Linear magnetohydrodynamic stability in reversed field pinch with distant and multiple resistive walls

A linear resistive magnetohydrodynamic (MHD) analysis of current driven instabilities in the reversed field pinch is presented. The presence of multiple resistive walls is taken into account using appropriate boundary conditions. A qualitative understanding of the effect of two walls, together with an approximate formula for the growth rate, is given by studying a simple skin pinch model. In particular, it is found that the mode growth rate is influenced by both wall time constants only for intermediate values of r(w) (the position of the outermost shell). More realistic equilibria are then analysed, comparing the stability results obtained with an ideal or resistive wall with those with two resistive walls. It has been found that all the modes considered (m = 0 and m = 1) are sensitive to the wall resistivity and position, but the growth rates are reduced (even strongly in some circumstances) by the presence of a relatively `thin' wall at the plasma edge. Finally, a comparison between the experimental results and the linear theory predictions in terms of marginally stable states is given.