NUMERICAL INTEGRATION OF THE NON-LINEAR VLASOV EQUATION

Journal Article · Fri Dec 01 04:00:00 EST 1961 · Zeitschrift fuer Naturforschung (West Germany) Divided into Z. Nautrforsch., A, and Z. Naturforsch., B: Anorg. Chem., Org. Chem., Biochem., Biophys.,

OSTI ID:4817300

Knorr, G

The Vlasov equation, i.e., the Boltzmann equation without collision term, was numerically integrated as an initial value problem together with the second Maxwell equation for a one-dimensional electron plasma with smeared-out ion background. The initial values were taken as a Maxwellian distribution in velocity space and a cosine distribution in position, resulting in a sinusoidal form for the electric field. The Landau damping of the total energy of the electric field turned out to be valid for times larger- than those given by a formal estimation of the validity of the linear solution. For still later times, the decay rate of the electric energy is less than that given by Landau damping. The period of validity of Landau danmping was computed by estimating the influence of the trapped particles. As a nonlinear effect the first harmonic of the electric field builds up within this period. The growth of the first harmonic is faster for larger wave numbers k. (auth)

• Research Organization: Max-Planck-Institut fur Physik und Astrophysik, Munich
• NSA Number: NSA-16-019858
• OSTI ID: 4817300
• Journal Information: Zeitschrift fuer Naturforschung (West Germany) Divided into Z. Nautrforsch., A, and Z. Naturforsch., B: Anorg. Chem., Org. Chem., Biochem., Biophys.,, Journal Name: Zeitschrift fuer Naturforschung (West Germany) Divided into Z. Nautrforsch., A, and Z. Naturforsch., B: Anorg. Chem., Org. Chem., Biochem., Biophys., Vol. Vol: 16a; ISSN ZNTFA
• Country of Publication: Country unknown/Code not available
• Language: German

Related Subjects

BACKGROUND
BOLTZMANN EQUATION
BOLTZMANN STATISTICS
BOLTZMANN- VLASOV EQUATION
CONFINEMENT
DIFFERENTIAL EQUATIONS
DISTRIBUTION
ELECTRIC FIELDS
ELECTRODYNAMICS
ELECTROMAGNETISM
ELECTRONS
ENERGY
FOURIER ANALYSIS
FREQUENCY
HARMONIC ANALYSIS
IONS
LANDAU DAMPING
MATHEMATICS
MAXWELL DISTRIBUTION
MAXWELL EQUATIONS
NONLINEAR PROBLEMS
NUMERICALS
OSCILLATIONS
PHYSICS
PLASMA
STATISTICS
THERMODYNAMICS
TRANSPORT THEORY
VELOCITY
VLASOV EQUATION