Magneto-Rayleigh-Taylor Instability: Theory and simulation in planar and cylindrical pulsed power targets

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 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 the presence of an axial magnetic field and the effects of sausage and kink modes (present in cylindrical coordinates only). In general, the total instability growth rates in cylindrical geometry are found to be larger than those in planar geometry. MRT and feedthrough is shown to be suppressed by strong magnetic field line bending (tension). However, for the same amount of field line bending, feedthrough is the most stabilized. Application of the planar and the cylindrical model to results from the Z-machine at Sandia National Laboratories is presented. 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). 1D HYDRA MHD simulations are used to generate realistic, evolving profiles (in density, pressure, and magnetic field) during the implosion from which instantaneous growth rates can be computed exactly, using either the planar or cylindrical analytic formulae developed in this thesis. Sophisticated 2D HYDRA MHD simulations were also performed to compare with the analytic theory and experimental results. In 2D, highly compressed axial magnetic fields can reduce the growth of perturbations at the fuel/liner interface during the implosion phase. This enhances the stability of a liner implosion. The effect of shock compression was also examined using HYDRA. It was found 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. This result implies shock compression should occur before any substantial instability growth on the liner exterior. Large scale perturbations on the liner interior may also feedout to the liner exterior due to shock compression of the liner. These newly discovered shock effects are independent of and typically overwhelm feedthrough. The result is that perturbations on the liner interior have the potential to destabilize the liner during the implosion phase. Feedthrough is found to be dominant only when shock compression is minimized.