The small-amplitude motion of a relativistic beam passing through plasma is studied using transport theory. For the equilibrium state, a relativistic Maxwellian velocity distribution is obtained. The linearized Boltzmann equation is used to relate beam and plasma density and current perturbations to perturbations in the electromagnetic field. Approximate criteria are obtained to justify the neglect of static fields. Finally, these general results are specialized to those of a uniform beam.
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Watson et al. (1960) studied this question.
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