April 4-6

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Author: Philip J Morrison
Requested Type: Poster
Submitted: 2022-03-11 10:38:18

Co-authors: Francesco Pegoraro

Contact Info:
University of Texas at Austin
2515 Speedway
Austin, TX   78712

Abstract Text:
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, & 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 physically reasonable interaction model that lowers the dimension and brings such computations within reach.