Symmetry transforms for ideal magnetohydrodynamics equilibria

A method for constructing ideal magnetohydrodynamics (MHD) equilibria is introduced. The method consists of the application of symmetry transforms to any known MHD equilibrium [ O. I. Bogoyavlenskij, Phys. Rev. E. 62, 8616, (2000)]. The transforms break the geometrical symmetries of the field-aligned solutions and produce continuous families of the nonsymmetric MHD equilibria. The method of symmetry transforms also allows to obtain MHD equilibria with current sheets and exact solutions with noncollinear vector fields $B$ and $V.\mathrm{}$ A model of the nonsymmetric astrophysical jets outside of their accretion disks is developed. The total magnetic and kinetic energy of the jet is finite in any layer $c_1<z<\mathrm{}{c}_2.$ The jet possesses current sheets and is highly collimated in view of a rapid decrease of the magnetic field B in the transverse direction. The method gives also the MHD equilibria that model ball lightning with dynamics of plasma inside the fireball.