I. Holod

Physics of non-diffusive turbulent transport of momentum and the origins of spontaneous rotation in tokamaks

Recent results in the theory of turbulent momentum transport and the origins of intrinsic rotation are summarized. Special attention is focused on aspects of momentum transport critical to intrinsic rotation, namely the residual stress and the edge toroidal flow velocity pinch. Novel results include a systematic decomposition of the physical processes which drive intrinsic rotation, a calculation of the critical external torque necessary to hold the plasma stationary against the intrinsic residual stress, a simple model of net velocity scaling which recovers the salient features of the experimental trends and the elucidation of the impact of the particle flux on the net toroidal velocity pinch. Specific suggestions for future experiments are offered.

Electromagnetic formulation of global gyrokinetic particle simulation in toroidal geometry

The fluid-kinetic hybrid electron model for global electromagnetic gyrokinetic particle simulations has been formulated in toroidal geometry using magnetic coordinates, providing the capabilities to describe low frequency processes in electromagnetic turbulence with electron dynamics. In the limit of long wavelength and no parallel electric field our equations reduce to the ideal magnetohydrodynamic equations. The formulation has been generalized to include equilibrium flows. The equations for zonal components of electrostatic and vector potentials have been derived, demonstrating the electron screening of the zonal vector potential.

Gyrokinetic particle simulations of reversed shear Alfvén eigenmode excited by antenna and fast ions

Global gyrokinetic particle simulations of reversed shear Alfven eigenmode (RSAE) have been successfully performed and verified. We have excited the RSAE by initial perturbation, by external antenna, and by energetic ions. The RSAE excitation by antenna provides verifications of the mode structure, the frequency, and the damping rate. When the kinetic effects of the background plasma are artificially suppressed, the mode amplitude shows a near-linear growth. With kinetic thermal ions, the mode amplitude eventually saturates due to the thermal ion damping. The damping rates measured from the antenna excitation and from the initial perturbation simulation agree very well. The RSAE excited by fast ions shows an exponential growth. The finite Larmor radius effects of the fast ions are found to significantly reduce the growth rate. With kinetic thermal ions and electron pressure, the mode frequency increases due to the elevation of the Alfven continuum by the geodesic compressibility. The nonperturbative contributions from the fast ions and kinetic thermal ions modify the mode structure relative to the ideal magnetohydrodynamic (MHD) theory. The gyrokinetic simulations have been benchmarked with extended hybrid MHD-gyrokinetic simulations.

Gyrokinetic particle simulation of beta-induced Alfvén eigenmode

The beta-induced Alfven eigenmode (BAE) in toroidal plasmas is studied using global gyrokinetic particle simulations. The BAE real frequency and damping rate measured in the initial perturbation simulation and in the antenna excitation simulation agree well with each other. The real frequency is slightly higher than the ideal magnetohydrodynamic (MHD) accumulation point frequency due to the kinetic effects of thermal ions. Simulations with energetic particle density gradient show exponential growth of BAE with a growth rate sensitive to the energetic particle temperature and density. The nonperturbative contributions by energetic particles modify the mode structure and reduce the frequency relative to the MHD theory. The finite Larmor radius effects of energetic particles reduce the BAE growth rate. Benchmarks between gyrokinetic particle simulation and hybrid MHD-gyrokinetic simulation show good agreement in BAE real frequency and mode structure.

Linear properties of reversed shear Alfvén eigenmodes in the DIII-D tokamak

Linear properties of the reverse shear Alfven eigenmode (RSAE) in a well-diagnosed DIII-D tokamak experiment (discharge #142111) are studied in gyrokinetic particle simulations. Simulations find that a weakly damped RSAE exists due to toroidal coupling and other geometric effects. The mode is driven unstable by density gradients of fast ions from neutral beam injection. Various damping and driving mechanisms are identified and measured in the simulations. Accurate damping and growth rate calculation requires a non-perturbative, fully self-consistent simulation to calculate the true mode structure. The mode structure has no up–down symmetry mainly due to the radial symmetry breaking by the density gradients of the fast ions, as measured in the experiment by electron cyclotron emission imaging. The RSAE frequency up-sweeping and the mode transition from RSAE to TAE (toroidal Alfven eigenmode) are in good agreement with the experimental results when the values of the minimum safety factor are scanned in gyrokinetic simulations.

