Oblique proton fire hose instability in the expanding solar wind: Hybrid simulations

Oblique fire hose instability is investigated using hybrid simulations for proton betas of the order of one and for proton parallel temperatures sufficiently greater than the perpendicular ones. The simulations confirm previous simulation results showing that this instability has self-destructing properties and efficiently reduces the proton temperature anisotropy. A parametric study using one-dimensional standard hybrid simulations shows that stronger changes in the temperature anisotropy and stronger wave emissions appear for larger initial temperature anisotropies. An ideal, slow plasma expansion, modeled by a two-dimensional hybrid expanding box simulation, leads to a generation of proton temperature anisotropy. The anisotropy leads first to destabilization of the dominant parallel fire hose, which interacts mainly with minor supra-Alfvenic protons, whereas the evolution of core protons is determined by expansion. Consequently, the effective anisotropy is only slightly reduced and the system eventually becomes unstable with respect to the oblique fire hose instability. The oblique fire hose strongly scatters the protons and removes the anisotropy disrupting the parallel fire hose. An important portion of the fluctuating wave energy is dissipated to protons, and only long wavelength waves remain in the system. The system with low wave activity then develops again larger temperature anisotropies, and the evolution repeats itself. It is concluded that both parallel and oblique proton fire hose instabilities constrain the proton temperature anisotropy in the expanding solar wind, with the latter one constituting a final frontier for the anisotropy. These results give a possible explanation of some apparent discrepancies between observations and linear predictions. In addition, a simple bounded anisotropy model is developed to include some of the kinetic effects of the fire hose instabilities in fluid models.