Parallel proton fire hose instability in gyrotropic Hall MHD model

Abstract

[1] The linear theory and nonlinear evolution of parallel or classical fire hose instability previously studied based on hybrid particle simulations are examined within the framework of a gyrotropic Hall magnetohydrodynamic (MHD) model that incorporates the ion inertial effects arising from the Hall current but neglects the electron inertia in the generalized Ohm's law. Both the ion cyclotron and whistler waves become fire hose unstable for b k − b ? > 2 + l i 2 k 2 /2 with right-handed circular polarization, where l i and k are the ion inertial length and wave number, respectively, implying that the ion inertia plays a stabilizing role in parallel fire hose instability. Substantial noncoplanar components of the magnetic field and flow velocity may develop as a result of Hall current. The evolution characteristics of magnetic field fluctuations may depend on the Hall parameter h = l i /l r , where l r is the resistive length. For moderately and highly dispersive cases the instability may be purely growing in the early stage with the development of soliton-like structures with depressed magnetic field on the order of a few ion inertial lengths and become propagating with right-handed circular polarization in the late phase when the waves have inversely cascaded to large-amplitude Alfvén waves of longer wavelengths. Oscillatory and damping behavior resembling those found in the kinetic model may be reproduced for single-mode perturbations of long wavelengths with h ≤ 1. The saturated magnetic field is found to comply with the quasi-linear theory.

Effects of Hall current and electron temperature anisotropy on proton fire-hose instabilities

“…The present study has focused on the effects of ion inertia including the Hall current and electron temperature anisotropy on the properties of fire-hose type instabilities, which is an extension of our prior works based on the gyrotropic MHD and Hall MHD models. 13,15,16 As for the pure MHD case, there exists one type of FHI for parallel propagation while there are two fire-hose modes for oblique propagation. However, in contrast to the pure MHD case, for which the oblique FHI may grow faster than the parallel FHI only for c jj;i c ?…”

“…It can be shown that both intermediate and slow mode waves may become unstable for b k À b ? > 2 and h < h c , where : (16) In the limit of cold electrons and for the parameter values of c ? ;i ¼ 2, c jj;i ¼ 1=2, the above expression is the same as the condition obtained from the Vlasov theory in hydromagnetic limit for the compressible slow mode to become fire hose unstable.…”

“…16 The gyrotropic Hall MHD model includes the pressure anisotropy of protons and the Hall current in the generalized Ohm's law but neglects the inertia and temperature anisotropy of electrons. For parallel proton FHI, the instability criterion has the simple form of b k À b ?…”

On the Parallel and Oblique Firehose Instability in Fluid Models

“…Here we consider only very simple fluid models based on the CGL description without any form of collisionless damping, the only extensions are the Hall-term and the FLR corrections, both of which allow us to explore the firehose instability in sufficient detail. The firehose instability in a fluid formalism was also investigated by Wang & Hau (2003); Schekochihin et al (2010); Wang & Hau (2010); Rosin et al (2011) and references therein.…”

“…Here we concentrate only on the parallel and oblique firehose instability, which are two of the four basic instabilities typically considered in solar wind observational studies and in numerous theoretical developments and numerical simulations, the other two being the mirror instability and the ion-cyclotron anisotropy instability (Gary (1993); Yoon et al (1993); Gary et al (1998); Hellinger & Matsumoto (2000); Hollweg & Isenberg (2002); Kasper et al (2002); Wang & Hau (2003); Marsch et al (2004); Marsch (2006); Hellinger et al (2006); Matteini et al (2006Matteini et al ( , 2007; ; Hellinger & Trávníček (2008); Bale et al (2009) ;Schekochihin et al (2010); Wang & Hau (2010); Rosin et al (2011);Laveder et al (2011);Isenberg (2012); Passot et al (2012); Seough & Yoon (2012); Kunz et al (2014); Hellinger et al (2015); Klein & Howes (2015); Sulem & Passot (2015); Yoon et al (2015); Matteini (2016); Melville et al (2016); Hellinger (2017), and references therein). That the CGL model contains the correct parallel and oblique firehose instability threshold is already known from the work of Abraham-Shrauner (1967) and the CGL dispersion relations were further studied for example by (Ferrière & André 2002;Hunana et al 2013Hunana et al , 2016.…”