Magneto-Rayleigh-Taylor Instability: Theory and Simulation in Planar and Cylindrical Pulsed Power Targets.

Abstract

Cylindrical liner implosions in the Magnetized Liner Inertial Fusion (MagLIF) concept are susceptible to the magneto-Rayleigh-Taylor instability (MRT). The danger of MRT enters in two phases, (1) during the main implosion, the outer surface of the liner is MRT unstable, and (2) during the short time period when the liner decelerates onto the hot fuel, the inner surface becomes unstable. Growth of MRT on the outer surface may also feedthrough, which may seed the inner surface leading to high MRT growth in the second phase. If MRT growth becomes large enough, confinement of the fuel is lost.

To characterize MRT, we solve the linearized, ideal MHD equations in both planar and cylindrical geometries, including an axial magnetic field and the effects of sausage and kink modes. To evaluate our analytic growth rates, 1D HYDRA MHD simulations are used to generate realistic, evolving profiles (in density, pressure, and magnetic field) during the implosion. In general, the total instability growth rates in cylindrical geometry are larger than those in planar geometry. MRT and feedthrough are suppressed by strong magnetic field line bending (tension). We apply our analytic MRT growth rates to experiments on the Z-machine at Sandia National Laboratories. Analytic MRT growth rates for a typical magnetized MagLIF-like implosion show the kink mode to be the fastest growing early and very late in the liner implosion (during deceleration).

Sophisticated 2D HYDRA simulations show that highly compressed axial magnetic fields can reduce the growth of perturbations at the fuel/liner interface during the implosion phase, enhancing the stability of the implosion. HYDRA 2D simulations also show that a non-uniform shock, driven from the liner exterior, can seed the liner interior, leading to substantial growth of instability far in excess of feedthrough. Large-scale perturbations on the liner interior may also feedout to the liner exterior when a shock wave interacts with the surface, which further destabilizes the liner. These effects are reduced when shock compression is minimized or significant perturbations are not present during shock compression. The feedthrough effects then dominate.