Explicit analytical solution of the nonlinear Vlasov--Poisson system

Journal Article · Tue Mar 01 04:00:00 EST 1994 · Physics of Plasmas; (United States)

DOI:https://doi.org/10.1063/1.870797· OSTI ID:6686932

Skarka, V; Mahajan, S M ^[1]; Fijalkow, E ^[2]

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1. International Centre for Theoretical Physics, Trieste (Italy)
2. Physique, Mathematique, Modelisation et Simulation, C.N.R.S., Orleans (France)

In order to describe the time evolution of an inhomogeneous collisionless plasma, the nonlinear Vlasov equation is solved perturbatively, using the subdynamics approach and the diagrammatic techniques. The solution is given in terms of a double perturbation series: one with respect to the nonlinearities and the other with respect to the interaction between particles. The infinite sum of interaction terms can be performed exactly due to the property of dynamical factorization. Following the methodology, the exact solution in each order with respect to nonlinearities is computed. For a choice of initial perturbation the first-order exact solution is numerically integrated in order to find the local density excess. The approximate analytical solution is found to be in excellent agreement with exact numerical integration as well as with [ital ab] [ital initio] numerical simulations. Analytical computation gives a better insight into the problem, and it has the advantage to be simpler, and also accessible, in some range of parameters where it is difficult to find numerical solutions.

• OSTI ID: 6686932
• Journal Information: Physics of Plasmas; (United States), Journal Name: Physics of Plasmas; (United States) Vol. 1:3; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700330* -- Plasma Kinetics
Transport
& Impurities-- (1992-)
ANALYTICAL SOLUTION
BOLTZMANN-VLASOV EQUATION
COLLISIONLESS PLASMA
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
EQUATIONS
FUNCTIONS
INHOMOGENEOUS PLASMA
KINETIC EQUATIONS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
PLASMA
POISSON EQUATION