Simulation and quasilinear theory of proton firehose instability

Abstract

The electromagnetic proton firehose instability is driven by excessive parallel temperature anisotropy, T∥ > T⊥ (or more precisely, parallel pressure anisotropy, P∥ > P⊥) in high-beta plasmas. Together with kinetic instabilities driven by excessive perpendicular temperature anisotropy, namely, electromagnetic proton cyclotron and mirror instabilities, its role in providing the upper limit for the temperature anisotropy in the solar wind is well-known. A recent Letter [Seough et al., Phys. Rev. Lett. 110, 071103 (2013)] employed quasilinear kinetic theory for these instabilities to explain the observed temperature anisotropy upper bound in the solar wind. However, the validity of quasilinear approach has not been rigorously tested until recently. In a recent paper [Seough et al., Phys. Plasmas 21, 062118 (2014)], a comparative study is carried out for the first time in which quasilinear theory of proton cyclotron instability is tested against results obtained from the particle-in-cell simulation method, and it was demonstrated that the agreement was rather excellent. The present paper addresses the same issue involving the proton firehose instability. Unlike the proton cyclotron instability, however, it is found that the quasilinear approximation enjoys only a limited range of validity, especially for the wave dynamics and for the relatively high-beta regime. Possible causes and mechanisms responsible for the discrepancies are speculated and discussed.

Kinetic Simulations of the Interruption of Large-Amplitude Shear-Alfvén Waves in a High- β Plasma

“…The firehose modes' evolution is governed by Δp [12], which varies in space. Near the wave nodes, where S ¼ j∇uj ≈ 0 and δB z ≈ 0, Δp is not driven by a large-scale dB=dt and can freely decay [29,32,34,35]. Near the wave antinodes, where S ∼ β −1=2 ω A ≈ 6 × 10 −5 Ω i [10] and δB z ≠ 0, Δp is continuously driven by the decreasing field [29,31,[36][37][38].…”

Kinetic instabilities in the solar wind driven by temperature anisotropies

“…Four different initial conditions are indicated in different colors and also labeled. Time evolution of the perpendicular and parallel betas, temperature ratio, and wave energy density are plotted as a function of normalized time order to test whether such an assumption is valid we have carried out onedimensional particle-in-cell simulations (Seough et al , 2015a. We found that the agreement between the simplified quasilinear theory and PIC simulation is quite good in the case of proton-cyclotron instability, but for parallel proton firehose instability the agreement became poorer.…”

“…This contributes to the distortion of the initial biMaxwellian form into a dumb-bell shape distribution (Astfalk and Jenko 2017), and leads to the premature quenching of the instability. The time evolution of the initially bi-Maxwellian distribution in PIC code runs is discussed in Seough et al ( , 2015a, and shows that indeed, for EMIC case, the quasi-bi-Maxwellian shape is maintained throughout most of the simulation time. In contrast, for PFH case, the bi-Maxwellian form gets distorted quite early on, even though later on, the quasi-bi-Maxwellian shape appears to be restored.…”

“…The details of the 1D PIC simulation setup are described in Seough et al ( , 2015a, so we will not repeat them here. In Fig.…”

“…It was also successfully employed by Moya et al to discuss solar wind heating (Moya et al 2012, for which the free energy resides with finite amplitude waves while the particles are initially isotropic. The recent application of such a method to the solar wind temperature anisotropy instability was initiated by the present author and his colleagues Seough et al 2013Seough et al , 2015aStockem Novo et al 2015;. We also recently initiated a research program to test and verify the accuracy and reliability of the quasilinear moment method by comparing the theoretical calculation against particle-in-cell simulation .…”