Numerical simulations and analysis indicate that the Richtmyer-Meshkov instability (RMI) is suppressed in ideal magnetohydrodynamics (MHD) in Cartesian slab geometry. Motivated by the presence of hydrodynamic instabilities in inertial confinement fusion and suppression by means of a magnetic field, we investigate the RMI via linear MHD simulations in cylindrical geometry. The physical setup is that of a Chisnell-type converging shock interacting with a density interface with either axial or azimuthal (2D) perturbations. The linear stability is examined in the context of an initial value problem (with a time-varying base state) wherein the linearized ideal MHD equations are solved with an upwind numerical method. Linear simulations in the absence of a magnetic field indicate that RMI growth rate during the early time period is similar to that observed in Cartesian geometry. However, this RMI phase is short-lived and followed by a Rayleigh-Taylor instability phase with an accompanied exponential increase in the perturbation amplitude. We examine several strengths of the magnetic field (characterized by β=2pBr2) and observe a significant suppression of the instability for β ≤ 4. The suppression of the instability is attributed to the transport of vorticity away from the interface by Alfvén fronts.

We investigate the linear stability of both positive and negative Atwood ratio interfaces accelerated either by a fast magnetosonic or hydrodynamic shock in cylindrical geometry. For the magnetohydrodynamic (MHD) case, we examine the role of an initial seed azimuthal magnetic field on the growth rate of the perturbation. In the absence of a magnetic field, the Richtmyer-Meshkov growth is followed by an exponentially increasing growth associated with the Rayleigh-Taylor instability. In the MHD case, the growth rate of the instability reduces in proportion to the strength of the applied magnetic field. The suppression mechanism is associated with the interference of two waves running parallel and anti-parallel to the interface that transport vorticity and cause the growth rate to oscillate in time with nearly a zero mean value. IntroductionThe Richtmyer-Meshkov instability (RMI) occurs when a shock wave impulsively accelerates a perturbed density interface separating two different fluids [1,2]. RMI may not be classified as a classical hydrodynamic instability with modal analysis because the perturbations grow algebraically (linearly in time) rather than exponentially. The RMI occurs in a variety of physical applications. It is important in astrophysical phenomena such as supernova explosions, supersonic combustion in hypersonic air-breathing engines, and inertial confinement fusion (ICF) [3,4,5]. In direct-drive ICF, small capsules containing a deuterium and tritium fuel are compressed by laser-generated shock waves, where achieving sufficiently high pressures and temperatures inside the compressed ICF targets to ignite the fuel is the primary goal of this process. On the other hand, in indirect drive approach to ICF, the driver energy (from laser beams or ion beams) is first absorbed in a high-Z enclosure (a hohlraum), which surrounds the capsule. The material heated by the driver releases X-rays, which drive the capsule implosion [6]. The mixing between the outer shell and the inner fuel inhibits the fusion reaction due to RMI and RTI (Rayleigh Taylor instability) which limits the energy production [7,8,9].The RMI in the presence of a magnetic field initially oriented parallel to the incident shock direction has been investigated numerically and theoretically. Nonlinear ideal magnetohydrodynamics (MHD) simulations of a shock interaction with an oblique planar contact discontinuity were discussed by Samtaney [10]. It was demonstrated that the RMI is suppressed by the existence of such a magnetic field. The primary suppression mechanism may be attributed to transport of baroclinic vorticity away from the density interface by slow-or intermediate mode shocks reducing the vorticity at the interface. This results were reconfirmed in the context of incompressible MHD linear stability analysis by Wheatley et al. [11]. They demonstrated that vorticity is transported away from the interface by Alfvén fronts. More detailed nonlinear MHD simulations extending the parameter ranges of earlier investigations [12] demo...

The Richtmyer-Meshkov instability (RMI) occurs when a shock impulsively accelerates an interface between two different fluids, and it is important in many technological applications such as inertial confinement fusion (ICF) and astrophysical phenomena such as supernova. Here, we present incompressible models of an impulsively accelerated interface separating conducting fluids of different densities in cylindrical geometry. The present study complements earlier investigations on linear and nonlinear simulations of RMI. We investigate the influence of a normal or an azimuthal magnetic field on the growth rate of the interface. This is accomplished by solving the linearized initial value problem using numerical inverse Laplace transform. For a finite normal magnetic field, although the initial growth rate of the interface is unaffected by the presence of the magnetic field, at late-time the growth rate of the interface decays. This occurs by transporting the vorticity by two Alfvén fronts which propagate away from the interface. For the azimuthal magnetic field configuration, the suppression mechanism is associated with the interference of two waves propagating parallel and antiparallel to the interface that transport vorticity and cause the growth rate to oscillate in time with nearly a zero mean value. Comparing the results of the incompressible models with linear compressible MHD simulations show reasonable agreement at early time of simulations.

We investigate the linear evolution of the Richtmyer–Meshkov instability (RMI) in the framework of an ideal two-fluid plasma model. The two-fluid plasma equations of motion are separated into a base state and a set of linearized equations governing the evolution of the perturbations. Different coupling regimes between the charged species are distinguished based on a non-dimensional Debye length parameter [Formula: see text]. When [Formula: see text] is large, the coupling between ions and electrons is sufficiently small that the induced Lorentz force is very weak and the two species evolve as two separate fluids. When [Formula: see text] is small, the coupling is strong and the induced Lorentz force is strong enough that the difference between state of ions and electrons is rapidly decreased by the force. As a consequence, the ions and electrons are tightly coupled and evolve like one fluid. The temporal dynamics is divided into two phases: an early phase wherein electron precursor waves are prevalent and a post-ion shock-interface interaction phase wherein the RMI manifests itself. We also examine the effect of an initially applied magnetic field in the streamwise direction characterized by the non-dimensional parameter β0. For a short duration after the ion shock-interface interaction, the growth rate is similar for different initial magnetic field strengths. Time progresses the suppression of the instability because the magnetic field is observed. The growth rate shows oscillations with a frequency that is related to the ion or electron cyclotron frequency. The instability is suppressed due to the oscillation of vorticity on the interface caused by the perturbed Lorentz force.