Long-time quasilinear evolution of the free-electron laser instability for a relativistic electron beam propagating through a helical magnetic wiggler

Journal Article · Thu Aug 01 04:00:00 EDT 1985 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.865415· OSTI ID:5649928

Davidson, R C; Yin, Y Z

The long-time quasilinear development of the free-electron laser instability is investigated for a tenuous electron beam propagating in the z direction through a helical wiggler field B/sub 0/ = -B cos k/sub 0/ze/sub x/-B sin k/sub 0/ze/sub y/. The analysis neglects longitudinal perturbations (deltaphiapprox. =0) and is based on the nonlinear Vlasov--Maxwell equations for the class of beam distributions of the form f/sub b/(z,p,t) = n/sub 0/delta(P/sub x/)delta(P/sub y/)G(z,p/sub z/,t), assuming partial/partialx = 0 = partial/partialy. The long-time quasilinear evolution of the system is investigated within the context of a simple ''water-bag'' model in which the average distribution function G/sub 0/( p/sub z/,t) = (2L)/sup -1/..integral../sup L//sub -L/ dz G(z,p/sub z/,t) is assumed to have the rectangular form G/sub 0/( p/sub z/,t) = (2..delta..(t))/sup -1/ for Vertical Barp/sub z/-p/sub 0/(t)Vertical Bar < or =..delta..(t), and G/sub 0/( p/sub z/,t) = 0 for Vertical Barp/sub z/-p/sub 0/(t)Vertical Bar >..delta..(t).

• Research Organization: Science Applications International Corporation, Boulder, Colorado 80302
• OSTI ID: 5649928
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 28:8; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420300* -- Engineering-- Lasers-- (-1989)
BEAMS
BOLTZMANN-VLASOV EQUATION
COUPLING
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ELECTRICAL EQUIPMENT
ELECTROMAGNETS
ELECTRON BEAMS
ENERGY RANGE
EQUATIONS
EQUIPMENT
FREE ELECTRON LASERS
FUNCTIONS
HELICITY
INSTABILITY
KINETIC EQUATIONS
LASERS
LEPTON BEAMS
MAGNETS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE BEAMS
PARTICLE PROPERTIES
RELATIVISTIC RANGE
SATURATION
WIGGLER MAGNETS