Slow Resonant MHD Waves in One-dimensional Magnetic Plasmas with Anisotropic Viscosity and Thermal Conductivity
Slow resonant MHD waves are studied in a compressible plasma with strongly anisotropic viscosity and thermal conductivity. It is shown that anisotropic viscosity and/or thermal conductivity removes the slow singularity which is present in the linear ideal MHD equations. Simple analytical solutions to the linear dissipative MHD equations are obtained which are valid in the dissipative layer and in two overlap regions to the left and the right of the dissipative layer. Asymptotic analysis of the dissipative solutions enables us to obtain connection formulae specifying the variations or jumps of the different wave quantities across the dissipative layer. These connection formulae coincide with those obtained previously for plasmas with isotropic viscosity and finite electrical conductivity. The thickness of the dissipative layer is inversely proportional to the Reynolds number, in contrast to the case of isotropic dissipative coefficients, where it is inversely proportional to the cube root of the Reynolds number. The behavior of the perturbations in the dissipative layer is described in terms of elementary functions of complex argument.