Particle-in-cell simulations of velocity scattering of an anisotropic electron beam by electrostatic and electromagnetic instabilities

Abstract

The velocity space scattering of an anisotropic electron beam (T⊥b/T∥b>1) flowing along a background magnetic field B0 through a cold plasma is investigated using both linear theory and 2D particle-in-cell simulations. Here, ⊥ and ∥ represent the directions perpendicular and parallel to B0, respectively. In this scenario, we find that two primary instabilities contribute to the scattering in electron pitch angle: an electrostatic electron beam instability and a predominantly parallel-propagating electromagnetic whistler anisotropy instability. Our results show that at relative beam densities nb/ne≤0.05 and beam temperature anisotropies Tb⊥/Tb∥≤25, the electrostatic beam instability grows much faster than the whistler instabilities for a reasonably fast hot beam. The enhanced fluctuating fields from the beam instability scatter the beam electrons, slowing their average speed and increasing their parallel temperature, thereby increasing their pitch angles. In an inhomogeneous magnetic field, such as the geomagnetic field, this could result in beam electrons scattered out of the loss cone. After saturation of the electrostatic instability, the parallel-propagating whistler anisotropy instability shows appreciable growth, provided that the beam density and late-time anisotropy are sufficiently large. Although the whistler anisotropy instability acts to pitch-angle scatter the electrons, reducing perpendicular energy in favor of parallel energy, these changes are weak compared to the pitch-angle increases resulting from the deceleration of the beam due to the electrostatic instability.

On Whistler Mode Wave Relation to Electron Field‐Aligned Plateau Populations

“…We slightly relax this criterion and consider an comprising not necessarily a plateau but at least electron beams, because such beams should quickly (on plasma time scales) relax to plateaus through the excitation of electrostatic waves (Vedenov, ). Full numerical simulations have indeed demonstrated the relaxation of electron beams over typical time scales of tens of inverse plasma frequencies (see, e.g., Fu et al, ; Gary et al, , and reference therein). Moreover, electrons scattering by whistler mode waves may also contribute to beam relaxation and plateau formation (e.g., An et al, ; Zhang et al, , and references therein).…”

The electron foreshock at high-Mach-number non-relativistic oblique shocks

“…Studying beam instabilities that may be important in the solar-wind context, several groups have analyzed PIC simulations of the electrostatic two-beam instability, the electromagnetic oblique-whistler instability, and the anisotropy-driven whistler heat-flux instability 32,33 . These simulations started with initial conditions that correspond to solar-wind parameters, often with a larger beam anisotropy than one would expect for a shock-reflected beam.…”

Electron-beam instabilities in the foreshock of high Mach number oblique shocks

“…In the context of bow shocks with lower Mach numbers ( 20), the instabilities which may arise in electron foreshocks have long been studied in the space-physics community [3][4][5]. More recently, particle-in-cell (PIC) simulations of the electrostatic two-beam instability, the electromagnetic oblique-whistler instability and the anisotropy-driven whistler heat-flux instability (WHFI) have become possible [6,7]. These previous simulations used initial conditions that correspond to solar-wind observations, often with a larger beam anisotropy than one would expect for a shock-reflected beam.…”