The impact of viscosity on the linear growth of the sausage and magneto-Rayleigh–Taylor instabilities in imploding cylindrical liners

Magnetised liner inertial fusion (MagLIF) has attracted attention in the past decade for its high obtained Lawson triple products and prospects to scale to ignition. In this work, we investigate the effect of viscosity on the sausage instability and magneto-Rayleigh–Taylor instability (MRTI) in conditions relevant for MagLIF implosions. First, we quantify the amount of damping that viscosity has on instability growth by deriving an expression for the ratio between viscous and inviscid growth rates. This expression is parameterised by a single non-dimensional number: the Galilei number $Ga$ , which measures the ratio of gravitational and viscous forces. We discuss in detail the physical intuition $Ga$ provides on instability growth. The derived growth rates are then validated against FLASH simulations. We then calculate a critical viscosity threshold $\eta _{c}$ required for viscosity to dampen the instability growth rate by 5 %. From this analysis, we show that, for drive currents relevant to laboratory MagLIF experiments (of the order of tens of MA), this critical viscosity threshold is much greater than realistic liner viscosity values except for the shortest perturbation wavelength regimes. We conclude that viscosity does not play a significant role in the initial linear growth of the sausage instability and MRTI in MagLIF liners, but our results motivate future investigation into effects of viscosity in nonlinear and high temperature regimes.