Test particle simulation of the Electron Firehose instability

Abstract

Abstract. In the course of the energization of electrons to energies of some tens of keV during the impulsive phase of a solar flare, the velocity distribution function of the electrons is predicted to become anisotropic with T e > T e ⊥ (Here, and ⊥ denote directions with respect to the background magnetic field). Such a configuration can become unstable to the so-called Electron Firehose instability (EFI). Left hand circularly polarized electromagnetic waves propagating along the magnetic field are excited via a non-resonant mechanism: electrons non-resonantly excite the waves while the protons are in resonance and carry the wave. The non-resonant nature of the instability raises the question of the response of the electron population to the growing waves. Test particle simulations are carried out to investigate the pitch-angle development of electrons injected to single waves and wave spectra. To interpret the simulation results, a drift kinetic approach is developed. The findings in the case of single wave simulations show the scattering to larger pitch-angles in excellent agreement with the theory. The situation dramatically changes when assuming a spectrum of waves. Stochasticity is detected at small initial parallel velocities resulting in significant deviations from drift kinetic theory. It enhances the scattering rate of electrons with initial parallel velocity below to the mean thermal perpendicular velocity. Increased scattering is also noticed for electrons having initial parallel velocity within an order of magnitude of the resonance velocity. The resulting pitch-angle scattering is proposed to be an important ingredient in Fermi-type electron acceleration models, particularly transit-time acceleration by compressional MHD waves.

Acceleration and Enrichment of3He in Impulsive Solar Flares by Electron Firehose Waves

“…This shows that for reasonable anisotropies the slope in the growth rate profile in the vicinity of the gyrofrequency of 3 He is always positive, such that waves around the 3 He resonance grow faster than waves around the 4 He gyrofrequency. This is a very stable feature of the EF wave spectrum and can be expected, once above the instability threshold, for a large range of plasma parameters that allow instability and reasonable anisotropies of protons and electrons (for a detailed analysis of EFI thresholds and spectra in dependence on plasma parameters see Paesold & Benz 1999). …”

“…Although it is not expected that acceleration retains a bi-Maxwellian distribution function, it is a good approximation in order to describe propagation properties of plasma waves. As shown in Paesold & Benz (1999), the EFI can occur in such a situation and give rise to EF waves. The parallel EF waves are purely transverse electromagnetic and left-hand circularly polarized.…”

“…The analysis in Paesold & Benz (1999) shows that the positive slope in the growth rate profile around the 3 He and 4 He gyrofrequency that is needed to selectively enhance 3 He is a stable feature of the EFI and not very sensitive to changes in the plasma parameters for solar preflaring conditions.…”

“…The authors also want to acknowledge Gérard Belmont and Laurence Rezeau, who gave them free access to their improved version of the WHAMP code, which has become the mathematical core of IDLWhamp (Paesold 2002). This work was financially supported by the Swiss National Science Foundation (grant 2000-061559).…”

Electromagnetic electron whistler-cyclotron instability in bi-Kappa distributed plasmas

“…Collisions are less effective at time and space scales in the solar wind plasma, but the limits observed for the temperature anisotropy seem to be well explained by the resulting wave fluctuations and their effects on plasma particles. Thus, for electrons, linear dispersion theory predicts that any excess of temperature in the direction parallel to the magnetic field (T > T ⊥ ) is constrained by the firehose instability (Paesold & Benz 1999;Gary & Nishimura 2003;Stverak et al 2008), while perpendicular temperature (T ⊥ > T ) is limited by the whistler instability (Gary & Wang 1996;Stverak et al 2008;Schlickeiser et al 2011).…”