剪切片近似下的线性Vlasov理论及其在磁转动不稳定性中的应用
Linear Vlasov Theory in the Shearing Sheet Approximation with Application to the Magneto-Rotational Instability
摘要：
在剪切片近似下，我们导出了热的、无碰撞的、电荷中性等离子体的轴对称扰动的电导率张量。我们的结果推广了著名的线性Vlasov理论的均匀等离子体差分旋转等离子体，可用于广泛的动力学稳定性计算。我们将这些结果应用于无碰撞等离子体中的磁旋转不稳定性（MRI）的线性理论。我们的分析和数值计算表明，一般动力学理论的结果在这里得到减少在适当的限制以前的结果在文献中，包括低频引导中心（或“动力学MHD”）近似，霍尔MHD，和陀螺粘性近似。我们重新审视冷等离子体模型的MRI和表明，与以前的结果相反，最初未磁化的碰撞等离子体是线性稳定的轴对称扰动的冷等离子体近似。除了他们的应用天体物理等离子体，我们的研究结果提供了一个有用的框架，在实验室实验中评估差分旋转等离子体的线性稳定性。
英文摘要：
We derive the conductivity tensor for axisymmetric perturbations of a hot, collisionless, and charge-neutral plasma in the shearing sheet approximation. Our results generalize the well-known linear Vlasov theory for uniform plasmas to differentially rotating plasmas and can be used for wide range of kinetic stability calculations. We apply these results to the linear theory of the magneto-rotational instability (MRI) in collisionless plasmas. We show analytically and numerically how the general kinetic theory results derived here reduce in appropriate limits to previous results in the literature, including the low frequency guiding center (or "kinetic MHD") approximation, Hall MHD, and the gyro-viscous approximation. We revisit the cold plasma model of the MRI and show that, contrary to previous results, an initially unmagnetized collisionless plasma is linearly stable to axisymmetric perturbations in the cold plasma approximation. In addition to their application to astrophysical plasmas, our results provide a useful framework for assessing the linear stability of differentially rotating plasmas in laboratory experiments.
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