A dynamo effect of multiple tearing modes on Taylor relaxation

Abstract

The dynamo effect of multiple tearing modes in a force-free plasma is investigated using resistive magnetohydrodynamics equations. In a steady state, two tearing modes are considered. It is found that the dynamo effect is related to the distance between the two rational surfaces and the magnetic island width. The λ=j·B/|B|2 profile is flatter for closer rational surfaces and wider magnetic islands. The case of an arbitrary number of tearing modes is also considered, and it is found that the λ profile in a finite plasma region can be flattened by the dynamo effect if there are enough tearing modes. This indicates that λ can be flattened in the entire plasma region, which makes it clear that the dynamo effect actually flattens λ rather than the current density. In the growth stage, the case of a growing tearing mode and two saturated modes is considered. The calculation shows that the middle tearing mode makes connections between the two modes on each side, playing the role of a mediator. Our results provide a more clear explanation for the dynamo effect of multiple tearing modes as a possible mechanism behind the Taylor relaxation process.