Optical Guiding In The Cyclotron Autoresonance Maser

Abstract

Robert G. Kleva, Baruch Levush, and P. SprangleLaboratory for Plasma ResearchUniversity of MarylandCollege Park, MD 20742ABSTRACTThe effect of the electron beam on the propagation of a three-dimensional radiation beam in a cyclotron autoresonance maser (CARM) amplifier is investigated numerically. In the exponential gain regime, it is shown that the natural tendency of the radiation beam to spread diffractively is overcome and the radiation beam is focused due to the interaction with the electron beam. The nature of the focusing is found to depend on the relative magnitude of the Doppler-shifted wave frequency, WD E w - k |V > and the relativistic gyrofrequency, Q. The radiation beam can be transported without defocusing following saturation only if w is slightly larger than ft. Efficiencies in excess of 50% can be attained through the use of a tapered magnetic field.INTRODUCTIONAn electromagnetic wave can be amplified by interaction with an electron beam which is injected along an applied magnetic field when there is a resonance between the electron's cyclotron motion and the Doppler-shif ted wave frequency. In a CARM the electron beam is injected along the direction of wave propagation and the ? interaction frequency is Doppleryupshifted to u) ~ YH^J where y = (1 - 3 ) , ft = aQ/Y an<! ^0 = eB /me il the nonrelativistic gyrofrequency. In some frequency ranges, the CARM has an advantage over the free electron laser (PEL) for moderate energy electron beams because it is difficult to create a magnetic field with a small wiggler period. The radiation beam in an PEL can be focused, and this has been an important point in favor of the PEL. However, since the wave and the electron beam are co- propagating in a CARM, it may also be possible to focus the radiation beam in a CARM.EQUATIONSConsider a CARM in cylindrical coordinates (r,8,z) with the electron beam propagating in the z-direction along the applied magnetic field. Our analysis proceeds from the wave equation for vector potential A of a right-hand circularly polarized wave, A (r,z,t) =yA(r,z) xexpfiCk^z - u)t)](y - ix) + c.c., where the complex amplitude A(r,z) is assumed to vary slowly in z, |(k A) dA/dz| « 1, the frequency w = k c, and^c.c. denotes the complex conjugate.' The wave equation is conveniently solved by the use of a source-dependent modal expansion [1] for the normalized vector potential a(r,z) = eA/mc . In the source-dependent expansion, the structure of the current source is incorporated into the functional dependence of the radiation spot size r n (:; and the wave front curvature a(z), as well as in t bp complex amplitude. The advantage of thesource-dependent expansion over an expansion in the vacuum modes is that far fewer modes are needed to accurately describe the radiation. Due to the source-dependent nature of the expansion, the lowest order fundamental mode, a(r,z) = a^Cz) x exp{-[l-ia(z)]r /r (z)}, provides a good approxi­ mation to the evolution of the radiation. Equations of evolution for aQ, r , and a can be obtained by inserting this expression for a(r,z) into the wave equation. In the source-dependent technique [1], rg(z) ar*d a(z) are chosen to obey the equations [2]Pz0dz k r z s