Non-linear coupling effects on the relaxation process in the reversed field pinch

Abstract

The relaxation process in the reversed field pinch has been studied extensively with three-dimensional magnetohydrodynamic simulations. It is found that the non-linear coupling between multiple helicity modes plays a leading role in the relaxation process. Specifically, the (m; n)=(0; 1) island is excited as a result of non-linear coupling between the linearly unstable m=l modes, with a toroidal mode number difference of one. The m=0 island is then subject to axisymmetric non-linear reconnection whereby reversed flux is effectively generated in the outer region. It should be noted that although the axisymmetric non-linear reconnection of m=0 island is the dominant relaxation process, helical non-linear reconnection of linearly unstable m=l modes also plays some role in the relaxation of the whole system. It is also found that through this multiple helicity relaxation process, Taylor's minimum energy state is realized. The simulation results are generally consistent with experimental observations in the sustainment phase. This indicates that the multiple helicity relaxation process is of fundamental importance in the maintenance of the reversed field during the sustainment phase as well as in the self-reversal during the set-up phase. The relation between relaxation and aspect ratio has also been examined and it is found that the relaxation process is not strongly affected by the aspect ratio.