Vlasov moments, integrable systems and singular solutions
Exactly Solvable and Integrable Systems
2008-04-25 v1 Mathematical Physics
math.MP
Accelerator Physics
Plasma Physics
Abstract
The Vlasov equation for the collisionless evolution of the single-particle probability distribution function (PDF) is a well-known Lie-Poisson Hamiltonian system. Remarkably, the operation of taking the moments of the Vlasov PDF preserves the Lie-Poisson structure. The individual particle motions correspond to singular solutions of the Vlasov equation. The paper focuses on singular solutions of the problem of geodesic motion of the Vlasov moments. These singular solutions recover geodesic motion of the individual particles.
Cite
@article{arxiv.0705.3603,
title = {Vlasov moments, integrable systems and singular solutions},
author = {John Gibbons and Darryl D Holm and Cesare Tronci},
journal= {arXiv preprint arXiv:0705.3603},
year = {2008}
}