Evolution of the fire-hose instability: Linear theory and wave-wave coupling

Large ion thermal or kinetic pressure anisotropies have been inferred to exist in conjunction with supernova shocks as well as in the solar wind/cometary interaction region and upstream from planetary bow shocks. For sufficiently strong thermal or beam-driven anisotropies, electromagnetic instability develops, isotropizing and scattering the ion populations. In particular, if the effective plasma beta > 2 (where beta is the ratio of plasma pressure to magnetic pressure), and if the anisotropy is such that the temperature parallel to the magnetic field exceeds the perpendicular, then fire-hose instability can result, generating transverse magnetic field fluctuations. In high-beta interstellar plasmas with large anisotropies, the level of the excited fluctuations may be quite large, exceeding even the ambient magnetic field. After a. period of inverse-cascade to longer wavelengths, it may provide a potential source for the scattering of cosmic rays. In this study we simulate the evolution of the fire-hose instability using a standard one-dimensional hybrid code (macroparticle ions, massless fluid electrons). We find that the wave evolution proceeds in two stages. A rapid period of growth brings the plasma back to approximate marginal stability. There follows a second stage of slower evolution dominated by wave-wave interaction. During the second stage, the wave energy spectrum clearly exhibits an inverse cascade. Implications for cosmic ray scattering will be discussed.