  The effect of magnetic tension and diffusion on the perturbation growth of a
liquid-metal liner subjected to the magneto-Rayleigh-Taylor (MRT) instability
is investigated. An initially magnetic-field-free liquid-metal slab of finite
thickness is surrounded by two lower-density regions. Within the lower region,
a constant axial magnetic field of arbitrary magnitude is applied. The
numerical examination of the MRT instability growth, initiated by a seeded
perturbation parallel to the magnetic field at the liner's unstable interface,
is performed for both perfectly conductive and resistive liners. To this end, a
novel level set-based two-phase incompressible solver for ideal/resistive
magnetohydrodynamic (MHD) flows within the finite-difference framework is
introduced. Utilizing the implemented numerical toolkit, the impact of
different Alfven numbers and magnetic Reynolds numbers on the MRT growth rate
and feedthrough at the upper interface of the liner is studied. Accounting for
the finite resistivity of the liner results in an increase in the MRT growth
and feedthrough compared to the ideal MHD case. The results indicate that
magnetic diffusion primarily affects the MRT growth rate for higher
wavenumbers, while for smaller wavenumbers, the effect of finite resistivity is
only observed over a longer duration of instability development. We further
demonstrate that decreasing the Alfven number results in the faster emergence
of the magnetic diffusion effect on the MRT growth rate. It is also observed
that a greater electrical conductivity jump across the liner results in an
increased perturbation growth. Lastly, the impact of surface tension on MRT
instability growth for both ideal and resistive MHD cases is studied across
different wavenumbers, specifically for Bond numbers related to fusion
applications.
