Transient Analysis of Multicavity Klystrons

We describe a model for analytic analysis of transients in multicavity klystron output power and phase. Cavities are mod-eled as resonant circuits, while bunching of the beam is modeled using linear space-charge wave theory. Our analysis has been implemented in a computer program which we use in designing multicavity klystrons with stable output power and phase. We present as examples transient analyses of a relativistic klystron using a magnetic pulse compression modulator, and of a conventional klystron designed to use phase shifting techniques for RF pulse compression. INTRODUCTION Large linear electron colliders require high power short pulsed RF sources in order to attain accelerating gradients of 100-200 MV/m. Two techniques being developed to supply this RF tire relativistic klystrons with modulators using magnetic pulse compression, and conventional klystrons using phase shifting techniques for RF pulse compression. The RF power and frequency range being explored is 100-500 MW at 11-17 GHz. The RF output pulse length desired is 50-100 nsec, making the transient behavior of the multicavity klystrons employed in both approdches important. This paper describes a model for analytic analysis of transients in muIticavity klystron output power and phase. Cavities are-modeled as resonant circuits, while bunching of the beam is modeled using linear space-charge wave theory. The model has been implemented in a computer program which is used in designing multicavity klystrons with stable output power and phase. R.F CAVITIES Each beam loaded klystron cavity is modeled as a parallel network of cavity and beam loading impedances as shown in Fig, 1. External resistance Z& includes additional resistive loading by.iris-coupled waveguides. The RF driver connected to the input cavity typically consists of a power source, isolator, wave-guide, and coupling iris. Th,e driverjs modeled as a generator of alternating current I, = Z# " with shunt resistance Z& attached to the beam loaded input cavity (Fig. 1). Downstream cavities are driven by the bunched beam current. The RF voltage on a cavity is V(t) = $'(t)@' where I?(t) is the transient modulation of the RF oscillation eiwt. The transient behavior of V(t) is calculated from the circuit equation-$cv+-$;+p=i which can be rewritten as where? L, R, and C are the beam loaded cavity inductance, resistance , and capacitance, respectively. L, R, and C may be time dependent due to resistive and reactive loading of the cavity by beam pulses with finite risetime. The current Z flowing in the circuit model is …