Self-consistent equilibrium of a helical magnetic flux rope in a finite-pressure plasma

We present an analytical model of the self-consistent equilibrium of a magnetic flux rope which is obtained in cylindrical geometry. The equilibrium azimuthal magnetic field and plasma pressure are determined in a self-consistent way through the current density which is derived as a solution of a nonlinear equation. By minimizing the energy functional, it was shown that the constrained equilibrium state is stable. The obtained results are also applicable to the cylindrical tokamak magnetic configurations. It is shown that the analytically predicted radial profiles of equilibrium quantities are in good agreement with the experimental data

Three-dimensional vortex dipole solitons in self-gravitating systems

We derive the nonlinear equations governing the dynamics of three-dimensional (3D) disturbances in a nonuniform rotating self-gravitating fluid under the assumption that the characteristic frequencies of disturbances are small compared to the rotation frequency. Analytical solutions of these equations are found in the form of the 3D vortex dipole solitons. The method for obtaining these solutions is based on the well-known Larichev-Reznik procedure for finding two-dimensional nonlinear dipole vortex solutions in the physics of atmospheres of rotating planets. In addition to the basic 3D x-antisymmetric part (carrier), the solution may also contain radially symmetric (monopole) or/and antisymmetric along the rotation axis (z-axis) parts with arbitrary amplitudes, but these superimposed parts cannot exist without the basic part. The 3D vortex soliton without the superimposed parts is extremely stable. It moves without distortion and retains its shape even in the presence of an initial noise disturbance. The solitons with parts that are radially symmetric or/and z-antisymmetric turn out to be unstable, although at sufficiently small amplitudes of these superimposed parts, the soliton retains its shape for a very long time.Comment: will be published in Phys. Rev.