Whistler anisotropy instability at low electron β: Particle-in-cell simulations

The whistler anisotropy instability is studied in a magnetized, homogeneous, collisionless plasma model. The electrons (denoted by subscript e) are represented initially with a single bi-Maxwellian velocity distribution with a temperature anisotropy $T_{\perp e}/T_{\parallel e}>1$ , where $\perp$ and $\parallel$ denote directions perpendicular and parallel to the background magnetic field ${\mathbf{B}}_o$ , respectively. Kinetic linear dispersion theory predicts that, if the ratio of the electron plasma frequency ${\omega }_e$ to the electron cyclotron frequency ${\Omega }_e$ is greater than unity and ${\beta }_{\parallel e}\ge 0.025$ , the maximum growth rate of this instability is at parallel propagation, where the fluctuating fields are strictly electromagnetic. At smaller values of ${\beta }_{\parallel e}$ , however, the maximum growth rate shifts to propagation oblique to ${\mathbf{B}}_o$ and the fluctuating electric fields become predominantly electrostatic. Linear theory and two-dimensional particle-in-cell simulations are used to examine the consequences of this transition. Three simulations are carried out, with initial ${\beta }_{\parallel e}=0.10$ , 0.03, and 0.01. The fluctuating fields of the ${\beta }_{\parallel e}=0.10$ run are predominantly electromagnetic, with nonlinear consequences similar to those of simulations already described in the literature. In contrast, the growth of fluctuations at oblique propagation in the low electron $\beta$ runs leads to a significant $\delta E_{\parallel }$ , which heats the electrons leading to the formation of a substantial suprathermal component in the electron parallel velocity distribution.