Content area
Abstract
A general gyrokinetic formalism and appropriate computational methods have been developed for electromagnetic perturbations in toroidal plasmas. This formalism and associated numerical code represent the first self-consistent, comprehensive, fully kinetic model for treating both magnetohydrodynamic (MHD) instabilities and electromagnetic drift waves.
The gyrokinetic system of equation is derived by phase-space Lagrangian Lie perturbation methods which enable applications to modes with arbitrary wavelength. An important component missing from previous electromagnetic gyrokinetic theories, the gyrokinetic perpendicular dynamics, is identified and developed in the present analysis. This is accomplished by introducing a new “distribution function” and an associated governing gyrokinetic equation. Consequently, the compressional Alfvén waves and cyclotron waves can be systematically treated. The new insights into the gyrokinetic perpendicular dynamics uncovered here clarify the understanding of the gyrokinetic approach—the real spirit of the gyrokinetic reduction is to decouple the gyromotion from the guiding center orbital motion, instead of averaging it out. The gyrokinetic perpendicular dynamics is in fact essential to the recovery of the MHD model from a fully kinetic derivation. In particular, it serves to generalize, in gyrokinetic framework, Spitzer's solution of the fluid/particle paradox to a broader regime of applicability.
The gyrokinetic system is also shown to be reducible to a simpler form to deal with shear Alfvén waves. This consists of an appropriate form of the gyrokinetic equation governing the distribution function, the gyrokinetic Poisson equation, and a newly derived gyrokinetic moment equation. If all of the kinetic effects are neglected, the gyrokinetic moment equation is shown to recover the ideal MHD equation for shear Alfvén modes. In addition, a gyrokinetic Ohm's law, including both the perpendicular and the parallel components, is derived.
The gyrokinetic equation is solved for the perturbed distribution function by integrating along the unperturbed orbits. Substituting this solution back into the gyrokinetic Poisson equation and the gyrokinetic moment equation yields the eigenmode equation. The eigenvalue problem is then solved by using a Fourier decomposition in the poloidal direction and a finite element method in the radial direction. Both analytic and numerical results from the gyrokinetic model were found to agree very well with the MHD results. Destabilization of the TAEs by energetic particles are known to be vitally important for ignition-class plasmas. For the test case with Maxwellian energetic hydrogen ions, comparisons have accordingly been made between the results from the present non-perturbative, fully kinetic calculation using the KIN-2DEM code and those from the perturbative hybrid calculation with the NOVA-K code. The agreement varies with hot particle thermal velocity. The discrepancy is mainly attributed to the differences in the basic models.
