Eur. Phys. J. D 46, 295-302 (2008)
https://doi.org/10.1140/epjd/e2007-00302-7

Poisson-Vlasov: stochastic representation and numerical codes

¹ Centre de Physique Théorique, CNRS Luminy, case 907, 13288 Marseille Cedex 9, France
² Centro de Fusão Nuclear, EURATOM/IST Association, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
³ CMAF, Complexo Interdisciplinar, Universidade de Lisboa, Av. Gama Pinto 2, 1649-003 Lisboa, Portugal

Corresponding author: ^a vilela@cii.fc.ul.pt

Received: 13 July 2007
Revised: 20 September 2007
Published online: 31 October 2007

Abstract

A stochastic representation for the solutions of the Poisson-Vlasov equation, with several charged species, is obtained. The representation involves both an exponential and a branching process and it provides an intuitive characterization of the nature of the solutions and its fluctuations. Here, the stochastic representation is also proposed as a tool for the numerical evaluation of the solutions.