Richtmyer–Meshkov instability of a thermal interface in a two-fluid plasma

Bond, D.; Wheatley, Vincent; Samtaney, Ravi; Pullin, D. I.

doi:10.1017/jfm.2017.693

Cited by 27 publications

(81 citation statements)

References 44 publications

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“…where m e;i are the electron and ion masses, e is the electron charge, n i is the ion number density, T is the temperature, k B is the Boltzmann constant, 0 is the vacuum permittivity, and ln K is the Coulomb potential which evaluates to be of order O (10) in most of the plasmas. The two-fluid plasma model, henceforth denoted as 2FP, is particularly relevant when the characteristic length scale is comparable to the ion skin depth, and the characteristic time scale is comparable to the ion cyclotron period.…”

Section: Introductionmentioning

confidence: 99%

On the magnetohydrodynamic limits of the ideal two-fluid plasma equations

Shen

Pullin

et al. 2018

Physics of Plasmas

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The two-fluid plasma equations describing a magnetized plasma, originating from truncating moments of the Vlasov-Boltzmann equation, are increasingly used to describe an ion-electron plasma whose transport phenomena occur on a time scale slower and a length scale longer than those of particle collisions. A similar treatment under more stringent constraints gives the single-fluid magnetohydrodynamic (MHD) equations for low-frequency macroscopic processes. Since both stem from kinetic theory, the two-fluid plasma and MHD equations are necessarily related to each other. Such a connection is often established via ad hoc physical reasoning without a firm analytical foundation. Here, we perform a sequence of formal expansions for the dimensionless ideal two-fluid plasma equations with respect to limiting values of the speed-of-light c, the ion-to-electron mass ratio M, and the plasma skin depth dS. Several different closed systems of equations result, including separate systems for each limit applied in isolation and those resulting from limits applied in combination, which correspond to the well-known Hall-MHD and single-fluid ideal MHD equations. In particular, it is shown that while the zeroth-order description corresponding to the c→∞ limit, with M and dS fixed, is strictly charge neutral, it nonetheless uniquely determines the perturbation charge non-neutrality at the first order. Furthermore, the additional M→∞ limit is found to be not required to obtain the single-fluid MHD equations despite being essential for the Hall-MHD system. The hierarchy of systems presented demonstrates how plasmas can be appropriately modeled in situations where only one of the limits applies, which lie in the parameter space in between where the two-fluid plasma and Hall-MHD models are appropriate.

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Section: Introductionmentioning

confidence: 99%

On the magnetohydrodynamic limits of the ideal two-fluid plasma equations

Shen

Pullin

et al. 2018

Physics of Plasmas

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“…The extreme temperatures required for ICF implosion inevitably causes rapid ionization of the involved materials, which then leads to interaction between the conducting fluids and magnetic fields that are imposed or self-generated [9][10][11][12]. In order to model the coupled evolution of plasmas and magnetic fields, several theoretical descriptions have been considered.…”

Section: Introductionmentioning

confidence: 99%

“…Srinivasan and Tang [18] adopted the Hall-MHD model to examine the magnetic field generation and growth for the gravity induced Rayleigh-Taylor instabilities (RTI). More recently, Bond et al [12] investigated computationally the RMI without initial magnetic field using the ideal two-fluid plasma equations. In order of decreasing complexity, Shen et al [19] showed that the ideal two-fluid plasma equations, the Hall-MHD and regular MHD models, are connected via a series of limiting processes with respect to the appropriately scaled parameters including the speed of light, the ion skin depth, and ion-to-electron mass ratio.…”

Section: Introductionmentioning

confidence: 99%

Impulse-driven Richtmyer-Meshkov instability in Hall-magnetohydrodynamics

et al. 2019

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We utilize the incompressible, Hall-magnetohydrodynamics (MHD) model for conducting fluids to investigate the effect of Hall current on the stability of an impulsively accelerated, perturbed density interface, or contact discontinuity (CD) separating two fluids in the presence of a background magnetic field. This is used as a simple model, in a conducting fluid, of a Richtmyer-Meshkov type flow that is characterized in a neutral fluid by a shock-wave-density-interface interaction. Two versions of the Hall-MHD equations are explored. In the first, the ions are treated as an incompressible fluid but the electron gas retains its compressibility, while for the second version the incompressible limit for both species is invoked. The linearized equations of motion are first formulated for a sinusoidal interface perturbation and then solved as an initial-value problem using a Laplace transform method with general numerical inversion but with analytical inversion for some limitingparameter cases. While the field equations are identical for both Hall-MHD models, the CD-jump conditions differ leading to qualitatively similar but quantitatively different CD dynamics. For both models, the presence of the magnetic field is found to suppress the incipient interfacial growth associated with neutral-gas, Richtmyer-Meshkov instability (RMI). When the ion skin depth is finite, the vorticity dynamics that drive the suppression of the RMI differ markedly from the ideal MHD, RMI flow. On the interface, the Hall-MHD description allows the presence of a tangential slip velocity which leads to finite circulation deposition. Away from the interface, vorticity is produced by the perturbed magnetic fields and transported to infinity by a dispersive wave system. This leads to decay of the velocity slip at the interface with the effect that interface growth remains bounded but distorted by damped oscillations associated with the ion cyclotron effect. The flow behavior for several limits of the ion skin depth and the Larmor radius is explored. Specific comparisons with the results from both models against ideal MHD are presented.

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“…Moreover, a shock which formation not mediated by collisionless plasma instabilities will not inherit the downstream electromagnetic patterns formed by these instabilities. Collisions of shells with curved boundaries may trigger downstream vorticity that could generate magnetic fields [54]. But colliding planar shells like those considered here, will yield a field-free downstream if the formation is collisional.…”

Section: Discussionmentioning

confidence: 88%

On the formation and properties of fluid shocks and collisionless shock waves in astrophysical plasmas

Bret

Pe’er

2018

J. Plasma Phys.

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When two plasmas collide, their interaction can be mediated by collisionless plasma instabilities or binary collisions between particles of each shell. By comparing the maximum growth rate of the collisionless instabilities with the collision frequency between particles of the shells, we determine the critical density separating the collisionless formation from the collisional formation of the resulting shock waves. This critical density is also the density beyond which the shock downstream is field free, as plasma instabilities do not have time to develop electromagnetic patterns. We further determine the conditions on the shells initial density and velocity for the downstream to be collisional. If these quantities fulfil the determined conditions, the collisionality of the downstream also prevents the shock from accelerating particles or generating strong magnetic fields. We compare the speed of sound with the relative speed of collision between the two shells, thus determining the portion of the parameter space where strong shock formation is possible for both classical and degenerate plasmas. Finally, we discuss the observational consequences in several astrophysical settings.

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Richtmyer–Meshkov instability of a thermal interface in a two-fluid plasma

Cited by 27 publications

References 44 publications

On the magnetohydrodynamic limits of the ideal two-fluid plasma equations

On the magnetohydrodynamic limits of the ideal two-fluid plasma equations

Impulse-driven Richtmyer-Meshkov instability in Hall-magnetohydrodynamics

On the formation and properties of fluid shocks and collisionless shock waves in astrophysical plasmas

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