Two-dimensional Vlasov treatment of free-electron laser sidebands

Journal Article · Thu Mar 01 04:00:00 EST 1990 · Physics of Fluids B; (USA)

DOI:https://doi.org/10.1063/1.859295· OSTI ID:7245465

Sharp, W M; Yu, S S ^[1]

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1. Lawrence Livermore National Laboratory, University of California, P.O. Box 808 L-626, Livermore, California 94550 (US)

The Kroll--Morton--Rosenbluth equations (IEEE J. Quantum Electron. {bold QE}-{bold 17}, 1436 (1981)) for a helical-wiggler free-electron laser are generalized to treat an electron beam with a prescribed radial density profile and an equilibrium distribution function that is an arbitrary function of the longitudinal action {ital J}. The principal approximation is the assumption that betatron frequencies of beam particles are low compared with typical synchrotron frequencies. Vlasov equilibria for finite-amplitude primary waves with time-varying phase are calculated for several distribution functions. Using these equilibria, radial eigenvalue equations for the frequency and growth rate of small-amplitude sidebands are derived and solved numerically. The radial mode structure is found to have no appreciable effect on sideband growth when the beam radius is large compared with (2{ital k}{sub {ital s}} min({Omega}{sub 0}, {ital d}{phi}{sub 0}/{ital dz})){sup {minus}1/2}, where {ital k}{sub {ital s}} and {phi}{sub 0} are the wavenumber and phase of the primary wave and {Omega}{sub 0} is the maximum synchrotron frequency'' in {ital z} of trapped electrons. In these effectively one-dimensional cases, the dispersion relation depends only on the distribution function and on a dimensionless density parameter {bar {eta}}={ital k}{sub {ital w}}{ital a}{sup 2}{sub {ital w}}{omega}{sup 2}{sub {ital b}}/({ital c}{sup 2}{gamma}{sup 3}{sub {ital r}}{Omega}{sup 3}{sub 0}i), where {ital k}{sub {ital w}} is the wiggler wavenumber, {ital a}{sub {ital w}}={ital eA}{sub {ital w}}/({ital mc}{sup 2}) is the dimensionless wiggler vector potential, {omega}{sub {ital b}} is the maximum plasma frequency of the beam, and {gamma}{sub {ital r}} is the Lorentz factor for resonant particles.

• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 7245465
• Journal Information: Physics of Fluids B; (USA), Journal Name: Physics of Fluids B; (USA) Vol. 2:3; ISSN 0899-8221; ISSN PFBPE
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
426002* -- Engineering-- Lasers & Masers-- (1990-)
AMPLITUDES
BOLTZMANN-VLASOV EQUATION
CONFIGURATION
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ELECTRICAL EQUIPMENT
ELECTROMAGNETS
EQUATIONS
EQUIPMENT
FREE ELECTRON LASERS
FUNCTIONS
HELICAL CONFIGURATION
INSTABILITY
INSTABILITY GROWTH RATES
LASERS
MAGNETS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
TENSORS
TRANSIENTS
TRAPPING
TWO-DIMENSIONAL CALCULATIONS
VECTORS
WAVE FORMS
WIGGLER MAGNETS