Space-charge waves on annular beams in drift tubes

The general theory of the excitation of space-charge modes on an annular electron beam in a cylindrical drift tube is established for the case of infinite magnetic-focusing field. Computations for various tunnel diameters have been made, showing that, if thin annular beams are utilized, the normalized tunnel diameter which is around unity for a solid beam may be increased by a considerable factor. This factor is about 4 for a particular case. Variations of the spacing between beam and tunnel consequent upon aberrations of the focusing system should not introduce serious loss of gain or variation in performance. Since annular beams can be designed for higher perveances than can solid beams, important gains in performance can be expected.