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 predicted by Rutherford theory. Plasma gradient effects provide the mechanism for island excitation even in situations when the linear tearing mode stability parameter Delta is negative. The magnetic islands are sustained by the differential response of electron and ion components of a plasma in a fluctuating electric field. Such nonlinear magnetic islands are not related to the linear instability of drift-tearing modes. The nonlinear equations describing the evolution of the width and frequency of the rotating islands are derived. In the framework of one-fluid MHD, the general equation for a neighbouring equilibrium in a finite pressure plasma is considered. The dynamics of unstable m=2 and m=1 magnetic islands based on this equation is described. The quasilinear saturation of island growth in a finite pressure plasma leads to the bifurcation of the island type equilibrium into states without islands. A new evolution equation of m=1 islands is derived. For monotonic safety factor and temperature profiles this equation predicts saturation of the m=1 island growth.
Plasma Oscillations: II. Kinetic theory of waves in plasmas