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 effecu provide the mechanism for island excitation even in situations when the linear tearing mode stability parameter A is negative. The magnetic islands a x susfained by the differential response of electron and ion components of a plasma in a fluctuating eleclric field. Such nonlinear magnetic islands are not related to the linear inslability 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 rhe bifurcation of the island type equilibrium into states without islands. A new evolution equation for m = 1 islands is derived. For monotonic safety factor and temperature profiles this equation predicts saturation of the m = I island p w t h .
Generalized action invariants are identified for various models of drift wave turbulence in the presence of the mean shear flow. It is shown that the wave kinetic equation describing the interaction of the small scale turbulence and large scale shear flow can be naturally writen in terms of these invariants. Unlike the wave energy, which is conserved as a sum of small-and large-scale components, the generalized action invariant is shown to correspond to a quantity which is conserved for the small scale component alone. This invariant can be used to construct canonical variables leading to a different definition of the wave action ( as compared to the case without shear flow). It is suggested that these new canonical action variables form a natu-1
The revision of the previous theory of the shear Alfven vortices in a homogeneous plasma is given. The necessity of such a revision is due to the fact that in the previous papers the solutions were not matched adequately on the singular line of the vortex so that these solutions do not satisfy to the charge conservation law. The influence of the magnetic viscosity on the character of the admitted discontinuities in the shear Alfven vortices is studied. The nonlinear equations of the shear Alfven waves in the usual approximation of cold ions and also with the allowance for the ion temperature are obtained. The solution of these equations in the form of the dipole vortex with the spatially decreasing ampitude is found. The specific character of the obtained solution consists in a power decreasing of the transverse potential on sufficiently far vortex periphery. It is shown that the integral characteristics of the vortices (energy, generalized enstrophy) are finite. The numerical analysis of the obtained solution is performed.
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