Resolution Issues in Continuum Gyrokinetic Simulations

In the absence of collisions, particle distribution functions quickly develop fine scales in velocity-space. This makes it very difficult for kinetic codes to resolve weakly-collisional plasma processes. For many basic processes in gyrokinetics, few systematic numerical studies exist. We present results from a study on resolution requirements for a number of important problems in weakly-collisional plasmas using the continuum gyrokinetic code GS2. The problems considered include: long-time limit of Landau-damped ion acoustic waves; long-time limit of Barnes-damped kinetic Alfven waves; and neoclassical ion thermal conduction in a tokamak as a function of collisionality. For each problem, we compare the numerically generated distribution functions with theory and suggest useful measures of the quality of numerical results. The insight gained from this study is then used to propose a series of test problems applicable for a generic gyrokinetic solver. Additionally, we consider neoclassical transport in stellarator equilibria and the velocity space structure of microinstabilities in tokamaks, with and without equilibrium ExB shear.