MHD aspects of fire-hose type instabilities

In a homogeneous anisotropic plasma the magnetohydrodynamic (MHD) shear Alfvén wave may become unstable P_||> p_⊥+ B²/μ_o. Recently, a new type of fire-hose instability was found by Hellinger and Matsumoto [2000] that has maximum growth rate occurring for oblique propagation and may grow faster than the Alfvén mode. This new mode is compressional and may be more efficient at destroying pressure anisotropy than the standard fire hose. This paper examines the fire-hose type (p_|| > p_⊥) instabilities based on the linear and nonlinear double-polytropic MHD theory. It is shown that there exist two types of MHD fire-hose instabilities, and with suitable choice of polytropic exponents the linear instability criteria become the same as those based on the Vlasov theory in the hydromagnetic limit. Moreover, the properties of the nonlinear MHD fire-hose instabilities are found to have great similarities with those obtained from the kinetic theory and hybrid simulations. In particular, the classical fire-hose instability evolves toward the linear fire-hose stability threshold, while the nonlinear marginal stability associated with the new fire hose is well below the condition of β_|| - β_⊥ = 2 but complies with less stringent linear stability threshold for compressible Alfvén waves.