarios demonstrate that increasing elongation, triangularity, or Shafranov shift decreases radial blob velocities, but neutral interactions have a minor effect. Fully turbulent simulations of DIII-D IWL plasmas include both open- and closed-field-line regions. The negative triangularity (NT) simulation has lower average core T e , lower normalized T e fluctuations, and lower fluxes, but a greater number of coherent structures (blobs) identified with increased size and velocity, on average. Density and electron temperature profiles are within a factor of 2 of experimental values. In conclusion, the increased trapped electron particle fraction in NT simulations is consistent with previous studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Gyrokinetic simulation of pedestal degradation correlated with enhanced magnetic turbulence in a DIII-D ELMy H-mode discharge

Gyrokinetic simulation of a dedicated pedestal density ramping-up discharge on DIII-D can reproduce the enhancement of magnetic turbulence in the pedestal, which is identified to be caused by micro-tearing modes (MTMs). Here, an increase of MTM amplitude results in higher electron thermal diffusivity, consistent with experimentally observed lower electron temperature gradient and degraded pedestal height. Gyrokinetic simulation identifies the major cause of MTM enhancement to be the increase of collisionality, which has a significant impact on the MTM intensity and is beyond the description of any (quasi-)linear theory.

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↗

Gyrokinetic simulations of the effects of magnetic islands on microturbulence in KSTAR

Gyrokinetic simulations are utilized to study effects of magnetic islands (MIs) on the ion temperature gradient (ITG) turbulence in the KSTAR tokamak with resonant magnetic perturbations. Simulations show that the transport is controlled by the nonlinear interactions between the ITG turbulence and self-generated vortex flows and zonal flows, leading to an anisotropic structure of fluctuation and transport on the poloidal plane and in the toroidal direction. MIs greatly enhance turbulent transport of both particle and heat. The turbulent transport exhibits variations in the toroidal direction, with transport through the resonant layer near the island X-point being enhanced when the X-point is located at the outer mid-plane. A quantitative agreement is shown between simulations and KSTAR experiments in terms of time frequency and perpendicular wavevector spectrum.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Global gyrokinetic simulations of electrostatic microturbulent transport in LHD stellarator with boron impurity

Abstract Global gyrokinetic simulations of electrostatic microturbulent transport for discharge # 166256 of the Large Helical Device stellarator in the presence of boron impurity show the co-existence of the ion temperature gradient (ITG) turbulence and trapped electron mode (TEM) turbulence before and during boron powder injection. ITG turbulence dominates in the core, whereas TEM dominates near the edge, consistent with the experimental observations. Linear TEM frequency increases from ∼ 80 kHz to ∼ 100 kHz during boron injection, and ITG frequency decreases from ∼ 20 kHz to ∼ 13 kHz, consistent with the experiments. The poloidal wave number spectrum is broad for both ITG (0–0.5 mm −1 ) and TEM (0–0.25 mm −1 ). The nonlinear simulations with boron impurity show a reduction in the heat conductivity compared to the case without boron. The comparison of the nonlinear transport before and during boron injection shows that the ion heat transport is substantially reduced in the region where the TEM is dominant. However, the average electron heat transport throughout the radial domain and the average ion heat transport in the region where the ITG is dominant are similar. The simulations with boron show the effective heat conductivity values qualitatively agree with the estimate obtained from the experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Global Gyrokinetic Simulations of Isotope Effects under Ambipolar Electric Fields and Advances Toward Whole-Volume Modeling

We review global gyrokinetic simulation studies on plasma transport in the Large Helical Device using XGC-S. XGC-S is an extended version of X-point Gyrokinetic Code for stellarators and has been progressively verified throughout the code development process. Verification tests of neoclassical transport successfully demonstrate the generation of an ambipolar electric field due to ripple-trapped particles. We perform quasi-linear analyses of the ion temperature gradient mode under the influence of the ambipolar electric field. The results reveal that the ambipolar electric field and the heavy hydrogen component in mixed isotope plasmas can lead to the favorable isotope effect observed in recent deuterium experiments. We also present recent efforts in code development toward whole-volume simulations, including the helical divertor region. A mesh generation scheme based on field-line tracing and the construction of curved surfaces perpendicular to the magnetic field would be promising for global field calculations in the whole-volume simulations.

Basic Plasma Phenomena and Gas Discharges↗

Neoclassical transport of tungsten ion bundles in total-f neoclassical gyrokinetic simulations of a whole-volume JET-like plasma

Here, the application of a bundling technique to model the diverse charge states of tungsten impurity species in total-f gyrokinetic simulations is demonstrated. The gyrokinetic bundling method strategically groups tungsten ions of similar charge, optimizing computational efficiency. The initial radial configuration of these bundles and their respective charges are derived from a coronal approximation and the quasi-neutrality of the plasma. A low-density JET H-mode like plasma is simulated using the neoclassical version of XGC across the entire plasma volume, spanning from the magnetic axis to the divertor. An accumulation of tungsten is observed at the pedestal top, as a result of low-Z tungsten ions moving inward from the scrape-off-layer into the core region and high-Z tungsten ions moving outward from the core into the pedestal. This organization of the fluxes cannot be captured by a single tungsten-ion simulation. Large up-down poloidal asymmetries of tungsten form in the pedestal and strongly influence the direction of neoclassical fluxes. The temperature screening effect and its correlation with asymmetries are analyzed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Linearised Fokker–Planck collision model for gyrokinetic simulations

