On the theory of Alfven vortices

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Abstract
The revision of the previous theory of shear Alfven vortices in a homogeneous plasma is given. In the previous papers the solutions were not matched adequately on the singular line of the vortex so that they do not satisfy 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 allowance for the ion temperature are obtained. The solution, in the form of the dipole vortex with spatially decreasing amplitude, is found. The specific character of the solution obtained consists of a power decrease 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 solution obtained is performed.