Focusing and guiding intense electron beams by a superconductor tube

An intense electron beam travelling axially through the opening of a superconductor tube is studied. Our model calculations show that the beam is focused by the superconductor tube when the space-charge effect of the beam electrons is compensated. The tube functions as a lens for electrons injected parallel to the tube axis and also for electrons having a small initial radial velocity component. The electron trajectories are computed, and the focal length of the superconductor tube is estimated.