On the design of the transition region of axisymmetric, magnetically focused beam valves

Assumption of a particular magnetic-field variation in the transition region of an axially symmetric beam-type device (e.g., klystron, travelling-wave tube) leads to the solution of the equations of electron motion by means of an analogue computer. To illustrate this novel method of solution, beam envelopes are presented for Brillouin flow, periodic magnetic focusing, and space-charge-balanced flow. By matching the beam envelopes with those obtained from the theory of the Pierce gun, dimensions are obtained for an electron gun that produces the required beam.