Parallel proton fire hose instability in gyrotropic Hall MHD model

[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 β_∥ - β_⊥ > 2 + λ_i²k²/2 with right-handed circular polarization, where λ_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 = λ_i/λ_r , where λ_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.