Quasilinear stabilization of the free electron laser instability for a relativistic electron beam propagating through a transverse helical wiggler magnetic field
A quasilinear model is developed that describes the nonlinear evolution and stabilization of the free electron laser instability in circumstances where a broad spectrum of waves is excited. The relativistic electron beam propagates perpendicular to a helical wiggler magnetic field B/sub 0/ = -B cos k/sub 0/ z e/sub x/-B sin k/sub 0/ z e/sub y/, and the analysis is based on the Vlasov--Maxwell equations assuming partial/partialx = 0 = partial/partial y and a sufficiently tenuous beam that the Compton-regime approximation is valid (deltaphiapprox. =0). Coupled kinetic equations are derived that describe the evolution of the average distribution function G/sub 0/( p/sub z/,t) and spectral energy density E/sub k/(t) in the amplifying electromagnetic field perturbations. A thorough exposition of the theoretical model and general quasilinear formalism is presented, and the stabilization process is examined in detail for weak resonant instability with small temporal growth rate ..gamma../sub k/ satisfying Vertical Bar..gamma../sub k//..omega../sub k/Vertical Bar<<1 and Vertical Bar..gamma../sub k//k ..delta..v/sub z/Vertical Bar<<1.
- Research Organization:
- Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- OSTI ID:
- 5892432
- Journal Information:
- Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 28:2; ISSN PFLDA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
420300* -- Engineering-- Lasers-- (-1989)
BOLTZMANN-VLASOV EQUATION
COUPLING
DIFFERENTIAL EQUATIONS
EFFICIENCY
ELECTRICAL EQUIPMENT
ELECTROMAGNETS
EQUATIONS
EQUIPMENT
FREE ELECTRON LASERS
HELICITY
INSTABILITY
KINETIC EQUATIONS
LASERS
MAGNETIC FIELDS
MAGNETS
MATHEMATICAL MODELS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE PROPERTIES
RESONANCE
STABILIZATION
WIGGLER MAGNETS