Charged Particle Motion in Electromagnetic Fields Varying Moderately Rapidly in Space

For electromagnetic fields varying on the space scale of the geometric mean of the Larmor radius and the macroscopic scale length of the magnetic field lines it is shown that the magnetic moment remains an adiabatic invariant. This result is not included in the standard theories of single particle motion. The guiding center dynamics is also described and is shown to vary significantly from the normal results. The guiding center motion is along a generalized electrostatic potential surface, instead of along a magnetic field line. Under appropriate circumstances a second adiabatic invariant exists, the magnetic flux enclosed by the orbit. The usual second invariant, the longitudinal bounce integral, fails.