Numerical Instability in a 2D Gyrokinetic Code Caused by Divergent E × B Flow

Abstract

In this paper, a numerical instability first observed in a 2D electrostatic gyrokinetic code is described. The instability should also be present in some form in many versons of particle-in-cell simulation codes that employ guiding center drifts. A perturbation analysis of the instability is given and its results agree quantitatively with the observations from the gyrokinetic code in all respects. The basic mechanism is a false divergence of the E × B flow caused by the interpolation between the grid and the particles as coupled with the specific numerical method for calculating E - ∇φ. Stability or instability depends in detail on the specific choice of particle interpolation method and field method. One common interpolation method, subtracted dipole, is stable. Other commonly used interpolation methods, linear and quadratic, are unstable when combined with a finite difference for the electric field. Linear and quadratic interpolation can be rendered stable if combined with another method for the electric field, the analytic differential of the interpolated potential.