Constants of motion in a minimum-B mirror magnetic field -: art. no. 026408

A complete description of the particle motion in a three-dimensional marginal minimum-B mirror field is obtained, including two new constants of motion. The energy and the two Clebsch coordinates of the gyrocenter motion are constants of motion, and the magnetic moment is an adiabatic invariant. The invariance of the gyrocenter Clebsch coordinates implies that each gyrocenter bounces back and forth on a single magnetic field line. Complete solutions of the Vlasov equation can be constructed in the equilibrium field. A small gyroradius expansion of the Clebsch coordinate invariants splits the distribution function into a gyroaveraged part and a new gyro-oscillating part that gives rise to perpendicular plasma current. Locally omnigenous Vlasov equilibria to the first order in the plasma beta can be constructed by including the diamagnetic drift. More than three time-independent invariants are required to obtain the general solution of the stationary Vlasov equation.