General formulation for magnetohydrodynamic wave propagation, fire-hose, and mirror instabilities in Harris-type current sheets

Harris-type current sheets with the magnetic field model of (B) over bar = B-x(z)(x) over cap + B-y(z)(y) over cap have many important applications to space, astrophysical, and laboratory plasmas for which the temperature or pressure usually exhibits the gyrotropic form of (p) over right arrow = p(parallel to)(b) over cap(b) over cap + p(perpendicular to) ((I) over right arrow - (b) over cap(b) over cap). Here, p(parallel to) and p(perpendicular to) are, respectively, to be the pressure component along and perpendicular to the local magnetic field, (b) over cap = (B) over right arrow /B. This study presents the general formulation for magnetohydrodynamic (MHD) wave propagation, fire-hose, and mirror instabilities in general Harris-type current sheets. The wave equations are expressed in terms of the four MHD characteristic speeds of fast, intermediate, slow, and cusp waves, and in the local (k(parallel to), k(perpendicular to), z) coordinates. Here, k(parallel to) and k(perpendicular to) are, respectively, to be the wave vector along and perpendicular to the local magnetic field. The parameter regimes for the existence of discrete and resonant modes are identified, which may become unstable at the local fire-hose and mirror instability thresholds. Numerical solutions for discrete eigenmodes are shown for stable and unstable cases. The results have important implications for the anomalous heating and stability of thin current sheets. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4789383]