发表机构
Auburn University; University of California, Los Angeles（奥本大学; 加州大学洛杉矶分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过线性化完全可压缩MHD方程研究无力电流片中撕裂模的线性增长率，发现可压缩性在高伦德奎斯特数下影响可忽略，在低伦德奎斯特数下显著，并可能影响临界伦德奎斯特数。
AI 中文摘要
我们利用线性化的完全可压缩磁流体动力学（MHD）方程组，研究了电阻性无力电流片中撕裂模不稳定性的线性增长率。结果表明，随着等离子体β（$β$，与热压和磁压之比成正比）的增加，色散关系趋近于不可压缩撕裂模的色散关系。随着$β$的减小，增长率增加，但这种增加即使在$β\rightarrow 0$的极限下也是有限的。从$β= +\infty$到$β=0$增长率的相对增加取决于伦德奎斯特数，较低的伦德奎斯特数显示出更明显的增加。这些发现表明，虽然在高伦德奎斯特数范围内，可压缩性对撕裂模不稳定性增长率的影响可以忽略不计，但在低伦德奎斯特数下其影响变得显著。这表明可压缩性可能影响从层流到等离子体团主导的磁重联转变的临界伦德奎斯特数。此外，在低$β$（$β< 1$）范围内，产生的密度扰动可能相当大，与磁场扰动相当甚至更大，尽管增长率仅受到可压缩性的轻微修正。
英文摘要
We investigate the linear growth rate of tearing instability in a resistive force-free current sheet using the linearized fully-compressible magnetohydrodynamics (MHD) equations. Our results show that, as the plasma beta ($β$), which is proportional to the ratio of thermal pressure to magnetic pressure, increases, the dispersion relation approaches that of the incompressible tearing mode. As $β$ decreases, the growth rate increases but this increase remains finite even in the limit $β\rightarrow 0$. The relative increase in the growth rate from $β= +\infty$ to $β=0$ depends on the Lundquist number, with lower Lundquist numbers showing a more pronounced increase. These findings indicate that, while compressibility has a negligible effect on the growth rate of tearing instability in high Lundquist number regimes, its effect becomes significant at low Lundquist numbers. This suggests that compressibility may influence the critical Lundquist number for the transition from laminar to plasmoid-dominated magnetic reconnection. Moreover, in low-$β$ regimes ($β< 1$), the generated density perturbation can be substantial, comparable to or even larger than the magnetic field perturbation, even though the growth rate is only slightly modified by the compressibility.