We introduce a gyrokinetic, linearised Fokker–Planck collision model that satisfies conservation laws and is accurate at arbitrary collisionalities. The differential test-particle component of the operator is exact; the integral field-particle component is approximated using a spherical harmonic and a modified Laguerre polynomial expansion developed by Hirshman and Sigmar (1976 Phys. Fluids 19 1532). The numerical methods of the implementation in the δf-gyrokinetic code stella (Barnes et al 2019 J. Comput. Phys. 391 365–80) are discussed, and conservation properties of the operator are demonstrated. The collision model is then benchmarked against the collision model of the gyrokinetic solver GS2 in the limiting cases of a reduced test-particle collision operator and energy- and momentum-conserving operator. The accuracy of the full collision model is investigated by solving the parallel Spitzer-Härm problem for the transport coefficients. It is shown that retaining collisional energy flux and higher-order terms in the field-particle operator reduces errors in the transport coefficients from 10%–25% for a simple momentum- and energy-conserving model to under 1%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Verification of global gyrokinetic simulation of low frequency mode excited by thermal plasma in spherical tokamak

A low frequency Alfven eigenmode in the ST40 spherical tokamak (ST) is found to be resonantly excited by thermal ions from global gyrokinetic GTC simulations. The analyses of phase-space resonances and wave-particle energy exchanges show that the Beta-induced Alfvén-Acoustic Eigenmode (BAAE) is primarily driven unstable by thermal ions, but is stabilized by energetic particles (EPs). When all kinetic effects are artificially suppressed, GTC simulations in the ideal magnetohydrodynamic (MHD) limit confirm the existence of the MHD eigenmode with a frequency in the BAAEs gap, as previously found by the ideal MHD code NOVA. The kinetic effects of thermal ions induce a frequency downshift compared to the stable BAAE in the MHD simulations. These results support the verification for global gyrokinetic simulations of the BAAE in the ST. However, the simulations do not explain the experimental observations of the BAAE in the ST40, possibly owing to the limitation of the collisionless gyrokinetic Monte Carlo model for the EPs.

Alfvén eigenmode↗

Axisymmetric gyrokinetic simulation of ASDEX-Upgrade scrape-off layer using a conservative implicit BGK collision operator

Collisions play an important role in turbulence and transport of fusion plasmas. For kinetic simulations, as the collisionality increases in the domain of interest, the size of the time step to resolve the collisional physics can become overly restrictive in an explicit time integration scheme, leading to high computational cost. With the aim of overcoming such restriction, we have implemented an implicit Bhatnagar–Gross–Krook (BGK) collision operator for use in the discontinuous Galerkin full-f gyrokinetic solver within the Gkeyll framework, which, when combined with Gkeyll's traditional explicit time integrator for collisionless advection, can significantly increase the time step in gyrokinetic simulations of highly collisional regimes. To ensure conservation of density, momentum, and energy, we utilize an iterative scheme to correct the discretized approximation to the equilibrium Maxwellian distribution to which the BGK collision operator relaxes. We have further generalized the BGK infrastructure, both the implicit scheme and the correction routine, to handle cross-species collisions. This improved implicit and conservative BGK operator is benchmarked against the more accurate but more computationally expensive Lenard–Bernstein–Dougherty (LBD) operator, which has been utilized in prior studies with Gkeyll. The implicit BGK operator enables 2D axisymmetric simulations of the ASDEX-Upgrade scrape-off layer to run 56 times faster to completion than the simulations with the LBD operator, because the BGK operator is more robust and converges at a lower resolution than is required by the LBD operator. Additionally, in this more collisional limit, we demonstrate that the results of our simulations utilizing the implicit BGK operator agreed well with simulations utilizing the more computationally expensive LBD operator.

Gyrokinetic simulations↗

Linear gyrokinetic simulations of toroidal Alfvén eigenmodes in the Mega-Amp Spherical Tokamak

