The Study of a Certain Type of Resonant Cavity and Its Application to a Charged Particle Accelerator

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Abstract
A linear accelerator for charged particles, consisting of a number of cavity resonators placed end to end with the inside end plates removed, and thus forming a wave guide with two closed ends, is discussed. The shape of each section must be so chosen that the velocity of the particle will correspond to the phase velocity of the radiation of the cavity. In order to determine possible shapes for the cavity, the stationary TM01 modes between two parallel conducting planes are determined. In Part 1, excitation of a single mode is discussed, including the shape of the conducting surface that can be used to connect the planes and thus form a cavity. Three cases are considered—when the phase velocity in the cavity is greater than, equal to, and less than that of light. If only one mode is excited, and the phase velocity is not greater than that of light, then the radius of the cavity becomes infinite at the two plates. In Part 2, the simultaneous excitation of two modes is considered. The phase velocity of one mode is that of light; the other has a phase velocity 1/n that of light, where n is an odd integer. The cavity can be made finite by a suitable choice of the relative amplitude of the two modes, and the radius of one end of the cavity. This requires a rather elaborate discussion. This case is of particular interest for the acceleration of electrons. It is shown, furthermore, that only the first mode contributes to the acceleration of the electron. In Section 4, the application of the methods used in Part 3 to the case of an accelerator for heavy particles is touched upon.

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