Steady Flow in the Axially Symmetric Torus Using the Guiding-Center Equations

General steady flow in an axially symmetric torus is investigated using the guiding-center equations. Several constants of the macroscopic and microscopic motion are obtained, and a second-order quasilinear partial differential equation is derived for the self-consistent magnetic flux function. The condition specifying that this equation be hyperbolic or elliptic is given. For the former case, jump conditions are given when weak (discontinuous) solutions are admitted.