Analysis of preheat propagation in MagLIF-like plasmas

The preheating and pre-magnetization of fusion fuel are key features in magnetized liner inertial fusion (MagLIF) configurations. Typically, the energy of the preheat laser is deposited in a central region of the fuel and propagates outward, generating magneto-hydrodynamic structures that impact the fuel mass distribution and magnetic flux compression during the subsequent implosion. We present a theoretical analysis of preheat propagation in a magnetized plasma under conditions typical for MagLIF. The analysis is based on the acoustic timescale for the propagation of pressure disturbances being much shorter than the conductive timescale for heat diffusion. In this regime, the preheat-driven expansion induces the stratification of the fuel and magnetic field, which accumulate in a dense outer shelf bounded by the leading shock. We derive self-similar solutions of the model that describe the hydrodynamic profiles of the expansion and evaluate the evolution of the magnetic field in this configuration. These solutions are supported by FLASH simulations of preheat propagation. Our analysis shows that, asymptotically in time, the regions where the magnetization of the fuel is significant tend to become localized at the interface separating the outer shelf from the inner hot core. We assess the implications of this stratification on the magnetic flux conservation and performance of fully integrated MagLIF FLASH simulations.