New velocity-space discretization for continuum kinetic calculations and Fokker-Planck collisions

TL;DR

This paper introduces a spectral collocation method using novel orthogonal polynomials for discretizing velocity space in continuum kinetic calculations, improving accuracy and efficiency especially for Fokker-Planck collision problems in plasma physics.

Contribution

It develops a new velocity-space discretization technique employing non-classical orthogonal polynomials and detailed procedures for Fokker-Planck collision operators in plasma simulations.

Findings

Enhanced accuracy in neoclassical bootstrap current calculations

Efficient treatment of Fokker-Planck collision terms

Effective handling of multiple species with different masses

Abstract

Numerical techniques for discretization of velocity space in continuum kinetic calculations are described. An efficient spectral collocation method is developed for the speed coordinate - the radius in velocity space - employing a novel set of non-classical orthogonal polynomials. For problems in which Fokker-Planck collisions are included, a common situation in plasma physics, a procedure is detailed to accurately and efficiently treat the field term in the collision operator (in the absence of gyrokinetic corrections). When species with disparate masses are included simultaneously, a careful extrapolation of the Rosenbluth potentials is performed. The techniques are demonstrated in neoclassical calculations of the bootstrap current and plasma flows in a tokamak.