Local analysis of fast magnetic reconnection

TL;DR

This paper provides a rigorous analysis of fast magnetic reconnection, showing it occurs under general conditions with modest current enhancements, and reveals exponential growth in particle energy during magnetic evolution.

Contribution

It introduces a new analytical approach to understanding magnetic reconnection, emphasizing the role of magnetic field line separation and non-ideal effects.

Findings

Reconnection occurs with modest current density increases.

Magnetic field line separation grows exponentially in ideal evolution.

Particle energy increases exponentially during magnetic evolution.

Abstract

Fast magnetic reconnection is defined by the topology of the magnetic field lines changing on a timescale that is approximately an order of magnitude longer than the topology-conserving ideal-evolution timescale. Fast reconnection is an intrinsic property of Faraday's law when the evolving magnetic field depends non-trivially on all three spatial coordinates and is commonly observed -- even when the effects that allow topology breaking are arbitrarily small. The associated current density need only be enhanced by a factor of approximately ten and flows in thin but broad ribbons along the magnetic field. These results follow from the variation in the separation of neighboring pairs of magnetic field lines, which in an ideal evolution typically increases exponentially with time, and the existence of a spatial scale below which magnetic field lines freely change their identities due to non-ideal effects such as resistivity. Traditional reconnection theory ignores exponentially large variations and relies on the current density reaching a magnitude that is exponentially larger than is actually required. Here, an analysis of the behavior of magnetic field lines in the neighborhood of an arbitrarily chosen line is used to obtain more precise and rigorous results on intrinsic reconnection. The maximum parallel kinetic energy of collisionless charged particles is shown to have an exponential increase in time during a generic magnetic evolution.