m = 1 Resistive internal reconnection in a two fluid

The m = 1, n = 1 resistive reconnecting mode in a tokamak is investigated numerically in the two fluid approximation, using a version of the initial value code MH3DK. The effect of introducing the Hall term J x B into the Ohm's law is discussed, first for the linear perturbation eigenmode and growth rate and then for the nonlinear evolution, in order to compare the effects to those involved in the crash phase of a sawtooth. Different plasma geometries are used to clarify different aspects of the process, in particular the two dimensional configuration with m = 1, n = 1 helical symmetry, corresponding to the usual analytical approximation, and also the full 3D toroidal geometry, where both include the effects of plasma compressibility. The effects of the diamagnetic frequencies ω*j = (cTj/B)(1/n)(dpj/dr), j = e, i, and the corresponding rotation of the inner part of the plasma, which are introduced by the Hall term, are investigated. The role played by the Hall term relative to that of the electron pressure gradient in the Ohm's law is also considered. Linear perturbation results are compared with the theoretical results and the nonlinear evolution is discussed