A theory of cavity excitation by modulated electron beam in connection with application to a klystron amplifier

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Abstract
Based on an equivalent circuit representation of a cavity impedance, a theoretical model of the cavity excitation by a modulated electron beam is developed. The beam current modulation is initiated by the first cavity and amplified in drift section between the first and second cavities. Properties of the second cavity excitation by the beam are described in terms of the phase shift Ψ and amplitude φ2 of induced voltage in the cavity. The phase shift Ψ and amplitude φ2 are determined in terms of the frequency difference (η), the cavity Q value, the voltage multiplication factor (χ), and magnitude (φ1) of the first cavity voltage. The voltage multiplication factor is proportional to the beam intensity, Q value, and distance between the first and second cavities. On the other hand, it is inversely proportional to frequency and capacitance of the cavity, and beam electron velocity. Because the induced voltage in the second cavity is in phase with the first cavity voltage at upshifted cavity frequency, amplitude of the current modulation at the upshifted frequency is larger than that at the downshifted cavity frequency. Experimental study is carried out by making use of a klystron amplifier operable from 4.4 to 5 GHz. Experimental data from the klystron agree remarkably well with amplifier performance profiles predicted by the theory.