Titre :

On a Vlasov-Fokker-Planck equation for stored electron beams

Auteur(s) :

Cesbron, Ludovic [Auteur]
Analyse, Géométrie et Modélisation [AGM - UMR 8088]
Herda, Maxime [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]

Titre de la revue :

Journal of Differential Equations

Pagination :

316-353

Éditeur :

Elsevier

Date de publication :

2024-09-25

ISSN :

0022-0396

Mot(s)-clé(s) en anglais :

Vlasov-Fokker-Planck
Hypocoercivity
Hypoellipticity
Synchrotron radiation
Wakefield
Haissinski solutions

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

In this paper we study a self-consistent Vlasov-Fokker-Planck equations which describes the longitudinal dynamics of an electron bunch in the storage ring of a synchrotron particle accelerator. We show existence and ...
Lire la suite >In this paper we study a self-consistent Vlasov-Fokker-Planck equations which describes the longitudinal dynamics of an electron bunch in the storage ring of a synchrotron particle accelerator. We show existence and uniqueness of global classical solutions under physical hypotheses on the initial data. The proof relies on a mild formulation of the equation and hypoelliptic regularization estimates. We also address the problem of the long-time behavior of solutions. We prove the existence of steady states, called Haissinski solutions, given implicitly by a nonlinear integral equation. When the beam current (i.e. the nonlinearity) is small enough, we show uniqueness of steady state and local asymptotic nonlinear stability of solutions in appropriate weighted Lebesgue spaces. The proof is based on hypocoercivity estimates. Finally, we discuss the physical derivation of the equation and its particular asymmetric interaction potential.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL