Test Particles in a Completely Ionized Plasma

Starting from the Liouville equation, a chain of equations is obtained by integrating out the coordinates of all but one, two, etc., particles. One ``test'' particle is singled out initially. All other ``field'' particles are assumed to be initially in thermal equilibrium. In the absence of external fields, the chain of equations is solved by expanding in terms of the parameter g = 1/nLD3. For the time evolution of the distribution function of the test particle, an equation is obtained whose asymptotic form is of the usual Fokker‐Planck type. It is characterized by a frictional‐drag force that decelerates the particle, and a fluctuation tensor that produces acceleration and diffusion in velocity space. The expressions for these quantities contain contributions from Coulomb collisions and the emission and absorption of plasma waves. By consideration of a Maxwell distribution of test particles, the total plasma‐wave emission is determined. It is related to Landau's damping by Kirchoff's law. When there is a...