Self-consistent Vlasov description of the free electron laser instability

Journal Article · Wed Oct 01 04:00:00 EDT 1980 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.862895· OSTI ID:5074525

Davidson, R C; Uhm, H S

A self-consistent description of the free electron laser instability is developed for a relativistic electron beam with uniform density propagating through a helical wiggler field B/sup 0/=-B cosk/sub 0/ze/sub x/-B sink/sub 0/ze/sub y/. The analysis is carried out for the class of solutions to the Vlasov--Maxwell equations described by f/sub b/(z,p,t)=n/sub 0/delta(P/sub x/)delta(P/sub y/)G(z,p/sub z/,t), where P/sub x/ and P/sub y/ are the exact canonical momenta invariants perpendicular to the beam propagation direction. The linearized Vlasov--Maxwell equations lead to an exact matrix dispersion relation which is valid for perturbations about general beam equilibrium G/sub 0/(P/sub z/) and which includes coupling to arbitrary harmonic number (n) of the fundamental wiggler wavenumber k/sub 0/. No a priori restriction is made to low beam density (as measured by ..omega../sup 2//sub P//c/sup 2/k/sup 2//sub 0/) or small wiggler amplitude (as measured by omega-circumflex/sub c//ck/sub 0/=eB/gamma-barmc/sup 2/k/sub 0/). Moreover, no assumption is made that any off-diagonal elements in the matrix dispersion relation are negligibly small. A detailed numerical analysis of the exact dispersion relation is presented for the case of a cold electron beam described by G/sub 0/(P/sub z/) =delta(p/sub z/-p/sub 0/). It is shown that the instability bandwidth increases rapidly with increasing wiggler amplitude omega-circumflex/sub c//ck/sub 0/. Moreover, except for very modest values of wiggler amplitude, it is shown that the growth rate calculated from an approximate version of the dispersion relation can be in substantial error for large values of (k+nk/sub 0/)/k/sub 0/. Preliminary estimates of the influence of beam thermal effects are also presented.

• Research Organization: Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
• OSTI ID: 5074525
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 23:10; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420300* -- Engineering-- Lasers-- (-1989)
BEAMS
BOLTZMANN-VLASOV EQUATION
DAMPING
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
ELECTRON BEAMS
ENERGY RANGE
EQUATIONS
FREE ELECTRON LASERS
INSTABILITY
KINETICS
LANDAU DAMPING
LASERS
LEPTON BEAMS
MATRICES
MAXWELL EQUATIONS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTICLE BEAMS
RELATIVISTIC RANGE