Comparison of multi-dimensional MHD simulations against exact solutions for a stagnating Z pinch

Summary form only given. Advanced simulations of high energy density plasma involve 2D and 3D computer codes. To ensure reliable results such codes should be subjected to verification tests, i.e., compared against exact analytic solutions. The present work examines the appropriateness of the 3D Cartesian code Athena for modeling stagnating Z-pinch implosions. The classic problem of a strong, self-similar expanding shock accreting inflowing gas of constant velocity by Noh is often used to benchmark codes, as done for a spherical implosion in. This is a pure hydrodynamic problem, and so to test the M in MHD for a cylindrical Z-pinch configuration one can use the shock-free, self-similar oscillations of a near-Bennett equilibrium pinch developed in. These solutions also allow optically thin Bremsstrahlung radiation, in which case the oscillations are damped. The most relevant tests for a stagnating pinch are the new, exact, self-similar solutions in that extend the Noh problem to include both ideal MHD with an azimuthal magnetic and/or various velocity profiles for the inflowing gas. Results using the Athena code will be compared to the near-Bennet oscillations, with and without radiation, and to the extension of Noh´s problem, with and without a magnetic field and velocity gradients. Numerical issues of grid imprint and divergence free magnetic fields are of primary concern when a Cartesian grid is used to model cylindrical dynamics. Further development of the code to include a circuit model, two temperatures, a “vacuum” treatment, thermal and resistive diffusion, and non-LTE radiation transport with tabular collisional radiative equilibrium will be discussed.