A 1-dimensional electrostatic plasma model for testing kinetic theory validity

A starting point for deriving the Vlasov equation with a collision operator is the BBGKY hierarchy that describes the dynamics of coupled marginal distribution functions. With a large plasma parameter (number of particles in a Debye sphere) one justifies dropping certain correlations and makes assumptions so as to eliminate 2-point correlations in terms of the 1-point function. Prior to making the assumptions that lead to the Vlasov equation with the Landau-Lenard-Balescu collision operator, there exists a closure that is a Hamiltonian field theory for the coupled dynamics of the 1-point and 2-point functions [J. Marsden, P. Morrison, and A. Weinstein, Cont. Math. 28, 115 (1984)], whence the Vlasov-Landau-Lenard-Balescu (VLLB) theory can be derived. Because of the curse of dimensions, numerically testing the assumptions of the VLLB theory is prohibitive. In this poster, we will present a 1-dimensional Hamiltonian model composed of interacting aligned charged disks in order to address the validity of the Bogoliubov assumption on the decay of correlations, a basic premise of plasma kinetic theory.