Secondary fast reconnecting instability in the sawtooth crash

TL;DR

This paper analyzes secondary magnetic reconnection instabilities in thin current sheets during sawtooth crashes, highlighting how non-collisional physics accelerates reconnection rates in tokamaks.

Contribution

It introduces a model for secondary instabilities in current sheets considering resistive and electron inertia effects, revealing faster reconnection timescales in sawtooth crashes.

Findings

Reconnection proceeds faster than primary instability timescales.

Non-collisional physics dominates above a critical Lundquist number.

Reconnection rate approaches Alfvénic speeds in collisionless regimes.

Abstract

In this work we consider magnetic reconnection in thin current sheets with both resistive and electron inertia effects. When the current sheet is produced by a primary instability of the internal kink type, the analysis of secondary instabilities indicates that reconnection proceeds on a time scale much shorter than the primary instability characteristic time. In the case of a sawtooth crash, non-collisional physics becomes important above a value of the Lundquist number which scales like S ~ (R/d_e)^{12/5}, in terms of the tokamak major radius R and of the electron skin depth d_e. This value is commonly achieved in present day devices. As collisionality is further reduced, the characteristic rate increases, approaching Alfv\'enic values when the primary instability approaches the collisionless regime.