Nonlinear Effects from Vlasov's Equation

Journal Article · Fri Feb 01 04:00:00 EST 1963 · Physics of Fluids (New York)

DOI:https://doi.org/10.1063/1.1706724· OSTI ID:4697262

Engelmann, F.; Feix, M.; Minardi, E.; Oxenius, J.

Nonlinear effects from Vlasov's equation are studied for a one- dimensional electron gas with fixed neutralizing background. The electron distribution function is expanded in Hermite polynomials and a closure condition is introduced to cut off the resulting infinite system of differential equations for the expansion coefficients. Then a nonlinear partial differential equation can be derived for the electric field. The consequences of some different closure conditions are studied. It turns out that their use implies severe restrictions on the physical situations described. In the discussed closed polynomial approximations no nonlinear instabilities are found. In particular, it results that with vanishing heat flux one has only stable linear or nonlinear oscillations showing that unstable situations are necessarily nonadiabatic. In an analogous manner, the condition that the plasma follows a state law with pressure proportional to density, like a perfect gas, eliminates unstable modes. (auth)

• Research Organization: Euratom, Brussels
• Sponsoring Organization: USDOE
• NSA Number: NSA-17-011848
• OSTI ID: 4697262
• Journal Information: Physics of Fluids (New York), Journal Name: Physics of Fluids (New York) Journal Issue: 2 Vol. 6; ISSN 0031-9171; ISSN PFLDAS
• Publisher: American Institute of Physics
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BACKGROUND
BOLTZMANN-VLASOV EQUATION
CLOSURES
DENSITY
DIFFERENTIAL EQUATIONS
DISTRIBUTION
ELECTRIC FIELDS
ELECTRONS
EXPANSION
GASES
HEAT TRANSFER
HERMITE POLYNOMIALS
MATHEMATICS
OSCILLATIONS
PHYSICS
PLASMA
PRESSURE
STABILITY
THERMODYNAMICS
TRANSPORT THEORY
VLASOV EQUATION