Resonant Cavities and Waveguides

Resonant Cavities and Waveguides35612 Resonant Cavities and WaveguidesThis chapter initiates our study of Resonant accelerators., The category includes rf(radio-frequency) linear accelerators, cyclotrons, microtrons, and synchrotrons. Resonantaccelerators have the following features in common:1. Applied electric fields are harmonic. The continuous wave (CW) approximation is valid;a frequency-domain analysis is the most convenient to use. In some accelerators, thefrequency of the accelerating field changes over the acceleration cycle; these changes arealways slow compared to the oscillation The longitudinal motion of accelerated particles is closely coupled to accelerating The frequency of electromagnetic oscillations is often in the microwave regime. Thisimplies that the wavelength of field variations is comparable to the scale length ofaccelerator structures.

(12.11) tan 1 Im(A)/Re(A). (12.12) The coefficients A and B may be complex numbers if there is a phase difference between the voltage and the current. They are determined by substituting Eq. (12.6) into Eq. (12.1) and recognizing that the terms involving exp(j t) and exp(-j t) must be separately equal if the solution is to hold at all times.

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