Parallel Viscous Modification of the Resistive "Tearing" Instability in a Cartesian Model of the Hard-Core Pinch

There is continuing interest in the possibility that a diffuse pinch may be used to achieve plasma containment in the laboratory, and ultimately lead to a successful thermonuclear reactor. Such a system is likely to be stabilized against hydromagnetic modes by strong magnetic field shear, but the question of stability against resistive modes remains. In this note, a Cartesian model is adopted, and the influence of "parallel" viscosity (Stringer 1970) on the resistive "tearing" instability in the hard-core pinch is examined. Previously, purely resistive calculations of growth rates in this configuration have been reported by Hosking (1967) and Lister and Hosking (1970).