Influence of the trapped-electron distribution on the sideband instability in a helical wiggler free-electron laser

Journal Article · Mon Oct 01 00:00:00 EDT 1990 · Physics of Fluids B; (USA)

DOI:https://doi.org/10.1063/1.859511· OSTI ID:6432065

Yang, T B; Davidson, R C ^[1]

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1. Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, MA (USA)

Use is made of the Vlasov--Maxwell equations to investigate detailed properties of the sideband instability for a helical wiggler free-electron laser with wiggler wavelength {lambda}{sub {ital w}}=2{pi}/{ital k}{sub 0}=const and normalized wiggler amplitude {ital a}{sub {ital w}}={ital e{cflx B}}{sub {ital w}}/{ital mc}{sup 2}{ital k}{sub 0}=const. The model describes the nonlinear evolution of a right circularly polarized primary electromagnetic wave with frequency {omega}{sub {ital s}}, wave number {ital k}{sub {ital s}}, and slowly varying amplitude {ital {cflx a}}{sub {ital s}}({ital z},{ital t}) and phase {delta}{sub {ital s}}({ital z},{ital t}) (eikonal approximation). The coupled Vlasov and field-evolution equations are analyzed in the ponderomotive frame ( primed'' variables) moving with velocity {ital v}{sub {ital p}}={omega}{sub {ital s}}/({ital k}{sub {ital s}}+{ital k}{sub 0}) relative to the laboratory. Detailed properties of the sideband instability are investigated for small-amplitude perturbations about a quasi-steady state characterized by an equilibrium electron distribution {ital f}{sup 0}({gamma}{sup {prime}}{sub 0}) and a primary electromagnetic wave with constant amplitude {ital {cflx a}}{sup 0}{sub {ital s}}=const (independent of {ital z}{prime} and {ital t}{prime}) and slowly varying phase {delta}{sup 0}{sub {ital s}}({ital z}{prime}). A formal dispersion relation is derived for perturbations about a general equilibrium distribution {ital f}{sup 0}({gamma}{sup {prime}}{sub 0}) that may include both trapped and untrapped electrons. For the case where only trapped electrons are present, the dispersion relation is reduced to a simple analytical form.

• OSTI ID: 6432065
• Journal Information: Physics of Fluids B; (USA), Vol. 2:10; ISSN 0899-8221
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
FREE ELECTRON LASERS
INSTABILITY
TRAPPED ELECTRONS
DISTRIBUTION
BOLTZMANN-VLASOV EQUATION
DISPERSION RELATIONS
HELICAL CONFIGURATION
NONLINEAR PROBLEMS
POLARIZATION
WIGGLER MAGNETS
CONFIGURATION
DIFFERENTIAL EQUATIONS
ELECTRICAL EQUIPMENT
ELECTROMAGNETS
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
EQUIPMENT
FERMIONS
LASERS
LEPTONS
MAGNETS
PARTIAL DIFFERENTIAL EQUATIONS
426002* - Engineering- Lasers & Masers- (1990-)