Dynamical Large Deviations for Plasmas Below the Debye Length and the Landau Equation

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