Noniterative method for the synthesis of convergent pierce electron guns

A simple noniterative method has been proposed to design a convergent Pierce electron gun. The logarithmic value of the ratio of cathode to anode radii of curvature is expressed in a power series directly in terms of beam convergence ratio. This made it possible to calculate the half-beam cone angle with the help of Langmuir-Blodgett's solution, which, in turn, facilitated the calculation of other output parameters. The throw of the gun is also expressed in a power series in terms of the ratio of the anode-aperature radius to the beam waist radius. It is numerically shown with practical examples that both the interelectrode distance and the throw decrease with the gun perveance and increase (the former almost linearly while the latter almost binomially) with the beam diameter.