  The focus of this work is to create benchmark simulations of decay rates to
statistical equilibrium in transport plasma models for Coulomb particle
interactions given by a coupled Vlasov-Poisson Fokker-Planck-Landau equation,
as well as with Maxwell type and hard sphere interactions. The qualitative
decay to the equilibrium Maxwell-Boltzmann distribution through relative
entropy is studied in detail for all three types of particle interactions by
means of a conservative hybrid spectral and discontinuous Galerkin scheme
adapted from previous work. More precisely, the Coulomb case shows that there
is a degenerate spectrum, with a decay rate close to the law of two thirds
predicted by upper estimates in a work of Strain and Guo in 2006, while the
Maxwell type and hard sphere examples both exhibit a spectral gap as predicted
by Desvillettes and Villani in 2000. Such decay rate behavior indicates that
the analytical estimates for the Coulomb case is sharp while, still to this
date, there is no analytical proof of sharp degenerate spectral behaviour for
the Fokker-Planck-Landau operator.
  Simulations are presented, both for the space-homogeneous case of just
particle potential interactions and the space-inhomogeneous case for the mean
field coupling through the Poisson equation for total charges in periodic
domains. New explicit derivations of spectral collisional weights are presented
in the case of Maxwell type and hard sphere interactions and the stability of
all three scenarios, including Coulomb interactions, is investigated.
