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The utilization of an external magnetic field greatly enhances the ion temperature and neutron yield from inertial confinement fusion capsule implosions, and viscosity is important in damping the small-scale mixing. In this paper, we present a linear analysis on Rayleigh–Taylor instability in the presence of viscosity and a vertical magnetic field. Unexpectedly, we find that the combined effects may strongly suppress the instability when the ratio S between the viscosity and the magnetic field strength is equal to 0.1, but enhance the instability for sufficiently large S, particularly for perturbations with high wave numbers. Moreover, the growth rate for S = 10 is broadly the same as when the magnetic field is absent, namely, S = 0. Therefore, the suppression or enhancement of the growth rates is greatly dependent on the ratio S. This phenomenon may play an essential role in the dynamics of intracluster gas in astrophysics and the uniformity of the compression target in magnetic inertial fusion. At last, we confirm that the viscosity instead of the electric resistivity plays a more important role to determine the interface motion in relation to inertial confinement fusion.

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Great attention has been attracted to study the viscous and elastic Rayleigh–Taylor instability in convergent geometries, especially for their low mode asymmetries that behave distinctively from the planar counterparts. However, most analyses have focused on the instability at static interfaces that excludes the studies of the Bell–Plesset effects and the elastic–plastic transition since they involve too complex mathematics. Herein, we perform detailed analyses on the dispersion relations by applying the viscous and elastic potential flow method to obtain their approximate growth rates compared with the exact ones to demonstrate: (i) The approximate growth rates based on potential flow method generally coincide with the exact ones. (ii) An alternative expression is proposed to overcome the discrepancy for the low mode asymmetries at fluid/fluid interface. (iii) Extra care must be taken in solids since the maximum discrepancies occur at the n = 1 mode and at the mode proximate to the cutoff. This analytical method of great simplicity is essential to describe the dynamic interface by including the overall motion of the interface based on the static construction, while the exact analysis involves too complex mathematics to be extended by including the Bell–Plesset effects and the elastic–plastic properties. To sum up, the approximate analytical dispersion relations derived in convergent geometries, have the potential for dealing with dynamic interfaces where Bell–Plesset effects are combined with elastic–plastic transition.