Behaviors of the effective potential for a single electron moving under the combined fields of a linear magnetic wiggler and an axial magnetic field

초록

The Hamiltonian formalism of the dynamics of a single electron transversing a drift tube under the combined influence of a linear magnetic wiggler and an axial magnetic guide field is used to study the behaviors of the effective potential wherein the particle propagates while satisfying the combined resonance condition. A canonical transformation is used to derive the energy conservation theorem, in which the effective potential is expressed as a function of the departure of the axial momentum from the resonant value. The effective potential is analyzed for various cases of resonance states. We conclude that a limit exists on the strength of the wiggler field (or axial field) above which the propagation of the beam is hampered because no resonance state exists. We also conclude that the drift tube has a limit on its size above which the resonance states vanish.

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