Eur. Phys. J. D (2014) 68: 370
https://doi.org/10.1140/epjd/e2014-50195-2

Regular Article

Hamiltonian models for resonant wave-particle interaction processes in magnetized and inhomogeneous plasmas^*

¹ Laboratoire de Physique des Plasmas, École Polytechnique, 91128 Palaiseau Cedex, France
² Université Paris Sud, 91405 Orsay Cedex, France
³ Space Research Institute (IKI), 84/32 Profsoyuznaya Str., 117997 Moscow, Russia
⁴ IZMIRAN, Troitsk, 142190 Moscow, Russia

^a e-mail: catherine.krafft@lpp.polytechnique.fr

Received: 10 March 2014
Received in final form: 24 September 2014
Published online: 11 December 2014

Abstract

The kinetic theory of plasmas, based on the Vlasov-Poisson system of equations, can efficiently solve only some aspects of the extremely large panel of problems involving wave-particle and wave-wave interaction processes in plasmas. Therefore the dynamics of charged particles and waves has been modeled by other approaches as, for example, Hamiltonian models describing the self-consistent wave-particle and wave-wave interactions in homogeneous or inhomogeneous magnetized plasmas. Various physical problems could be efficiently studied by such methods, concerning nonlinear and turbulent stages of different instabilities of electron or ion distributions, wave packets’ saturation and particles fluxes’ relaxation processes, particle trapping and detrapping mechanisms by waves, wave-particle interactions at multiple resonances, quasilinear diffusion processes of particles in waves, wave turbulence in randomly inhomogeneous plasmas, acceleration of particles, wave focusing, scattering, reflection and decay, etc. In particular, the aim of the paper, after a brief description of such Hamiltonian models, is to present the most recent simulation results obtained when studying Langmuir turbulence in the presence of electron beams propagating in inhomogeneous plasmas as the solar wind, where random density fluctuations with average levels up to several percents of the background plasma density have been measured.