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.

Atmospheric electric fields, connected with the ionization of particles and plasma processes, occur in the fields of pressure gradients of mosaic mesh topology. Atmospheric aerosol particles play a significant role in the vortex generation. The Coriolis force and the motion of charged particles in the geomagnetic field lead to gyrotropy of the atmosphere and ionosphere. Occurrence of plasma vortices is stochastically determined for such an inhomogeneous gyrotropic medium. The geomagnetic field influences the change of structures of inhomogeneous media in the process of excitation of plasma vortices and their interaction. If colliding vortices are centered on the one geomagnetic line, the merge of vortices and the generation of a joint powerful vortex are possible. If a collision of vortices with centers at different geomagnetic field lines occurs, then the emergence of areas of heating and jet streams and the generation of new vortices are possible.

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