Nonlinear variational method for predicting fast collisionless magnetic reconnection

TL;DR

This paper develops a nonlinear variational method to analytically estimate the explosive growth of magnetic reconnection driven by electron inertia, supported by numerical simulations, advancing understanding of sawtooth collapse in tokamaks.

Contribution

It introduces a nonlinear energy principle approach to predict fast collisionless magnetic reconnection, highlighting the role of electron inertia and nonlinear displacement.

Findings

Steeper decrease in potential energy in nonlinear regime

Unsteady, strong convective flows during reconnection

Numerical simulations confirm theoretical predictions

Abstract

A mechanism for fast magnetic reconnection in collisionless plasma is studied for understanding sawtooth collapse in tokamak discharges by using a two-fluid model for cold ions and electrons. Explosive growth of the tearing mode enabled by electron inertia is analytically estimated by using an energy principle with a nonlinear displacement map. Decrease of the potential energy in the nonlinear regime (where the island width exceeds the electron skin depth) is found to be steeper than in the linear regime, resulting in accelerated reconnection. Release of potential energy by such a fluid displacement leads to unsteady and strong convective flow, which is not damped by the small dissipation effects in high-temperature tokamak plasmas. Direct numerical simulation in slab geometry substantiates the theoretical prediction of the nonlinear growth.