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A theory of self-electric and self-magnetic fields of a relativistic electron
beam passing through a one-dimensional planar wiggler and an ion-channel
is presented. The equilibrium orbits and their stability, under the influence
of self-electric and self-magnetic fields, are analysed. New unstable orbits,
in the first part of the group I orbits, are found. It is shown that for a low
energy and high density beam the self-fields can produce very large effects.
Stabilities of quasi-steady-state orbits are investigated by analytical and
numerical methods and perfect agreement was found. The theory of small
signal gain is used to derive a formula for the gain with the self-field effects
included. A numerical analysis is conducted to study the self-field effects on
the quasi-steady-state orbits and the gain.
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