Dynamical large deviations for plasmas below the Debye length and the Landau equation

Ouassim Feliachi (1, 2) , Freddy Bouchet (2)

1 IDP - Institut Denis Poisson
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

We consider a homogeneous plasma composed of N particles of the same electric charge which interact through a Coulomb potential. In the large plasma parameter limit, classical kinetic theories justify that the empirical density is the solution of the Balescu-Guernsey-Lenard equation, at leading order. This is a law of large numbers. The Balescu-Guernsey-Lenard equation is approximated by the Landau equation for scales much smaller than the Debye length. In order to describe typical and rare fluctuations, we compute for the first time a large deviation principle for dynamical paths of the empirical density, within the Landau approximation. We obtain a large deviation Hamiltonian that describes fluctuations and rare excursions of the empirical density, in the large plasma parameter limit. We obtain this large deviation Hamiltonian either from the Boltzmann large deviation Hamiltonian in the grazing collision limit, or directly from the dynamics, extending the classical kinetic theory for plasmas within the Landau approximation. We also derive the large deviation Hamiltonian for the empirical density of N particles, each of which is governed by a Markov process, and coupled in a mean field way. We explain that the plasma large deviation Hamiltonian is not the one of N particles coupled in a mean-field way.

Mots clés: Plasma; Landau equation; Macroscopic fluctuation theory; Large deviation theory; Balescu-Guernsey-Lenard equation

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique des plasmas [physics.plasm-ph]; Dynamique Chaotique [nlin.CD]

Ouassim Feliachi, Freddy Bouchet. Dynamical large deviations for plasmas below the Debye length and the Landau equation. 2021. ⟨hal-03107192v2⟩