Abstract
We present the linear theory of two-dimensional incompressible magneto-Rayleigh–Taylor instability in a system composed of a linear elastic (Hookean) layer above a lighter semi-infinite ideal fluid with magnetic fields present, above and below the layer. As expected, magnetic field effects and elasticity effects together enhance the stability of thick layers. However, the situation becomes more complicated for relatively thin slabs, and a number of new and unexpected phenomena are observed. In particular, when the magnetic field beneath the layer dominates, its effects compete with effects due to elasticity, and counteract the stabilising effects of the elasticity. As a consequence, the layer can become more unstable than when only one of these stabilising mechanisms is acting. This somewhat unexpected result is explained by the different physical mechanisms for which elasticity and magnetic fields stabilise the system. Implications for experiments on magnetically driven accelerated plates and implosions are discussed. Moreover, the relevance for triggering of crust-quakes in strongly magnetised neutron stars is also pointed out.
Highlights
Rayleigh–Taylor (RT) instability is a well-known phenomenon in hydrodynamics that occurs whenever a denser medium lays on top of a lighter one in a uniform gravitational field g or, equivalently, when the denser medium is pushed and accelerated by the lighter one with an acceleration −g (Rayleigh 1883, Taylor 1950)
The slab overlays an ideal fluid of density ρ1 < ρ2 occupying the region y 0, which is filled with a uniform magnetic field B1 = B1ex
We have presented a linear theory for the two-dimensional magneto-Rayleigh– Taylor (MRT) instability in a system that is composed of an elastic layer that lies above a lighter ideal fluid
Summary
Rayleigh–Taylor (RT) instability is a well-known phenomenon in hydrodynamics that occurs whenever a denser medium lays on top of a lighter one in a uniform gravitational field g or, equivalently, when the denser medium is pushed and accelerated by the lighter one with an acceleration −g (Rayleigh 1883, Taylor 1950). The more interesting situation in which the heavy medium is a slab with elastic properties is of great relevance to many experiments on high-energy-density physics involving magnetically accelerated flyer plates that still retain its mechanical properties when it is impacted on a target sample (Lemke, Knudson & Davis 2011, Martin et al 2012) This problem is of interest in the recently proposed approach to inertial confinement fusion known as magnetic inertial fusion, in which a magnetic field is used to mitigate the thermal conduction losses from the compressed fusion fuel, so that the ignition requirements are relaxed (Davies et al 2017; Seyler et al 2018). This competition phenomenon may become an issue for the magnetic inertial fusion aiming to use solid slabs in combination with magnetic fields to mitigate the effects of the MRT instability during the acceleration process
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