The nonlinear g mode in the reverse field pinch

Abstract

A primarily numerical investigation of the nonlinear g mode in the reverse field pinch is presented. A two dimensional study of the nonlinear m=0 g mode is made using two computer codes. One code solves the resistive incompressible MHD equations, for the m=0 mode, using a mixed explicit/alternating direction implicit scheme. Whilst for the second code a truncated Fourier expansion is used to reduce the two dimensional m=0 equations to a larger one dimensional set, which are then solved using a mixed explicit/Crank-Nicholson scheme. A stabilising mechanism has been found in which the g mode acts to flatten the pressure in the vicinity of its singular surface. A quasi-linear scaling argument is given to explain this pressure flattening mechanism. Ohmic heating is found to counteract this stabilising effect by increasing the gross pressure in the pinch. The final nonlinear state of the g mode depends on the competition between the pressure flattening and ohmic heating mechanisms. To study modes of any helicity a spectral code is developed to solve the compressible resistive MHD equations in a periodic cylindrical system. Simulating energy loss processes by removing the ohmic heating terms is shown to lower the final nonlinear growth rate of the m=0 g mode. The m=l mode is examined and the same dominant nonlinear mechanisms are found to apply. Some tentative mixed helicity calculations are also presented, but these studies are far from complete. The two dimensional studies allow the magnitudes of typical magnetic fluctuations due to the g mode to be estimated. Using a field line tracing code these fluctuations are shown to give rise to ergoaic field line behaviour. Estimates of the enhanced electron transport which occurs because of this behaviour are given. The relevance of these results to experimentally observed phenomena is discussed.