Abstract
The envelope of the adiabatic trajectory solution for particle motion that occurs in cone focusing of intense relativistic electron beams is investigated. Comparisons with exact trajectory envelopes (obtained numerically) show that the adiabatic envelope is an excellent approximation under a wide variety of circumstances. Consequently, several important effects are disclosed: (1) The axial dependence of the breakdown (and not the radial dependence) is explicitly shown to determine the focusing, (2) increasing the cone angle rapidly leads to increased losses, (3) angular momentum created by scatter in the anode foil typically should not cause significant losses, and (4) increase of the beam temperature along the cone axis is demonstrated. A novel explanation of “adiabatic envelope conservation” is included.
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