Nonlinear study of the dynamics of Z-pinch implosions: The role of azimuthal magneto Rayleigh-Taylor instabilities in performance degradation

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 (MagLIF) platform. The MRT instability decreases the efficiency of conversion of the shell kinetic energy to the fuel internal energy and reduces 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 [1]. The model is based on the thin-shell approximation and takes into account the reorganization of the current density on the liner surface due to magnetic-tension effects. 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). We find 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 a constitutive relation between the degradation of the fuel pressure and the residual kinetic energy of the liner at stagnation. Finally, we identify the position of the return-current path as an interesting design parameter to enhance the stabilizing effects of azimuthal magnetic fields.