Chakrabarti Nikhil, Maity Chandan, Schamel Hans
Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta 700 064, India.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):023102. doi: 10.1103/PhysRevE.88.023102. Epub 2013 Aug 7.
In a Lagrangian fluid approach, an explicit method has been presented previously to obtain an exact nonstationary magnetosonic-type wave solution in compressible magnetized plasmas of arbitrary resistivity showing competition among hydrodynamic convection, magnetic field diffusion, and dispersion [Chakrabarti et al., Phys. Rev. Lett. 106, 145003 (2011)]. The purpose of the present work is twofold: it serves (i) to describe the physical and mathematical background of the involved magnetosonic wave dynamics in more detail, as proposed by our original Letter, and (ii) to present an alternative approach, which utilizes the Lagrangian mass variable as a new spatial coordinate [Schamel, Phys. Rep. 392, 279 (2004)]. The obtained exact nonlinear wave solutions confirm the correctness of our previous results, indicating a collapse of the magnetic field irrespective of the presence of dispersion and resistivity. The mean plasma density, on the other hand, is less singular, showing collapse only when dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas, and they are expected to be of special importance in the astrophysical context of magnetic star formation.
在拉格朗日流体方法中，之前已经提出了一种显式方法，用于在具有任意电阻率的可压缩磁化等离子体中获得精确的非定常磁声型波解，该解展示了流体动力对流、磁场扩散和色散之间的竞争关系[查克拉巴蒂等人，《物理评论快报》106, 145003 (2011)]。本工作有两个目的：其一，如我们最初的论文所提议，更详细地描述所涉及的磁声波动力学的物理和数学背景；其二，提出一种替代方法，该方法将拉格朗日质量变量用作新的空间坐标[沙梅尔，《物理报告》392, 279 (2004)]。所获得的精确非线性波解证实了我们先前结果的正确性，表明无论色散和电阻率是否存在，磁场都会坍缩。另一方面，平均等离子体密度的奇异性较小，仅在色散效应可忽略不计时才会出现坍缩。这些结果可能有助于我们理解等离子体中强局部磁场（和电流）的产生，并且预计它们在磁星形成的天体物理背景中具有特殊重要性。
