THE GYRATION OF A CHARGED PARTICLE

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Abstract

The equations of motion of a charged particle tightly gyrating in a given electromagnetic field are expanded asymptotically to all orders in the radius and the period of gyration. The existence of an adiabatic invariant (essentially the magetic moment'' of the particle or equivalently the amount of flux encircled by its orbit), proved to lowest order by Alfven and to the next order by Hellwig, is proved to all orders. The invariant is obtained explicitly to the lowest two orders. The method can be applied to prove the existence of an adiabatic invariant to all orders for a large class of Hamiltonian systems with conventional lowest order adiabatic invariants. (auth)

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