Effects of variations in electron thermal velocity on the whistler anisotropy instability: Particle-in-cell simulations

Abstract

This paper investigates how the physics of the whistler anisotropy instability (WAI) is affected by variations in the electron thermal velocity vte, referred to here in terms of the ratio v̂te=vte/c, where c is the speed of light. The WAI is driven by the electron condition RT>1, where RT=Te⊥/Te∥ is the temperature anisotropy ratio and ⊥/∥ signify directions perpendicular/parallel to the background magnetic field B0. While a typical value of v̂te in the solar wind is ∼0.005, electromagnetic (EM) particle-in-cell (PIC) simulations often use a value near 0.1 in order to maximize the computational time step. In this study, a two-dimensional (2D) Darwin particle-in-cell (DPIC) code, MDPIC2, is used. The time step in the DPIC model is not affected by the choice of v̂te, making DPIC suited for this study. A series of simulations are carried out under the condition that the electron βe is held fixed, while v̂te is varied over the range 0.1≥v̂te≥0.025. The results show that, with βe held fixed, the linear dispersion properties and the nonlinear saturation amplitude and pitch angle scattering rates associated with the WAI are insensitive to the value of v̂te. A supplementary investigation is conducted which characterizes how the WAI model is affected at various values of v̂te by noise associated with the limited number of particles in a typical PIC simulation. It is found that the evolution of the WAI is more strongly influenced by electrostatic noise as v̂te is decreased. The electrostatic noise level is inversely proportional to the number of particles per computational cell (Nc); this implies that the number of particles required to remove nonphysical effects from the PIC simulation increases as v̂te decreases. It is concluded that PIC simulations of this instability which use an artificially large value of v̂te accurately reproduce the response of a cooler plasma as long as a realistic value of βe is used. Moreover, for a fixed number of particles, the quantitative accuracy of the model improves with increasing v̂te.