Abstract
Propagation of space-charge waves in a Raman free-electron laser is analyzed. The device under consideration consists of a cylindrical metallic waveguide filled with a relativistic electron beam which passes through a helical wiggler magnetic field and a uniform axial magnetic field. A solution of the fluid equations and Gauss’s law is developed in the form of truncated Fourier and Fourier–Bessel series. The dispersion relation is derived and the combined effects of the waveguide boundary and the wiggler and axial magnetic fields on cyclotron-like waves are studied numerically. In the limit of infinite waveguide radius, the dispersion relation yields a well-known expression in which the combined wiggler and axial fields determine an effective plasma frequency. In the limit of zero wiggler field, it reduces to the dispersion relation for axisymmetric space-charge waves which, in the beam frame, are purely electrostatic.
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