Space-charge limits in unneutralized relativistic electron beams

Limiting currents in annular unneutralized relativistic electron beams are calculated and compared with experiment. The limiting factor for short beams is found to be the space-charge depression of the potential due to the unneutralized beam; in longer beams self-magnetic and electric fields impose a power limit. Typical beam impedances are found to be of the order of 15 Ω with a 350 keV beam. The role of shear in the axial velocity of the beam is discussed.