Exact Vlasov–Maxwell equilibria with sheared magnetic fields

A theoretical formalism which allows the generation of a large class of exact Vlasov–Maxwell equilibria with sheared magnetic fields is presented. All quantities are assumed to vary in only one spatial direction, x, and the magnetic field has components only in the y and z directions. The Vlasov equations are solved by making the distribution functions depend only on constants of the motion. The Maxwell equations are then reduced to finding the motion of a pseudo-particle in a two-dimensional potential. Three examples corresponding to sheet-like, sheath-like, and wave-like equilibria are presented.