Linear Growth Rate of Compressible Tearing Instability in a Force-Free Current Sheet
Abstract
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→ 0. The relative increase in the growth rate from β= +∞ 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.
Related
- Nonlinear Tearing Modes in Current-Vortex Sheets
- Normal-Field Evolution and the Breakdown of Classical Tearing in Current Sheets
- A Compressible Miles Instability for Wind-Wave Generation in a Neutral Atmosphere
- Plasmoid Instability in Inhomogeneous Current Sheets
- The linear instability of Kasner spacetimes
BibTeX
@misc{shi2026linear,
title = {{Linear Growth Rate of Compressible Tearing Instability in a Force-Free Current Sheet}},
author = {Chen Shi and Marco Velli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28379},
eprint = {2609.28379},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28379},
}
RIS
TY - UNPB
TI - Linear Growth Rate of Compressible Tearing Instability in a Force-Free Current Sheet
AU - Chen Shi
AU - Marco Velli
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28379
UR - https://arxiv.org/abs/2609.28379
AB - 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→ 0. The relative increase in the growth rate from β= +∞ 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.
ER -