自引力均匀电阻等离子体的稳定性
Stability of a self-gravitating homogeneous resistive plasma
摘要：
本文分析了具有非零电阻率的均匀自引力等离子体的稳定性。这项研究提供了一个概括的金斯范式确定的临界尺度以上的引力坍缩是允许的。我们首先讨论了一个理想的自引力等离子体嵌入恒定磁场的稳定性。我们概述了引力坍缩的各向异性特征的存在。事实上，在与磁场正交的平面内，由于磁压的作用，金斯长度增大，而在此平面外，扰动则由通常的金斯判据控制。的密度对比的各向异性崩溃的细节勾勒，这表明线性演化提供了各向异性的初始条件的非线性阶段，这种效果可以强烈执行。在非零电阻率存在的情况下也面临同样的问题，相应地扩展了引力坍缩的条件。出现在这个电阻的情况下的相关功能是弱导电等离子体中的崩溃各向异性的取消。在这种情况下，自引力电阻等离子体的不稳定性的特征在于在任何方向上的标准各向同性牛仔裤长度。最后讨论了电阻率系数很小的极限，阐明了在与磁场正交的平面内外扰动频率不同的情况下，塌陷各向异性是如何体现的。
英文摘要：
In this paper, we analyze the stability of a homogeneous self-gravitating plasma, having a non-zero resistivity. This study provides a generalization of the Jeans paradigm for determining the critical scale above which gravitational collapse is allowed. We start by discussing the stability of an ideal self-gravitating plasma embedded in a constant magnetic field. We outline the existence of an anisotropic feature of the gravitational collapse. In fact, while in the plane orthogonal to the magnetic field the Jeans length is enhanced by the contribution of the magnetic pressure, outside this plane perturbations are governed by the usual Jeans criterium. The anisotropic collapse of a density contrast is sketched in details, suggesting that the linear evolution provides anisotropic initial conditions for the non-linear stage, where this effect could be strongly enforced. The same problem is then faced in the presence of non-zero resistivity and the conditions for the gravitational collapse are correspondingly extended. The relevant feature emerging in this resistive scenario is the cancellation of the collapse anisotropy in weakly conducting plasmas. In this case, the instability of a self-gravitating resistive plasma is characterized by the standard isotropic Jeans length in any directions. The limit of very small resistivity coefficient is finally addressed, elucidating how reminiscence of the collapse anisotropy can be found in the different value of the perturbation frequency inside and outside the plane orthogonal to the magnetic field.
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