Free electron laser with longitudinal wiggler and finite axial magnetic field

Abstract

An analysis of the excitation of a space charge wave and a predominantly transverse magnetic mode in a cylindrical metallic waveguide filled with a relativistic electron beam is presented. The beam is guided by a uniform, axial magnetic field of arbitrary magnitude and passes through a spatially periodic, longitudinal electric (wiggler) field. A non-linear wave equation is derived in a form which includes the coupling of TM and TE modes due to the finite axial magnetic field. For the case of a weak and purely axial wiggler field, a solution of this wave equation is developed with each of the two excited waves expressed as a sum of three partial waves. A spatial growth rate formula is derived in a form appropriate for operation infinitesimally above cut-off of the TM mode. Numerical calculations indicate that the axial magnetic field magnitude should be somewhat larger than the value which maximizes the growth rate in order to achieve high efficiency.

Free electron laser in a partially filled waveguide

“…Analysis of the resulting excitation of a spacecharge wave and a backscattered EH waveguide mode, which are considered as small perturbations, will be carried out in the beam frame using SI units. Uddholm et al 9 have derived the nonlinear wave equation for the three-wave interaction. Their assumption of nonrelativistic oscillations of electrons in the wiggler field limits their results to weak wiggler.…”

“…9 can be used as the relativistic nonlinear wave equation for the axial electric field E z (1) within the electron beam:…”

Free electron laser with bunched relativistic electron beam and electrostatic longitudinal wiggler

“…In a real device, the beam would only partially fill the waveguide, allowing space to insert charged rings to create the wiggler electric field. 1, 9 Theoretical studies involving a partially filled waveguide with an infinite axial magnetic field have been carried out by Fenstermacher and Seyler 10 and by Mehdian et al 11 Some theoretical works with considering finite magnetic field in the completely filled waveguide 12,13 and in the partially filled waveguide 14 have been done. The more realistic assumption of an annular electron beam was used by Maraghech and Sepehri Javan in Ref.…”

Field distribution in a coaxial electrostatic wiggler

“…A free-electron laser (FEL) based on the three-wave (incident wave, pump wave, and space-charge wave) interaction mechanism in an electrostatic wiggler for a relativistic electron beam to generate millimeter waves was first suggested by Bekefi and Shefer [1,2]. Then it was verified by in-principle experiments [3,4], and further studies were continued by several authors [5][6][7][8][9][10][11]. Typically, the electrostatic wiggler is a configuration with the periodic electrostatic field distribution produced by the ripple corrugations on the inside surface of the metallic pipe connected with an electrostatic voltage [1,2].…”