Nonlinear Tearing Modes in Current-Vortex Sheets
Abstract
The linear and nonlinear development of instabilities and Alfvén resonances in a plane current-vortex sheet is presented here for sheared equilibrium profiles By0 = tanh(z)ŷ and Vy0 = M0tanh(z/r)ŷ. We extend Rutherford's nonlinear model for constant-psi magnetic islands to account for a sheared equilibrium flow and determine the flow's impact on the magnetic island's nonlinear evolution for M0<1. In this regime, the flow introduces two nonlinear contributions: a polarization current term and a modification of the saturation term derived by Militello and Porcelli (2004). We find that the polarization current generated by the equilibrium flow consistently reduces the nonlinear growth rate of the tearing mode. The flow-induced modification of the saturation term, however, depends on the magnetic-to-velocity shear width ratio, r. For r=1, the saturation term is unchanged from the case without flow. For r>1, it increases in magnitude with M0, strengthening its stabilizing effect and further reducing the island growth rate. In contrast, for r<1, the saturation term decreases in magnitude with increasing M0 and can become positive, leading to a transition from a stabilizing to a destabilizing contribution. Nevertheless, throughout the parameter range considered, the combined effect of the polarization current and modified saturation term is to slow the growth of the magnetic island. Finally, we find that, in the presence of Alfvén resonances, the magnetic island's growth in the nonlinear regime is no longer adequately characterized by constant-psi, and the dynamics of such islands are not captured by the model.
Related
- Normal-Field Evolution and the Breakdown of Classical Tearing in Current Sheets
- Ion-Acoustic-Like Modes in Ion-Loaded Pulsar-Wind Current Sheets: A Pressure-Balanced Existence Criterion
- Linear Growth Rate of Compressible Tearing Instability in a Force-Free Current Sheet
- Plasmoid Instability in Inhomogeneous Current Sheets
- Power-Law Injection Spectrum from an Ensemble of Reconnecting Current Sheets
BibTeX
@misc{urbanski2026nonlinear,
title = {{Nonlinear Tearing Modes in Current-Vortex Sheets}},
author = {D. Urbanski and F. L. Waelbroeck and A. Tenerani},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.12291},
eprint = {2607.12291},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.12291},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Nonlinear Tearing Modes in Current-Vortex Sheets
AU - D. Urbanski
AU - F. L. Waelbroeck
AU - A. Tenerani
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2607.12291
UR - https://arxiv.org/abs/2607.12291
AB - The linear and nonlinear development of instabilities and Alfvén resonances in a plane current-vortex sheet is presented here for sheared equilibrium profiles B_y0 = tanh(z)ŷ and V_y0 = M_0tanh(z/r)ŷ. We extend Rutherford's nonlinear model for constant-psi magnetic islands to account for a sheared equilibrium flow and determine the flow's impact on the magnetic island's nonlinear evolution for M_0<1. In this regime, the flow introduces two nonlinear contributions: a polarization current term and a modification of the saturation term derived by Militello and Porcelli (2004). We find that the polarization current generated by the equilibrium flow consistently reduces the nonlinear growth rate of the tearing mode. The flow-induced modification of the saturation term, however, depends on the magnetic-to-velocity shear width ratio, r. For r=1, the saturation term is unchanged from the case without flow. For r>1, it increases in magnitude with M_0, strengthening its stabilizing effect and further reducing the island growth rate. In contrast, for r<1, the saturation term decreases in magnitude with increasing M_0 and can become positive, leading to a transition from a stabilizing to a destabilizing contribution. Nevertheless, throughout the parameter range considered, the combined effect of the polarization current and modified saturation term is to slow the growth of the magnetic island. Finally, we find that, in the presence of Alfvén resonances, the magnetic island's growth in the nonlinear regime is no longer adequately characterized by constant-psi, and the dynamics of such islands are not captured by the model.
ER -