Single-mode saturation of a linearly unstable plasma

Journal Article · Tue Jan 01 04:00:00 EST 1985 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.865190· OSTI ID:6145010

Burnap, C; Miklavcic, M; Willis, B L; Zweifel, P F

The nonlinear oscillations of an electron plasma described by the collisionless Vlasov equation are studied using a perturbation technique previously applied by Simon and Rosenbluth (Phys. Fluids 19, 1567 (1976)). It is proved by a characteristic argument that the plasma is globally stable, so that Bogoliuboff's method of ''secular regularization'' is applicable. Assuming the plasma is confined in a box, and that only the lowest mode is unstable, it is shown that the ''eigenmode dominance'' approximation of Simon and Rosenbluth fails to conserve energy, but that energy and momentum conservation can be regained by considering interaction between the discrete and continuum modes. A formula is derived for the amplitude and phase of the saturated nonlinear oscillations. In a subsidiary result, it is shown that nonlinear effects damp the steady-state oscillations predicted by linearized theory for some stable plasmas.

• Research Organization: Laboratory for Transport Theory and Mathematical Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
• OSTI ID: 6145010
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 28:1; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700107* -- Fusion Energy-- Plasma Research-- Instabilities
BOLTZMANN-VLASOV EQUATION
COLLISIONAL PLASMA
DIFFERENTIAL EQUATIONS
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
INSTABILITY
LEPTONS
NONLINEAR PROBLEMS
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
PLASMA
PLASMA INSTABILITY
SATURATION