Limiting currents for injection of an unneutralized magnetized relativistic electron beam into a cylindrical drift tube

Results of an investigation of the steady state injection of a uniform unneutralized, magnetized, relativistic electron beam into a cylindrical drift tube are presented. The space-charge limited current and the asymptotic kinetic energy of electrons on axis is determined both numerically and analytically as a function of the input kinetic energy (ΰo−1)mc² and of the ratio of beam-to-wall radii. A previously cited “interpolation formula” is obtained in the pencil beam limit, but more accurate limiting current expressions are developed for other cases (such as the fat beam limit) where the interpolation formula is as much as 20 percent in error. The corresponding axial electron energy is also found to be significantly smaller than the previously cited value of (γo^1/3−1 )mc² except in the strong pencil beam limit.