Stable and unstable supersonic stagnation of an axisymmetric rotating
  magnetized plasma
  The Naval Research Laboratory "Mag Noh problem", described in this paper, is
a self-similar magnetized implosion flow, which contains a fast MHD outward
propagating shock of constant velocity. We generalize the classic Noh (1983)
problem to include azimuthal and axial magnetic fields as well as rotation. Our
family of ideal MHD solutions is five-parametric, each solution having its own
self-similarity index, gas gamma, magnetization, the ratio of axial to the
azimuthal field, and rotation. While the classic Noh problem must have a
supersonic implosion velocity to create a shock, our solutions have an
interesting three-parametric special case with zero initial velocity in which
magnetic tension, instead of implosion flow, creates the shock at $t=0+$. Our
self-similar solutions are indeed realized when we solve the initial value MHD
problem with finite volume MHD code Athena. We numerically investigated the
stability of these solutions and found both stable and unstable regions in
parameter space. Stable solutions can be used to test the accuracy of numerical
codes. Unstable solutions have also been widely used to test how codes
reproduce linear growth, transition to turbulence, and the practically
important effects of mixing. Now we offer a family of unstable solutions
featuring all three elements relevant to magnetically driven implosions:
convergent flow, magnetic field, and a shock wave.
