The Richtmyer–Meshkov instability in magnetohydrodynamics

Abstract

In ideal magnetohydrodynamics ͑MHD͒, the Richtmyer-Meshkov instability can be suppressed by the presence of a magnetic field. The interface still undergoes some growth, but this is bounded for a finite magnetic field. A model for this flow has been developed by considering the stability of an impulsively accelerated, sinusoidally perturbed density interface in the presence of a magnetic field that is parallel to the acceleration. This was accomplished by analytically solving the linearized initial value problem in the framework of ideal incompressible MHD. To assess the performance of the model, its predictions are compared to results obtained from numerical simulation of impulse driven linearized, shock driven linearized, and nonlinear compressible MHD for a variety of cases. It is shown that the analytical linear model collapses the data from the simulations well. The predicted interface behavior well approximates that seen in compressible linearized simulations when the shock strength, magnetic field strength, and perturbation amplitude are small. For such cases, the agreement with interface behavior that occurs in nonlinear simulations is also reasonable. The effects of increasing shock strength, magnetic field strength, and perturbation amplitude on both the flow and the performance of the model are investigated. This results in a detailed exposition of the features and behavior of the MHD Richtmyer-Meshkov flow. For strong shocks, large initial perturbation amplitudes, and strong magnetic fields, the linear model may give a rough estimate of the interface behavior, but it is not quantitatively accurate. In all cases examined the accuracy of the model is quantified and the flow physics underlying any discrepancies is examined.

Linear simulations of the cylindrical Richtmyer-Meshkov instability in magnetohydrodynamics

“…The suppression was reconfirmed in the context of incompressible MHD linear stability analysis by Wheatley et al, 10 where it was demonstrated that Alfvén fronts were the vehicles of vorticity transport away from the interface. A more detailed investigation followed 11 in which nonlinear MHD simulations demonstrated the RMI suppression and extended the parameter ranges of earlier investigations. In these MHD investigations, the initial seed magnetic field was parallel to the incident shock front.…”

Linear Simulations of the Cylindrical Richtmyer-Meshkov Instability in Hydrodynamics and MHD

“…This was further reconfirmed by analytical incompressible Magnetohydrodynamics (MHD) theory of an impulsively accelerated interface developed by Wheatley et al [7,8,9]. In Samtaney's work, the magnetic field was aligned to the motion of the shock, the suppression of the RMI was caused by the bifurcation of the vortex sheet which transported the baroclinically generated vorticity away from the contact discontinuity by a pair of MHD shocks.…”

“…The "steady" means that the base state is not updated during every time step. In our test, the computational domain is set to be [R l , R r ] = [3,7].…”

Magnetohydrodynamic implosion symmetry and suppression of Richtmyer-Meshkov instability in an octahedrally symmetric field

“…Figure 5 shows snapshots of the density field, with magnetic field lines overlaid, at comparable times for L0, L1-32, L2-32, and L6-32 in the x-y plane. The suppression mechanism is the transport of vorticity away from the interface roughly along field lines, as extensively studied previously [11][12][13][14]20,30], by sub-fast MHD waves arising from the shock refraction process as the fast shock system processes the DI.…”

“…The application of such fields to flows of this kind has been seen in so-called magnetoinertial fusion techniques, from which the magnetized liner inertial fusion (MagLIF) concept has arisen (see Sefkow et al [7] and references); external fields have been used in the context of electron confinement to field lines with cited increased neutron yields at the hot spot [8,9], and of decreased alpha particle mobility [10]. The effects of such fields on hydrodynamic instabilities in conducting fluids, under the framework of magnetohydrodynamics (MHD), have also been investigated extensively in planar geometries in computational [11,12] and theoretical [13][14][15] contexts, with the strong suggestion that the RM instability is suppressed due to baroclinic vorticity transport away from the shocked interface by MHD waves. (Slightly different problem formulations, for example where the field is perturbed similarly to the density interface, result in different suppression mechanisms [16].)…”