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

Related Subjects

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