Exact, time-dependent solutions of the one-dimensional Vlasov--Maxwell equations

Journal Article · Sun Jan 01 04:00:00 EST 1984 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.864510· OSTI ID:5385108

Abraham-Shrauner, B

Coordinate transformations from a reference frame with electrostatic Bernstein--Greene--Kruskal equilibria produce exact, time-dependent one-particle distribution functions and electric fields that obey the nonlinear one-dimensional Vlasov--Maxwell equations. The Liouville equation invariant on which the distribution function depends is the transformed particle energy. Procedures for deriving invariants of more general momentum dependence than quadratic are suggested. The vanishing of the longitudinal current density is imposed upon the exact time-dependent Vlasov--Poisson solutions and a particular case of a time oscillatory Bernstein--Greene--Kruskal equilibria is solved. The existence of solutions with a nonconstant time-stretching factor rho(t) is demonstrated.

• Research Organization: Department of Electrical Engineering, Washington University, St. Louis, Missouri 63130
• OSTI ID: 5385108
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 27:1; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700105* -- Fusion Energy-- Plasma Research-- Plasma Kinetics-Theoretical-- (-1987)
ANALYTICAL SOLUTION
BOLTZMANN-VLASOV EQUATION
COORDINATES
DIFFERENTIAL EQUATIONS
EQUATIONS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
RECOMBINATION
TIME DEPENDENCE
TRANSFORMATIONS