Abstract
The problem of determining the stationary selfconsistent field of a beam of charged particles described by the Vlasov equation in a longitudinal magnetic field is considered. It is assumed that the particles are uniformly distributed over the cross-section of the beam. For the selfconsistent particle density, a representation in the form of a certain integral with an arbitrary function is proposed, which generalizes previously known distributions. An integral equation is also obtained for determining the selfconsistent particle density. New classes of solutions of the Vlasov equation are obtained on the basis of this representation and an integral equation, special cases of which are certain previously well-known solutions.
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