  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 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 exact solutions of two-dimensional BGK modes in a
magnetized plasma with finite magnetic field strength [Ng, Bhattacharjee, and
Skiff, Phys. Plasmas {\bf13}, 055903 (2006)] to cases with azimuthal magnetic
fields so that these structures carry electric current as well as steady
electric and magnetic fields. Such nonlinear solutions now satisfy exactly the
Vlasov-Poisson-Amp\`{e}re system of equations. Explicit examples with either
positive or negative electric potential structure are provided.
