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The time-independent slowing-in distribution is evaluated for a fast beam of test particles released in an infinite Maxwellian plasma background for various situations including quantum-mechanical and classical scattering regimes. The analysis involves considerations of small angle deflection and large angle scattering events. The results are determined for plasma electrons with thermal velocities larger or smaller than the test particle and plasma ions with thermal velocities lower than the test particle. When plasma electrons and ions are slow the slowing-in distribution behaves as E/sub j//sup $sup 1$/$sub 2$/, where E/sub j/ is the test particle energy. When plasma electrons are faster than the test particles, the high-energy tail acquires a 1/E/sub j/ shape. The origin of the test particle remains arbitrary and hence the results apply for particles produced by fusion events within the plasma proper and for particles externally injected. The total energy distribution is obtained and normalized, and ranges of validity are determined. The calculations are of the Boltzmann type, which is consistent with binary scattering models. The slowing-in distributions are also obtained from the Fokker--Planck equation, and as expected, the results agree with those obtained from the Boltzmann equation for large angle scattering only. (auth

Slowing-in distribution of fast particles released in Maxwellian plasma