On The Stability Of The Magnetized Noh Z-Pinch Problem

We have previously derived a semi-analytic self-similar solution to the ideal MHD equations that is a generalization of the classical Noh problem, and proposed that solution as a verification test for numerical codes designed to simulate Zpinch physics
¹
. This original work developed a solution for a radially imploding cylindrical plasma with an embedded magnetic field that was purely azimuthal. Subsequent work has yielded additional self-similar solutions, so far unpublished, that generalize that result to coexisting azimuthal and axial embedded magnetic fields. However, numerical simulations of one of these latter solutions has produced numerical results with a number of well-known MHD codes that would seem to indicate either numerical or physical azimuthal instability. These codes all used a Cartesian mesh, and thus checking for the growth of smallamplitude perturbations is significantly impeded by the imprint of the mesh itself.