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Register a new userRichtmyer-Meshkov Instability of an Imploding Flow with a Two-Fluid Plasma Model
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The two-fluid (ions and electrons) plasma Richtmyer-Meshkov instability of a cylindrical light/heavy density interface is numerically investigated without an initial magnetic field. Varying the Debye length scale, we examine the effects of the coupling between the electron and ion fluids. When the coupling becomes strong, the electrons are restricted to co-move with the ions and the resulting evolution is similar to the hydrodynamic neutral fluid case. The charge separation that occurs between the electrons and ions results in self-generated electromagnetic fields. We show that the Biermann battery effect dominates the generation of magnetic field when the coupling between the electrons and ions is weak. In addition to the Rayleigh-Tayler stabilization effect during flow deceleration, the interfaces are accelerated by the induced spatio-temporally varying Lorentz force. As a consequence, the perturbations develop into the Rayleigh-Taylor instability, leading to an enhancement of the perturbation amplitude compared with the hydrodynamic case.
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We study the Richtmyer--Meshkov (RM) instability of a relativistic perfect fluid by means of high order numerical simulations with adaptive mesh refinement (AMR). The numerical scheme adopts a finite volume Weighted Essentially Non-Oscillatory (WENO) reconstruction to increase accuracy in space, a local space-time discontinuous Galerkin predictor method to obtain high order of accuracy in time and a high order one-step time update scheme together with a cell-by-cell space-time AMR strategy with time-accurate local time stepping. In this way, third order accurate (both in space and in time) numerical simulations of the RM instability are performed, spanning a wide parameter space. We present results both for the case in which a light fluid penetrates into a higher density one (Atwood number $A>0$), and for the case in which a heavy fluid penetrates into a lower density one (Atwood number $A<0$). We find that, for large Lorentz factors gamma_s of the incident shock wave, the relativistic RM instability is substantially weakened and ultimately suppressed. More specifically, the growth rate of the RM instability in the linear phase has a local maximum which occurs at a critical value of gamma_s ~ [1.2,2]. Moreover, we have also revealed a genuine relativistic effect, absent in Newtonian hydrodynamics, which arises in three dimensional configurations with a non-zero velocity component tangent to the incident shock front. In this case, the RM instability is strongly affected, typically resulting in less efficient mixing of the fluid.
The paper presents a review of dynamic stabilization mechanisms for plasma instabilities. One of the dynamic stabilization mechanisms for plasma instability was proposed in the papers [Phys. Plasmas 19, 024503(2012) and references therein], based on a perturbation phase control. In general, instabilities emerge from the perturbations of the physical quantity. Normally the perturbation phase is unknown so that the instability growth rate is discussed. However, if the perturbation phase is known, the instability growth can be controlled by a superimposition of perturbations imposed actively: if the perturbation is introduced by, for example, a driving beam axis oscillation or so, the perturbation phase can be controlled and the instability growth is mitigated by the superimposition of the growing perturbations. Based on this mechanism we present the application results of the dynamic stabilization mechanism to the Rayleigh-Taylor (R-T) instability and to the filamentation instability as typical examples in this paper. On the other hand, in the paper [Comments Plasma Phys. Controlled Fusion 3, 1(1977)] another mechanism was proposed to stabilize the R-T instability based on the strong oscillation of acceleration, which was realized by the laser intensity modulation in laser inertial fusion [Phys. Rev. Lett. 71, 3131(1993)]. In the latter mechanism, the total acceleration strongly oscillates, so that the additional oscillating force is added to create a new stable window in the system. Originally the latter mechanism was proposed by P. L. Kapitza, and it was applied to the stabilization of an inverted pendulum. In this paper we review the two dynamic stabilization mechanisms, and present the application results of the former dynamic stabilization mechanism.
We investigate the flow of a nano-scale incompressible ridge of low-volatility liquid along a chemical channel: a long, straight, and completely wetting stripe embedded in a planar substrate, and sandwiched between two extended less wetting solid regions. Molecular dynamics simulations, a simple long-wavelength approximation, and a full stability analysis based on the Stokes equations are used, and give qualitatively consistent results. While thin liquid ridges are stable both statically and during flow, a (linear) pearling instability develops if the thickness of the ridge exceeds half of the width of the channel. In the flowing case periodic bulges propagate along the channel and subsequently merge due to nonlinear effects. However, the ridge does not break up even when the flow is unstable, and the qualitative behavior is unchanged even when the fluid can spill over onto a partially wetting exterior solid region.
The previous study regarding the stabilization of a magnetized constant temperature plasma by shear flow with vorticity is extended to a plasma of non-constant temperature, where in the presence of heat source or sinks the thermomagnetic Nernst effect becomes important. Of special interest is what this effect has on the stabilization of a linear z-pinch discharge for which exact solutions are given. Solutions which are unstable for subsonic shear flow become stable if the flow is supersonic.
We present the first observation of instability in weakly magnetized, pressure dominated plasma Couette flow firmly in the Hall regime. Strong Hall currents couple to a low frequency electromagnetic mode that is driven by high-$beta$ ($>1$) pressure profiles. Spectroscopic measurements show heating (factor of 3) of the cold, unmagnetized ions via a resonant Landau damping process. A linear theory of this instability is derived that predicts positive growth rates at finite $beta$ and shows the stabilizing effect of very large $beta$, in line with observations.
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