Gyrokinetic simulation model for kinetic magnetohydrodynamic processes in magnetized plasmas

A nonlinear gyrokinetic simulation model incorporating equilibrium current has been formulated for studying kinetic magnetohydrodynamic processes in magnetized plasmas. This complete formulation enables gyrokinetic simulation of both pressure-gradient-driven and current-driven instabilities as well as their nonlinear interactions in multi-scale simulations. The gyrokinetic simulation model recovers the ideal magnetohydrodynamic theory in the linear long wavelength regime including ideal and kinetic ballooning modes, kink modes and shear Alfven waves. The implementation of this model in the global gyrokinetic particle code has been verified for the simulation of the effects of equilibrium current on the reversed shear Alfven eigenmode in tokamaks.

Global gyrokinetic particle simulations with kinetic electrons

A toroidal, nonlinear, electrostatic fluid-kinetic hybrid electron model is formulated for global gyrokinetic particle simulations of driftwave turbulence in fusion plasmas. Numerical properties are improved by an expansion of the electron response using a smallness parameter of the ratio of driftwave frequency to electron transit frequency. Linear simulations accurately recover the real frequency and growth rate of toroidal ion temperature gradient (ITG) instability. Trapped electrons increase the ITG growth rate by mostly not responding to the ITG modes. Nonlinear simulations of ITG turbulence find that the electron thermal and particle transport are much smaller than the ion thermal transport and that small scale zonal flows are generated through nonlinear interactions of the trapped electrons with the turbulence.

Verification of electromagnetic fluid-kinetic hybrid electron model in global gyrokinetic particle simulation

The fluid-kinetic hybrid electron model is verified in global gyrokinetic particle simulation of linear electromagnetic drift-Alfvenic instabilities in tokamak. In particular, we have recovered the β-stabilization of the ion temperature gradient mode, transition to collisionless trapped electron mode, and the onset of kinetic ballooning mode as βe (ratio of electron kinetic pressure to magnetic pressure) increases.

Gyrokinetic particle simulation of microturbulence for general magnetic geometry and experimental profiles

Developments in gyrokinetic particle simulation enable the gyrokinetic toroidal code (GTC) to simulate turbulent transport in tokamaks with realistic equilibrium profiles and plasma geometry, which is a critical step in the code–experiment validation process. These new developments include numerical equilibrium representation using B-splines, a new Poisson solver based on finite difference using field-aligned mesh and magnetic flux coordinates, a new zonal flow solver for general geometry, and improvements on the conventional four-point gyroaverage with nonuniform background marker loading. The gyrokinetic Poisson equation is solved in the perpendicular plane instead of the poloidal plane. Exploiting these new features, GTC is able to simulate a typical DIII-D discharge with experimental magnetic geometry and profiles. The simulated turbulent heat diffusivity and its radial profile show good agreement with other gyrokinetic codes. The newly developed nonuniform loading method provides a modified radial transport profile to that of the conventional uniform loading method.

Microturbulence in DIII-D tokamak pedestal. I. Electrostatic instabilities

Gyrokinetic simulations of electrostatic driftwave instabilities in a tokamak edge have been carried out to study the turbulent transport in the pedestal of an H-mode plasma. The simulations use annulus geometry and focus on two radial regions of a DIII-D experiment: the pedestal top with a mild pressure gradient and the middle of the pedestal with a steep pressure gradient. A reactive trapped electron instability with a typical ballooning mode structure is excited by trapped electrons in the pedestal top. In the middle of the pedestal, the electrostatic instability exhibits an unusual mode structure, which peaks at the poloidal angle θ=±π/2. The simulations find that this unusual mode structure is due to the steep pressure gradients in the pedestal but not due to the particular DIII-D magnetic geometry. Realistic DIII-D geometry appears to have a stabilizing effect on the instability when compared to a simple circular tokamak geometry.