Forces and moments within layers of driven tearing modes with sheared rotation

摘要

For driven low amplitude tearing modes in a plasma with sheared rotation, forces on tearing layers due to Maxwell and Reynolds stresses are calculated. First moments about the center of the tearing layer, also due to Maxwell and Reynolds stresses, are also calculated. The forces tend to cause the tearing mode to lock to the phase of the driving perturbation, and the moments determine the evolution of the rotation shear within the layer. These forces and moments are calculated for two constant-delta regimes of tearing modes, namely, the viscoresistive (VR) regime and the resistiveinertial (RI) regime, and an ordering in terms of the constant-psi small parameter is an element of similar to delta Delta is introduced, with the velocity shear ordered as similar to is an element of. Here, delta is the layer width and Delta the logarithmic jump in the derivative of the flux function across the layer. The forces and first moments are reported to the lowest nonvanishing order in is an element of. The Reynolds moment is analogous to the effect that can drive zonal flows in other contexts. The treatment of the tearing layers is by means of variational principles using Pade approximants (A. J. Cole and J. M. Finn, Phys. Plasmas 21, 032508 (2014)). The usual result for the Maxwell force without rotation shear is recovered for both regimes. That is, the correction due to velocity shear is small; also, the lowest order contribution to the Reynolds force is zero. In the VR regime, we find no first moments up to second order in the constant-delta parameter. In the RI regime, we find N-m is zero to at least order is an element of(3/2). In the RI regime, the Reynolds moment N-r is found to be of order is an element of(3/2) and is proportional to minus the rotation shear in the layer; it thus tends to damp out any velocity shear across the layer. (C) 2015 AIP Publishing LLC.