Current-Sheet Formation in Electron Magnetohydrodynamics with Split Fractional Dissipation
Abstract
Thin current sheets are central small-scale structures in electron magnetohydrodynamics (EMHD), closely associated with energy dissipation and fast magnetic reconnection at electron scales. We study their formation numerically in a 21/2-dimensional EMHD system on a periodic domain with split fractional dissipation, where the magnetic potential and the vertical magnetic component are damped separately. The local theory is governed by a symmetric combined damping balance, but the numerical onset of small-scale growth need not follow this symmetry. A scaling analysis identifies the out-of-plane current as the primary concentration observable, since it is regularized only through the magnetic-potential equation. Using a validated Fourier pseudospectral exponential time-differencing solver with resolution-controlled diagnostics, we find a clear decay/concentration dichotomy. The onset boundary is markedly asymmetric: current-sheet formation appears to be controlled mainly by damping of the magnetic potential, rather than by the combined damping strength. The analyticity strip collapses to the grid scale, the concentration sharpens under grid refinement, and the observed growth is consistent with an energy-critical self-similar rate, with exponent near three. These experiments indicate that magnetic-potential damping is the apparent binding constraint for current-sheet concentration, refining the symmetric sum picture.
Related
- Regularising Flows and Singular Fractional SDEs with Superlinear Dissipation
- The local Cauchy problem for hyperbolic systems of equations with fractional dissipation
- Liouville-type theorems and perturbation uniqueness for stationary incompressible MHD with directional fractional dissipation
- Global Stability and Decay for the 2D Anisotropic Navier-Stokes Equations with Fractional Horizontal Dissipation
- Regularity of the solution map for the Oldroyd--B model with fractional stress dissipation
BibTeX
@misc{hu2026currentsheet,
title = {{Current-Sheet Formation in Electron Magnetohydrodynamics with Split Fractional Dissipation}},
author = {Ruimeng Hu and Qirui Peng and Xu Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.18648},
eprint = {2607.18648},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.18648},
}
RIS
TY - UNPB
TI - Current-Sheet Formation in Electron Magnetohydrodynamics with Split Fractional Dissipation
AU - Ruimeng Hu
AU - Qirui Peng
AU - Xu Yang
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2607.18648
UR - https://arxiv.org/abs/2607.18648
AB - Thin current sheets are central small-scale structures in electron magnetohydrodynamics (EMHD), closely associated with energy dissipation and fast magnetic reconnection at electron scales. We study their formation numerically in a 21/2-dimensional EMHD system on a periodic domain with split fractional dissipation, where the magnetic potential and the vertical magnetic component are damped separately. The local theory is governed by a symmetric combined damping balance, but the numerical onset of small-scale growth need not follow this symmetry. A scaling analysis identifies the out-of-plane current as the primary concentration observable, since it is regularized only through the magnetic-potential equation. Using a validated Fourier pseudospectral exponential time-differencing solver with resolution-controlled diagnostics, we find a clear decay/concentration dichotomy. The onset boundary is markedly asymmetric: current-sheet formation appears to be controlled mainly by damping of the magnetic potential, rather than by the combined damping strength. The analyticity strip collapses to the grid scale, the concentration sharpens under grid refinement, and the observed growth is consistent with an energy-critical self-similar rate, with exponent near three. These experiments indicate that magnetic-potential damping is the apparent binding constraint for current-sheet concentration, refining the symmetric sum picture.
ER -