Abstract
In this paper we develop a one class of solutions of the steady Vlasov-Maxwell equations, which describes two dimensional cylindrical current sheets with current directed azimuthally j = j θ(ρ, z)e θ. Magnetic field of these sheets has two components B = B z (ρ, z)e z + B ρ(ρ, z)e ρ. From mathematical point of view, we find solutions of the nonlinear equation in partial derivatives for some function u(ρ, z): ∂2 u/∂x 2 + x −1∂2 u/∂z 2 = e −u , where x = ρ2. We apply methods of group theory to develop three-parameter class of solutions. We also derive asymptotic behavior of these solutions for large values of ρ and for ρ ∼ 0. We discuss applications of these solutions for description of current sheets in magnetospheres of planets with magnetic dipoles located near the ecliptic plane.
Published Version
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