Nonlinear bound on unstable field energy in relativistic electron beams and plasmas

Journal Article · Sun Jan 01 00:00:00 EST 1989 · Phys Fluids B; (United States)

DOI:https://doi.org/10.1063/1.859087· OSTI ID:6636705

Davidson, R C; Yoon, P H

This paper makes use of Fowler's method (J. Math Phys. 4, 559 (1963)) to determine the nonlinear thermodynamic bound on field energy in unstable plasmas or electron beams in which the electrons are relativistic. Treating the electrons as the only active plasma component, the nonlinear Vlasov--Maxwell equations and the associated global conservation constraints are used to calculate the lowest upper bound on the field energy (..delta..E-script/sub F/)/sub max/ that can evolve for the general initial electron distribution function f/sub b//sub //sub 0/equivalentf/sub b/(x,p,0). The results are applied to three choices of the initial distribution function f/sub b//sub //sub 0/. Two of the distribution functions have an inverted population in momentum p/sub perpendicular/ perpendicular to the magnetic field B/sub 0/e/sub z/, and the third distribution function reduces to a bi-Maxwellian in the nonrelativistic limit. The lowest upper bound on the efficiency of radiation generation, eta/sub max/ = (..delta..E-script/sub F/)/sub max//(V/sup -1/..integral.. d/sup 3/x..integral.. d/sup 3/p(..gamma..-1)mc/sup 2/f/sub b//sub //sub 0/), is calculated numerically over a wide range of system parameters for varying degrees of initial anisotropy.

• Research Organization: Plasma Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
• OSTI ID: 6636705
• Journal Information: Phys Fluids B; (United States), Vol. 1:1
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ELECTRON BEAMS
NONLINEAR PROBLEMS
PLASMA
BOLTZMANN-VLASOV EQUATION
FOWLER-NORDHEIM THEORY
PLASMA SIMULATION
RELATIVISTIC RANGE
THERMODYNAMICS
BEAMS
DIFFERENTIAL EQUATIONS
ENERGY RANGE
EQUATIONS
LEPTON BEAMS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE BEAMS
SIMULATION
700103* - Fusion Energy- Plasma Research- Kinetics