NONLINEAR EVOLUTION OF TEARING MODES IN INHOMOGENEOUS PLASMAS

The nonlinear behaviour of tearing modes in a plasma with density and temperature gradients is reviewed. The effects of inhomogeneities can essentially modify the evolution of small scale islands from that pred icted by Rutherford theory. Plasma gradient effects provide the mechan ism for island excitation even in situations when the linear tearing m ode stability parameter DELTA is negative. The magnetic islands are su stained by the differential response of electron and ion components of a plasma in a fluctuating electric field. Such nonlinear magnetic isl ands are not related to the linear instability of drift-tearing modes. The nonlinear equations describing the evolution of the width and fre quency of the rotating islands are derived. In the framework of one-fl uid MHD, the general equation for a neighbouring equilibrium in a fini te pressure plasma is considered. The dynamics of unstable m = 2 and m = 1 magnetic islands based on this equation is described. The quasili near saturation of island growth in a finite pressure plasma leads to the bifurcation of the island type equilibrium into states without isl ands. A new evolution equation for m = 1 islands is derived. For monot onic safety factor and temperature profiles this equation predicts sat uration of the m = 1 island growth.