Linear Analysis of the m=0 Instability for a Visco-resistive Hall MHD Plasma

We present a comprehensive analysis of the linear dispersion relation for the axisymmetric (m=0) compressible interchange instability of Bennett equilibria in a visco-resistive, Hall MHD plasma. The full anisotropic stress tensor with Braginskii viscous coefficients is considered. The eigenvalues are obtained numerically. For small axial mode number, Hall currents enhance the growth rates, whereas in the limit of high mode number the growth rates are suppressed, eventually resulting in wave cutoff, even in the ideal limit. For the visco-resistive plasma the unstable spectra are weakly dependent on the off-diagonal elements of the stress tensor