Radially confined relativistic-electron-beam equilibria for longitudinal wiggler free-electron-laser applications

Journal Article · Sat Sep 01 04:00:00 EDT 1984 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.30.1518· OSTI ID:6478654

Davidson, R C; Johnston, G L; McMullin, W A

The purpose of the present article is to establish the properties of a class of radially confined relativistic-electron-beam equilibria for longitudinal wiggler free-electron-laser applications. The theoretical model is based on the steady-state (partial/partialt = 0) Vlasov equation, assuming a thin, tenuous electron beam with K/sub 0//sup 2/R/sub b//sup 2/<<1 and negligibly small equilibrium self-generated fields. For the approximate magnetic field configuration, B/sub r//sup 0/ = 0 and B/sub z//sup 0/ = B/sub 0/(1+(deltaB/B/sub 0/)sin (k/sub 0/z)), the single-particle constants of the motion are axial momentum p/sub z/, per- pendicular momentum p/sub perpendicular/ = (p/sub r//sup 2/+p/sub theta//sup 2/)/sup 1/2/ , energy ..gamma..mc/sup 2/ = (m/sup 2/c/sup 4/ +c/sup 2/p/sub z//sup 2/+c/sup 2/p/sub perpendicular//sup 2/)1 /2, and canonical angular momentum P/sub theta/ = r(p/sub theta/-(e/c)A/sub theta//sup 0/(r,x)), where A/sub theta//sup 0/(r,z) = (rB/sub 0//2)(1+( deltaB/B/sub 0/) x sin(k/sub 0/z)). Beam equilibrium properties are investigated for the class of self-consistent Vlasov equilibria F/sub b//sup 0/(x,p) = F(p/sub perpendicular//sup 2/ -2..gamma../sub b/m..omega../sub b/p/sub theta/)G(p/sub z/), where ..omega../sub b/ = const is related to the mean rotation of the electron beam, and ..gamma../sub b/mc/sup 2/ = const is the characteristic energy of a beam electron.

• Research Organization: Plasma Research Institute, Science Applications Incorporated, Boulder, Colorado 80302
• OSTI ID: 6478654
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 30:3; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420300* -- Engineering-- Lasers-- (-1989)
AXIAL SYMMETRY
BEAMS
CONFINEMENT
DIFFERENTIAL EQUATIONS
ELECTRICAL EQUIPMENT
ELECTROMAGNETS
ELECTRON BEAMS
ENERGY RANGE
EQUATIONS
EQUATIONS OF MOTION
EQUILIBRIUM
EQUIPMENT
FREE ELECTRON LASERS
LASERS
LEPTON BEAMS
MAGNETS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE BEAMS
RELATIVISTIC RANGE
SYMMETRY
WIGGLER MAGNETS