Kinetic flux ropes: Bernstein–Greene–Kruskal modes for the Vlasov–Poisson–Ampère system

Abstract

Electrostatic structures have been observed in many regions of space plasmas, including the solar wind, the magnetosphere, and the auroral acceleration region. One possible theoretical description of some of these structures is the concept of Bernstein–Greene–Kruskal (BGK) modes, which are exact nonlinear steady-state solutions of the Vlasov–Poisson system of equations in collisionless kinetic theory. We generalize the exact solutions of two-dimensional BGK modes in a magnetized plasma with a finite magnetic field strength [Ng et al., Phys. Plasmas 13, 055903 (2006)] to cases with azimuthal magnetic fields so that these structures carry the electric current as well as the steady electric and magnetic fields. Such nonlinear solutions now exactly satisfy the Vlasov–Poisson–Ampère system of equations. Explicit examples with either positive or negative electric potential structure are provided.