Nonlinear analysis of the degradation effects on Z-pinch implosions due to azimuthal magneto-Rayleigh–Taylor instabilities

Addressing the magneto-Rayleigh–Taylor (MRT) instability is crucial for enhancing the performance of magneto-inertial-fusion concepts, such as the Magnetized Liner Inertial Fusion platform. The MRT instability decreases the efficiency of conversion of the shell kinetic energy to the fuel internal energy, as well as reducing the confinement of the fuel near stagnation. We present a nonlinear, semi-analytical model for analyzing purely azimuthal MRT modes in an imploding Z-pinch. The model is based on the thin-shell approximation and fully takes into account the reorganization of the current density on the liner surface due to magnetic-tension effects. By numerically solving the governing equations, we investigate the degradation trends of the MRT instability on various performance metrics (e.g., stagnation pressure) as functions of MRT parameters (e.g., mode number and initial perturbation amplitude) and the 1D implosion characteristics (e.g., the 1D convergence ratio). Our findings suggest that, while azimuthal magnetic fields help correct initial asymmetries in the Z pinch, these corrections may often be excessive, developing asymmetry swings during the implosion and still resulting in an asymmetric stagnation event. Using a quasilinear analysis, we identify for the first time a constitutive relation between the degradation of the fuel pressure and the residual kinetic energy of the liner at stagnation while including the effects of magnetic fields on the Z pinch. Finally, we identify the position of the return-current path as an interesting design parameter to enhance the stabilizing effects of azimuthal magnetic fields toward initial asymmetries in the areal density of the liner.