Four motional invariants in adiabatic equilibria

Abstract

Recently published derivations of four stationary motional invariants in adiabatic equilibria are presented. The four invariants contains a radial drift invariant, which determines the density radial profile and the diamagnetic drift, and an additional parallel invariant that determines the plasma current along the magnetic field. Thus, there are in general more than three stationary invariants for the adiabatic motion of a gyrating particle. The result is valid to first order in the gyro radius, and is applicable to geometries with adiabatic fields, including toroidal as well as open trap geometry. In axisymmetric tori, the toroidal invariant can replace the longitudinal invariant in the analysis and the radial invariant can be determined from the projected gyro center motion. The four invariants is determined for passing as well as trapped particles. For equilibria with sufficiently small banana widths, the radial invariant can to lowest order be approximated by the gyro center value of the radial Clebsch coordinate. To this lowest order, the gyro centers drift on a magnetic flux surface.