Toroidal hollow-beam gun

A simple expression is derived for the focal length of the ring aperture of a toroidal hollow-beam gun. A digital-computer programme has been developed to determine the perveance from the potential, the electric field and the second derivative, with respect to toroidal radius, at the anode. With the expressions for the space-charge effect, the lens effect and the perveance, sets of design charts for possible gun parameters can be calculated. The outer electron-beam boundary is here defined by a parameter n, which describes the required minimum beam cross-section; the inner beam boundary is determined by the fact that the electron trajectories behind the anode must be made parallel to the axis, as no space-charge force is acting on the electrons of the inner beam boundary. Several guns have been built to verify the calculations experimentally. When designed according to the above calculations, they produce very well defined electron beams. These beams have been analysed with a pinhole probe and a pinhole-sector probe which permits measurement of the direction of the current density. These results also verify the calculations given in a previous paper, concerning the space-charge flow between cathode and anode of a toroidal hollow-beam gun.