dorsal/arxiv
View SchemaThe Topological Origin of Bohm Resistivity in Magnetic Reconnection
| Authors | Magnus F Ivarsen |
|---|---|
| Categories | |
| ArXiv ID | 2601.08054vv1 |
| URL | https://arxiv.org/abs/2601.08054 |
| License | http://creativecommons.org/licenses/by-nc-sa/4.0/ |
Abstract
The physical origin of 'anomalous' resistivity in magnetic reconnection remains one of the longest-standing problems in space plasma physics. While the empirical Bohm diffusion scaling ($\eta~\propto~T/B$) is widely invoked to explain fast reconnection rates, it lacks a rigorous derivation from first principles. Here, we derive this scaling by modeling the magnetized electron fluid as an overdamped spintronic condensate governed by the Landau-Lifshitz-Gilbert equation. We demonstrate that the breakdown of the "frozen-in" condition is rigorously identified as an Adler-Ohmic bifurcation in the model: a topological phase transition where electron gyro-axes lose synchronization with the magnetic field. By rigorously mapping the breakdown of adiabatic invariance to electron gyro axis slippage on the unit sphere, we show that the resulting resistivity naturally saturates at the Bohm limit. Numerical simulations of the $XY$ universality class confirm that the onset of this resistive state is explosive, following a logistic trigger consistent with the impulsive phase of solar flares. Furthermore, the topological defects in the condensate decay via a $t^{-0.75}$ power law, consistent with magnetic island coalescence as the mechanism of anomalous transport. These results suggest that Bohm resistivity is a universal topological property of magnetized matter at the critical point of reconnection.
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"abstract": "The physical origin of \u0027anomalous\u0027 resistivity in magnetic reconnection remains one of the longest-standing problems in space plasma physics. While the empirical Bohm diffusion scaling ($\\eta~\\propto~T/B$) is widely invoked to explain fast reconnection rates, it lacks a rigorous derivation from first principles. Here, we derive this scaling by modeling the magnetized electron fluid as an overdamped spintronic condensate governed by the Landau-Lifshitz-Gilbert equation. We demonstrate that the breakdown of the \"frozen-in\" condition is rigorously identified as an Adler-Ohmic bifurcation in the model: a topological phase transition where electron gyro-axes lose synchronization with the magnetic field. By rigorously mapping the breakdown of adiabatic invariance to electron gyro axis slippage on the unit sphere, we show that the resulting resistivity naturally saturates at the Bohm limit. Numerical simulations of the $XY$ universality class confirm that the onset of this resistive state is explosive, following a logistic trigger consistent with the impulsive phase of solar flares. Furthermore, the topological defects in the condensate decay via a $t^{-0.75}$ power law, consistent with magnetic island coalescence as the mechanism of anomalous transport. These results suggest that Bohm resistivity is a universal topological property of magnetized matter at the critical point of reconnection.",
"arxiv_id": "2601.08054",
"authors": [
"Magnus F Ivarsen"
],
"categories": [
"physics.plasm-ph",
"astro-ph.SR",
"cond-mat.soft",
"cond-mat.stat-mech",
"physics.space-ph"
],
"license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
"title": "The Topological Origin of Bohm Resistivity in Magnetic Reconnection",
"url": "https://arxiv.org/abs/2601.08054",
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