ASYMPTOTIC ELECTRON TRAJECTORIES AND AN ADIABATIC INVARIANT FOR A HELICAL-WIGGLER FREE-ELECTRON LASER WITH WEAK SELF-FIELDS

The dynamics of a relativistic electron in the field configuration con sisting of a constant-amplitude helical-wiggler magnetic field, a unif orm axial magnetic field, and the equilibrium self-fields is described by a near-integrable three-degree-of-freedom Hamiltonian system. The system is solved asymptotically for small epsilon by the method of ave raging, where epsilon measures the strength of the self-fields. Becaus e the Hamiltonian does not depend on one of the coordinates, it immedi ately reduces to a two-degree-of-freedom system. For epsilon=0, this r educed system is integrable, but is not in standard form. The action-a ngle transformation to standard form is derived explicitly in terms of elliptic functions, thus enabling the application of the averaging pr ocedure. For almost all regular electron trajectories the solution is explicitly derived in asymptotic form and an adiabatic invariant is co nstructed, both results are in a form that remains uniformly valid ove r the time interval for electrons to transit the laser. The analytical results are verified by numerical calculations for an example problem . (C) 1996 American Institute of Physics.