A. Mishchenko

Global particle-in-cell simulations of fast-particle effects on shear Alfvén waves

This paper reports self-consistent global linear gyrokinetic particle-in-cell simulations of shear Alfven waves destabilized by fast particles in tokamak geometry. Resonant excitation of toroidal Alfven eigenmodes by fast particles and their transition to energetic particle modes (when the fast-particle drive is large enough) has been observed in the simulations.

Conventional δf-particle simulations of electromagnetic perturbations with finite elements

The possibility of electromagnetic particle-in-cell simulations with a conventional δf approach is shown in slab geometry using finite elements. Both the ion-temperature-gradient driven mode and the shear Alfven wave are reproduced and benchmarked with the analytical linear dispersion relation. Particularly, the Alfven wave is simulated successfully at the limit k⊥→0.

Global particle-in-cell simulations of Alfvénic modes

Global linear gyrokinetic particle-in-cell (PIC) simulations of electromagnetic modes in pinch and tokamak geometries are reported. The global Alfven eigenmode, the mirror Alfven eigenmode, the toroidal Alfven eigenmode, and the kinetic ballooning modes have been simulated. All plasma species have been treated kinetically (i.e., no hybrid fluid-kinetic or reduced-kinetic model has been applied). The main intention of the paper is to demonstrate that the global Alfven modes can be treated with the gyrokinetic PIC method.

Particle simulations with a generalized gyrokinetic solver

This paper presents a generalized gyrokinetic solver which can be used for all perpendicular wavelengths of interest and allows to include the nonlinear gyrokinetic polarization density in the simulations. The polarization density, being an integral over the phase space is calculated using “numerical particles” (not to be confused with the marker particles which are used in the charge assignment) and finite elements. Integrals over the gyroangle are calculated using an N-point approximation. The accuracy requirements on the number of the gyropoints and numerical particles are discussed. The linear part of the solver has been implemented numerically and benchmarked with the slab dispersion relation for both the ion temperature gradient driven (ITG) mode and the electron temperature gradient driven (ETG) mode. Additionally, linear ITG and ETG modes are considered in a two-dimensional bumpy pinch configuration.

Global gyrokinetic particle-in-cell simulations of internal kink instabilities

Internal kink instabilities have been studied in straight tokamak geometry employing an electromagnetic gyrokinetic particle-in-cell (PIC) code. The ideal-MHD internal kink mode and the collisionless m=1 tearing mode have been successfully simulated with the PIC code. Diamagnetic effects on the internal kink modes have also been investigated.

Collisionless dynamics of zonal flows in stellarator geometry

The collisionless time evolution of zonal flows in stellarator systems is investigated. An analytical solution of the kinetic and quasineutrality equations describing the residual zonal flow is derived for arbitrary three-dimensional systems without approximations in the magnetic geometry. The theory allows for an arbitrary number of particle species. It has been found that in stellarators the residual zonal flows are not in general steady but oscillate with a certain frequency. This frequency is determined by the speed of the bounce-averaged radial drifts of the particles trapped in the magnetic field and vanishes in tokamaks, where such net drifts are absent. A reduction of the bounce-averaged radial drifts in configurations optimized with respect to neoclassical transport results in a smaller zonal-flow frequency.

Oscillations of zonal flows in stellarators

The linear response of a collisionless stellarator plasma to an applied radial electric field is calculated, both analytically and numerically. Unlike in a tokamak, the electric field and associated zonal flow develop oscillations before settling down to a stationary state, the so-called Rosenbluth–Hinton flow residual. These oscillations are caused by locally trapped particles with radially drifting bounce orbits. The particles also cause a kind of Landau damping of the oscillations that depends on the magnetic configuration. The relative importance of geodesic acoustic modes and zonal-flow oscillations therefore varies among different stellarators.

Global particle-in-cell simulations of plasma pressure effects on Alfvénic modes

Global linear gyrokinetic particle-in-cell simulations of electromagnetic modes in realistic tokamak geometry are reported. The effect of plasma pressure on Alfvenic modes is studied. It is shown that the fast-particle pressure can considerably affect the shear Alfven wave continuum structure and hence the toroidicity-induced gap in the continuum. It is also found that the energetic ions can substantially reduce the growth rate of the ballooning modes (and perhaps completely stabilize them in a certain parameter range). Ballooning modes are found to be the dominant instabilities if the bulk-plasma pressure gradient is large enough.

Pullback transformation in gyrokinetic electromagnetic simulations

It is shown that a considerable mitigation of the cancellation problem can be achieved by a slight modification of the simulation scheme. The new scheme is verified, simulating a Toroidal Alfven Eigenmode in tokamak geometry at low perpendicular mode numbers, the so-called “MHD limit.” Also, an electromagnetic drift mode has been successfully simulated in a stellarator.

New variables for gyrokinetic electromagnetic simulations

A new approach to electromagnetic gyrokinetic simulations based on modified gyrokinetic theory is described. The method is validated using a particle-in-cell code. The Toroidal Alfven Eigenmode at low perpendicular mode numbers, the so-called “magnetohydrodynamical limit,” has been successfully simulated using this method.