Motion of a Test Particle in a Plasma

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Abstract
The motion of a charged test particle in a completely ionized gas without a magnetic field is investigated. The possible trajectories of this test particle are described by a distribution function that spreads out in phase space as time increases. A convergent kinetic equation which accounts for long‐range collective effects and short‐range collisions in a consistent manner is derived to describe the time evolution of the distribution function. Expressions for the energy loss rate and dynamical friction are calculated from appropriate moments of the kinetic equation, and they show how the Coulomb logarithm, ln Λ, varies with the velocity of the test particle. The errors introduced by the use of a convergent kinetic equation are estimated, and these indicate that the kinetic equation method gives the test particle's diffusion in phase space only on coarse grained time and spatial scales. For the case of a fast electron, the time scale must be larger than the electron plasma period and the spatial scale larger than e2/KT.