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Electrostatic structures have been observed in many regions of space plasmas,including the solar wind, the magnetosphere, the auroral acceleration region.One possible theoretical description of some of these structures is the conceptof Bernstein-Greene-Kruskal (BGK) modes, which are exact nonlinear steady-statesolutions of the Vlasov-Poisson system of equations in collisionless kinetictheory. We generalize exact solutions of two-dimensional BGK modes in amagnetized plasma with finite magnetic field strength [Ng, Bhattacharjee, andSkiff, Phys. Plasmas {\bf13}, 055903 (2006)] to cases with azimuthal magneticfields so that these structures carry electric current as well as steadyelectric and magnetic fields. Such nonlinear solutions now satisfy exactly theVlasov-Poisson-Amp\`{e}re system of equations. Explicit examples with eitherpositive or negative electric potential structure are provided.

Kinetic Flux Ropes: Bernstein-Greene-Kruskal Modes for the Vlasov-Poisson-Amp\`{e}re System