Self-similar rotating magnetized implosions

NRL Mag Noh problem is a self-similar cylindrical implosion flow, with a fast MHD outward propagating shock of constant velocity. Inspired by the Noh shock, this solution includes magnetic field and rotation, making our family of ideal exact Mag Noh solutions five-parametric, each solution having its own self- similarity index, gas gamma, magnetization, ratio of axial to azimuthal field and rotation. While classic Noh problem must have a supersonic implosion velocity to create a shock, our solution has an interesting special case with zero initial velocity, which creates the shock instantaneously. Our self-similar solutions are indeed realized when we solve initial condition problem with finite volume MHD code Athena. We found our solutions can be stable or unstable to azimuthal perturbations. It is important to check how numerical codes handle instabilities, transition to turbulence and mixing because in high energy density physics we often deal with unstable plasmas. Our analytic test solution features all elements relevant to magnetically driven implosions: convergent flow, magnetic field and the shock. A subset of our solutions has singular azimuthal current at the origin. Such singularity may help to create a hot spot in magnetically driven implosions.