Structure of the sideband spectrum in free electron lasers

Journal Article · Wed Jun 01 04:00:00 EDT 1988 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.866709· OSTI ID:5180739

Riyopoulos, S; Tang, C M

The one-dimensional, fast time averaged Hamiltonian is derived in a free electron laser (FEL) for electrons passing through a constant parameter wiggler and a radiation field. The exact unperturbed orbits without sidebands are obtained for all particles and arbitrary strength of the main signal. Integration, in action-angle variables, of the linearized kinetic equation with perturbing sidebands over the unperturbed orbits yields the sideband growth rate including both trapped and untrapped particles. The structure and scaling of the unstable spectrum are different from previous results obtained for electrons localized at the bottom of the ponderomotive well. It is found that upper and lower sidebands that are symmetric relative to the FEL frequency have opposite growth rates. There is no differentiation in the magnitude of the gain between upper and lower sidebands. The stability is determined by the sign of df/sub 0/d..omega../sub b/, the relative population of quantized oscillators with energy quantum (h2..pi..)..omega../sub b/, where ..omega../sub b/ is the synchrotron frequency in resonance with the sideband. The shear d..omega../sub b/dJ, where J is the action variable, is stabilizing and distributions with gradients df/sub 0/dJ localized near the separatrix have the minimum growth rates.

• Research Organization: Plasma Physics Division, Naval Research Laboratory, Washington, D.C. 20375-5000
• OSTI ID: 5180739
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 31:6; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420300* -- Engineering-- Lasers-- (-1989)
BEAMS
ELECTRICAL EQUIPMENT
ELECTROMAGNETS
ELECTRON BEAMS
ENERGY SPECTRA
EQUATIONS
EQUIPMENT
FREE ELECTRON LASERS
HAMILTONIANS
INSTABILITY
KINETIC EQUATIONS
LASERS
LEPTON BEAMS
MAGNETS
MATHEMATICAL OPERATORS
ONE-DIMENSIONAL CALCULATIONS
PARTICLE BEAMS
QUANTUM OPERATORS
SCALING LAWS
SPECTRA
TRAJECTORIES
WIGGLER MAGNETS