Generalized representation of electric fields in interaction gaps of klystrons and traveling-wave tubes

Analytic expressions for axial and radial electric fields in axisymmetric interaction gaps of klystrons and coupled-cavity traveling-wave tubes are derived. Introduction of a field-shape parameter
m
allows a continuous transition in gap-edge field distribution between the limit of a uniform constant field for relatively blunt tunnel tips to the limit of a field rising to infinity with infinitely sharp tunnel tips. With values of
m = 0
and
m = \infin
corresponding to these limits, intermediate values of m yield field distributions that very closely approximate the actual field distributions occurring in interaction gaps. A comparison is made between the analytically computed field distribution and the field distribution obtained by experimental measurement and by relaxation computation in a klystron cavity.