AC-Space-Charge Effects on Gap Coupling Coefficient of a Klystron Cavity

A novel model was developed to evaluate gap coupling coefficient considering ac-space-charge effects due to the bunching in the interaction gap. The formulation was derived based on Webster's debunching theory and the electron-stream oscillation equation with arbitrary gap field distribution on the gridless gap. The coupling coefficient with ac-space-charge effects was investigated through both analysis and particle-in-cell simulation. The calculation results are in reasonable agreement with the simulation results. With the ac-space-charge effects, the coupling coefficient is lower than that calculated by ballistic theory. It is found that the plasma gap transit angle is a key factor in the effects of ac space charge on the coupling coefficient. Large beam current or gap length and, hence, mean large plasma transit angle indicate strong ac-space-charge effects on the coupling coefficient.

I. Introduction

The coupling coefficient is arguably the most important parameter used in the design of a klystron [1]–[4]. It is the ratio of effective voltage applied on the beam modulation, normalized to the RF voltage across the interaction gap. The coupling coefficient describes the interaction between the beam and the RF fields, and a higher value means better interaction, hence higher efficiency and gain, which is proportional to the value of   [5]. The conventional calculation adopted Branch's ballistic approach [1], which did not consider ac-space-charge effects [6]–[10] due to the electronic bunching in the cavity gap. in Branch's theory, is calculated based on the electron velocity modulation by a cavity gap electric field, with the assumption of no beam density modulation when transiting the gap. in a more realistic case, a klystron is designed with a long cavity gap or a large beam current; thus, the ac-space-charge effects in the gap are not negligible. in gridless cavity gaps, the effective length of the interaction gap is much longer than the real gap length. in addition, coupled cavities in extended interaction klystrons (EIKs) [5], [11]–[13] have longer gaps than those in traditional klystrons. Under these situations, the ac-space-charge effects due to the electron bunching in the gap cannot be ignored. The electronic kinetic energy produced through the modulation by the gap field converts partly into potential energy, so that the real value is lower than that obtained through Branch's method. in the 1960s, the ac-space-charge effects based on the debunching theory were taken into account, and a new formulation was derived [14]. However, this formulation was limited to a grid gap. in modern klystron cavities, the gap is always gridless, and therefore, the electric field distribution is nonuniform. To investigate the theory of the beam–wave interaction in cavity gaps and to develop a more precise computer simulation model [12], [15], [16], it is necessary to obtain a more accurate value of in the consideration of the effects of ac space charge.