Dynamics of an electron in an RF gap

An attempt is made to understand the limitation on the energy transfer efficiency of an electron beam to the RF output cavity of a klystron or a lasertron. An output cavity with drift tubes is modeled by a region of constant amplitude RF field with exponentially decreasing entrance and exit fringing fields. The exit velocity of an electron traversing such a gap is examined as a function of entrance phase for various values of the ratio of the peak RF cavity voltage to the electron entrance voltage. Depending on the ratio, the dynamics of the electron motion can become quite complex. For a gap with fringe fields it is found that, even if the gap voltage and phase are optimized, the maximum energy that can be extracted from a short bunch is always significantly less than 100%. The case in which the electron is created with zero velocity in the gap, and subsequently leaves the gap having extracted energy from the RF field, is also treated