Linear gyrokinetic (GK) simulations using the Gyrokinetic Toroidal Code (GTC) have been performed to investigate Toroidicity-driven Alfvén Eigenmodes (TAEs) driven by the neutral beam injection (NBI) induced fast ions in the Mega-Amp Spherical Tokamak (MAST) to identify the non-perturbative and kinetic effects of thermal plasma. A specific TAE in MAST discharge 26887, with an on-axis NBI power of approximately 1.5 MW and plasma current around 800 kA, exhibited frequency chirping, and the tangential soft x-ray camera array resolved the radial mode structure peaked near |q|=1.5. Various excitation methods were used in the GTC linear simulations, illustrating this code's capability to realistically represent the mechanisms and behaviors of fast ion-driven TAEs in spherical tokamaks. The radial structures from these GK simulations closely match measurements and calculations performed using the NOVA ideal MHD code, though with the frequencies approximately 10 kHz lower, likely due to various kinetic and non-perturbative effects. The simulations measured the damping rates due to continuum damping, radiative damping, and ion Landau damping, revealing that ion Landau damping has the most significant contribution to the total damping rate of the TAE. A comparison of growth rates of TAEs excited by fast ion Maxwellian and slowing-down distributions shows that the TAEs excited by a fast ion anisotropic pitch distribution (as part of the slowing-down distributions) are more unstable compared to those excited by a Maxwellian distribution with an equivalent fast ion beta. This shows that the use of fast ion anisotropy alters the number of fast ions to be in shear Alfvén resonance, and hence, it can greatly affect the stability of TAEs. These tests can be performed with the GTC but impossible with ideal MHD simulations, highlighting the necessity of kinetic simulations such as the GTC for a precise prediction of the TAE stability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Experiments and gyrokinetic simulations of the nonlinear interaction between spinning magnetized plasma pressure filaments

A set of experiments using controlled, skin depth-sized plasma pressure filaments in close proximity have been carried out in a large linear magnetized plasma device. Two- and three-filament configurations have been used to determine the scale of cross field nonlinear interaction. When the filaments are separated by a distance of approximately five times the size of a single filament or less, a significant transfer of charge and energy occurs, leading to the generation of inter-filament electric fields. This has the effect of rotating the filaments and influencing the merging dynamics. Nonlinear gyrokinetic simulations using seeded filaments confirm the presence of unstable drift-Alfvén modes driven by the steep electron temperature gradient. When the filaments are within a few collisionless electron skin depths (separations twice the size of a single filament), the unstable perturbations drive the convective mixing of the density and temperature and rearrange the gradients such that they maximize in the region surrounding the filament bundle.

Sydora, R. D. (ORCID:0000000192543149)↗

Global gyrokinetic simulations of kinetic-ballooning-mode turbulence in Wendelstein 7-X

We apply the global gyrokinetic code GENE-3D to perform kinetic-ballooning-mode (KBM) turbulence simulations in the Wendelstein 7-X (W7-X) stellarator using experimentally relevant parameters. In contrast to the flux-tube approach, we observe saturation of the turbulent fluctuations at finite amplitude. Analyzing the turbulent characteristics, we identify the presence of weakly driven KBM turbulence hybridizing with ion-temperature-gradient and trapped-electron-mode turbulence in the scenario under consideration, showing that it is possible that KBM activity can be driven in W7-X, opening up the path for studying this type of turbulence, which is highly relevant for future fusion power plants.

Electrostatics↗

Constructing field-aligned coordinate systems for gyrokinetic simulations of tokamaks in X-point geometries

Structures in tokamak plasmas are elongated along the direction of the magnetic field and short in the directions perpendicular to the magnetic field. Many tokamak simulation codes take advantage of this by using a field-aligned coordinate system. However, field-aligned coordinate systems have a coordinate singularity at magnetic X-points where the poloidal magnetic field vanishes, which makes it difficult to use field-aligned coordinate systems when simulating the core and scrape-off layer simultaneously. Here, we present an algorithm for grid generation and computing geometric quantities in a standard field-aligned coordinate system that avoids the singularity and allows one to conduct two-dimensional gyrokinetic axisymmetric simulations in X-point geometries. Convergence tests of advection, boundary value problems and geometric quantities all show greater than first-order convergence even in the vicinity of the X-point. We also demonstrate the geometric consistency of our algorithm with an example simulation of the spherical tokamak for energy production, which shows machine-precision particle conservation.

fusion plasma↗

Difference in neoclassical edge flows between strongly negative and positive triangularities in the XGC gyrokinetic simulation

The neoclassical baseline study of a strongly negative triangularity (NT) plasma and the corresponding positive triangularity (PT) plasma is performed using the edge-specialized, total-f gyrokinetic code (X-point Gyrokinetic Code, XGC). A DIII-D-like plasma is used, based on the negative triangularity discharge of DIII-D #193 793. An artificial positive triangularity (PT) equilibrium has been constructed to compare the edge rotation physics at the same triangularity strength but with opposite sign, while keeping the same elongation and other geometric parameters. Carbon(6+) ions are added to the deuterium plasma at an experimentally relevant level. By using the experimental profile of carbon toroidal rotation profile as an input, XGC finds that the deuteron rotation is significantly different from the carbon rotation at the inboard and outboard midplanes, mostly caused by the difference in the Pfirsch–Schlüter rotation. More importantly, a significant difference in the X-point orbit loss physics, thus the rotation source, is found between the positive and negative triangularity equilibrium models. However, it is also found that the agreement between the present neoclassical simulation and the experimental NT data is validated only within the middle of the pedestal slope, indicating the importance of edge turbulence. Finally, this study could establish a baseline for the multiphysics, multiscale studies that include turbulence of negative triangularity plasmas.

Deuterium↗