A model for the klystron cavity gap

Calculation of the fields in a klystron tunnel in the neighborhood of an ungridded gap requires an assumption about the field distribution across the open gap. Assumptions made in the past include the uniform field (Wang), the cosh variation (Kosmahl and Branch), and the variation of potential as a sin^-1function (Beck). This paper presents a set of empirical explicit equations for the field and other parameters in terms of the gap dimensions, including the radius of curvature of the noses. The gap coupling factor is then found by reduction of a set of numerical trajectory integrations. An explicit formula is given for the equivalent gridded-gap transit angle in terms of the corrected coupling factor.