Numerical Integration of Kinetic Equations

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Abstract
The problem of the relaxation to a Maxwellian of the Balescu‐Lenard equation is solved numerically as an initial value problem for isotropic distributions of electrons situated in a neutralizing, uniformly smeared out background of positive charge. Several different forms for the initial distribution function are chosen: a Gaussian peaked at about 0.28 of the electron thermal speed, a resonance function, and a Maxwellian coexisting with a sharply peaked Gaussian (the peak of the Gaussian being located at two thermal speeds of electrons). The Fokker‐Planck equation with the Rosenbluth‐MacDonald‐Judd collision term is also solved numerically under the same restrictions and with the same initial distribution functions. Comparison of the solutions of the two kinetic equations shows that the difference between them is very small, and a probable reason for this is advanced. The evolution of the distribution functions with time is studied, and a relaxation time is defined.