Energy balance of the collisional tearing mode

Abstract

The energy balance of the collisional tearing mode is examined within linear theory. It is found that in an asymmetric case the quadratic form given by Furth for the net release of magnetic energy must be completed with a term connected with the current gradient in the resistive layer. The growth-rate and the inner-layer solution are calculated in the limit where viscosity dominates over inertia. The amounts of energy going into Joule heating and either kinetic energy or viscous dissipation are calculated analytically. In the inertial regime 1/4 of the net decrease in magnetic energy goes into kinetic energy and (3)/(4) into Joule heating, while, in viscous regime, (1)/(6) goes into viscous dissipation and (5)/(6) into Joule heating. The analytical results, based on the constant-ψ approximation, are in good agreement with numerical simulations when the resistive layer is sufficiently narrow.