The orbits of electrons and ions in a rotating magnetic field

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Abstract
The motion of electrons and ions in a system which consists of a uniform rotating magnetic field and a steady uniform magnetic field which is aligned with the axis of rotation is re-examined. Stable orbits are identified and explicit expressions for these orbits are provided. The more realistic situation of motion in the non-uniform self-consistent fields appropriate to a cylindrical plasma equilibrium maintained by the rotating field is investigated. Again, stable orbits are found. The stability of orbits in this more complex situation is examined using an equivalent potential concept.