Magnetic reconnection as an Adler-Ohmic bifurcation: The topological origin of Bohm resistivity

TL;DR

This paper presents a topological phase transition model for magnetic reconnection, deriving Bohm resistivity from first principles and supported by data analysis, revealing a universal topological origin of anomalous resistivity in space plasmas.

Contribution

It introduces a novel topological phase transition framework for understanding Bohm resistivity, linking it to an Adler-Ohmic bifurcation and collective phase slippage.

Findings

Resistivity onset is a topological phase transition.

Data shows explosive phase space confinement during reconnection.

Bohm resistivity emerges as a universal topological property.

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 ensemble of electron gyro-axes in a magnetized plasma 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: a topological phase transition where electron gyro-axes lose synchronization with the mean magnetic field. Unlike stochastic turbulence models, this framework predicts a coherent, explosive onset of resistivity that naturally saturates at the Bohm limit. We support this thesis with renormalization group theory and a novel analysis of Magnetospheric Multiscale mission data, which reveals an explosive phase space confinement consistent with collective phase slippage rather than chaotic scattering. These results suggest that Bohm resistivity is a universal topological property of magnetized matter at the critical point of reconnection.