The effect of an initially uniform magnetic field of arbitrary orientation on the Richtmyer–Meshkov instability in Hall-magnetohydrodynamics (MHD) and ideal MHD is considered. Attention is restricted to the case where the initial density interface has a single-mode sinusoidal perturbation in amplitude and is accelerated by a shock traveling perpendicular to the interface. An incompressible Hall-MHD model for this flow is developed by solving the relevant impulse-driven linearized initial value problem. The ideal MHD theory is naturally obtained by taking the limit of vanishing ion skin depth. It is shown that the out-of-plane magnetic field component normal to both the impulse and the interface perturbation does not affect the evolution of the flow. For all field orientations other than strictly out-of-plane, the growth of interface perturbations is suppressed. However, the suppression is most effective for near tangential fields but becomes less effective with increasing ion skin depth and Larmor radius. The modeled suppression mechanism is transport of vorticity along magnetic field lines via Alfven fronts in ideal MHD, and via a dispersive wave system in Hall-MHD. Oscillation of the interface growth rate is caused by a continuous phase change of the induced velocities at the interface due to vorticity transport parallel to the perturbation direction in ideal MHD, while it can also result from interfacial vorticity production associated with the ion cyclotron effect in Hall-MHD with a finite Larmor radius. The limiting flow behavior of a large ion-skin-depth is explored. To assess the accuracy and appropriateness of the incompressible model, its ideal MHD predictions are compared to the results of the corresponding shock-driven nonlinear compressible simulations.

中文翻译：

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任意定向磁场下的磁流体动力学 Richtmyer-Meshkov 不稳定性

考虑了任意方向的初始均匀磁场对霍尔磁流体动力学 (MHD) 和理想 MHD 中 Richtmyer-Meshkov 不稳定性的影响。注意仅限于初始密度界面在幅度上具有单模正弦扰动并且由垂直于界面行进的激波加速的情况。通过解决相关的脉冲驱动线性化初始值问题，开发了该流动的不可压缩 Hall-MHD 模型。理想的 MHD 理论是取消失离子趋肤深度的极限自然得到的。结果表明，垂直于脉冲和界面扰动的平面外磁场分量不影响流动的演变。对于除严格平面外的所有场方向，抑制了界面扰动的增长。然而，抑制对近切线场最有效，但随着离子趋肤深度和拉莫尔半径的增加而变得不那么有效。建模的抑制机制是通过理想 MHD 中的 Alfven 前沿和霍尔-MHD 中的色散波系统沿磁场线传输涡量。界面生长速率的振荡是由在理想 MHD 中平行于扰动方向的涡量传输引起的界面处诱导速度的连续相变引起的，同时它也可能由与霍尔中的离子回旋加速器效应相关的界面涡量产生引起-MHD 具有有限的拉莫尔半径。探索了大离子趋肤深度的限制流动行为。为了评估不可压缩模型的准确性和适用性，