A theory of a planar wiggler free-electron laser with ion-channel guiding is developed. An analysis of the quasi-steady-state electron trajectories is first obtained by solving the equations of motion for an electron in the ion-channel electrostatic field and the wiggler magnetostatic field. Next a sixth-degree polynomial dispersion equation for electromagnetic and space-charge waves in the wiggler is derived. Numerical solutions of the polynomial equation yield the complex wave number as a function of the frequency of the waves. These results are used to illustrate the dependence of growth rate–frequency curves on the ion-channel frequency, and the peak growth rate and corresponding wave frequency as functions of the ion-channel frequency.
The propagation of space-charge waves through a coaxial waveguide containing an annular plasma in an axial magnetic field is investigated. Both plasma and cyclotron types of waves are analyzed in the electrostatic approximation. Equations for the determination of the dispersion relations are derived from the Poisson equation and the electron continuity and momentum transfer equations. A numerical study of the dispersion curves for azimuthally symmetrical waves is presented. A significant departure from the dispersion characteristics of a cylindrical plasma waveguide are found to occur unless the inner radius of the waveguide is small compared to the outer radius.
A new one-dimensional analysis of the collective interaction in a free-electron
laser with combined helical wiggler and uniform axial magnetic fields is
presented. Maxwell's curl relations and the cold-fluid equations are employed, with
the appropriate form of solution for right and left circularly polarized electromagnetic
waves and space-charge waves. A set of three linear homogeneous algebraic
equations for the electric field amplitudes of the three propagating waves is derived.
This set may be employed to obtain the general dispersion relation in the
form of a tenth-degree polynomial equation. With the left circular wave assumed
to be nonresonant, the dispersion relation reduces to a seventh-degree polynomial
equation corresponding to four space-charge modes and three right circular modes.
The results of a numerical study of the spatial growth rate and radiation frequency
are presented.
Parametric decay of a longitudinal electrostatic pump wave into two space-charge waves in a cylindrical metallic waveguide partially filled with relativistic beam electrons is analysed. The dependence of amplitude gain and frequency enhancement on the ratio of beam radius to waveguide radius is studied numerically.
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