Examination of the Coupling Between Electrothermal and Rayleigh-Taylor Instabilities in Pulsed Power Driven Implosions*

The electrothermal instability (ETI) and the magneto–Rayleigh-Taylor instability (MRTI) are two magnetohydrodynamic (MHD) instabilities that have impeded efforts to achieve nuclear fusion ignition in high energy density (HED) pulsed power fusion devices, such as magnetized liner inertial fusion (MagLIF). While the non-linear governing equations can be linearized to yield theoretical growth rates for each individual instability, further work is required to provide a comprehensive, quantitative description of how the ETI evolves into the MRTI. During liner evolution, the early-time ETI growth rate is non-trivial to derive analytically due to substantial phase changes accompanied by significantly varying temperatures and electrical conductivities, even during the linear growth phase. One promising analytical technique for extracting the underlying dynamics is Koopman theory, a framework for recasting non-linear equations into a set of measurement functions that can be advanced in time by an infinite-dimensional, linear operator known as the Koopman operator and whose spectral properties can describe the growth and decay rates of respective spatial modes. This talk describes the novel use of a Koopman neural network to extract coherent spatial structures and time-varying growth and decay rates from fluid flows in 2D resistive MHD simulations of pulsed-power–driven explosions/implosions.