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Calculation of the Limiting Perveance of a Round Beam Partially Filling a Cylindrical Vacuum Chamber

One of the effects of space charge is the charged particles current limitation in electron-optical systems. As a rule, for each specific system the limiting value of current can only be found on the results of numerical calculation, but the analytical treatment is necessary both for initial estimates of the parameters of the system and for understanding the physical basis of processes occurring in it. In this paper we consider a uniform circular beam of charged particles, partially filling a cylindrical vacuum chamber. The maximum perveance of this system depending on the ratio of pipe radius to beam radius is found, the comparison of this dependence with the results of numerical calculation of the system is carried out, as well as with the approximate analytical estimates