Stochastic equations arising from test particle problems

To compare the different kinetic equations derived in a previous paper for weakly coupled systems, the results are applied to coupled harmonic oscillators and a one-component plasma in a magnetic field. Using the harmonic interaction as an example, it is demonstrated that reasonable results can be inferred only from the kinetic equation, which is characterized by an additional time average. Applying this equation to an electron plasma in a magnetic field B, the Balescu-Lenard equation is recovered for B = 0, but a modification is obtained for B ≠. For strong fields the diffusion coefficient is discussed.