Resonant circuits are very commonly found in the many types of device where ac signals and fields are generated or used. One important class of resonator, used in a number of industrial and scientific applications, is the conducting cavity. Unlike the lumped element components usually found in electronic circuits, the cavity resonator is a distributed structure, in which the fields vary over its volume. Hence its electrical properties are determined by its size and shape, as well as by the properties of the materials used in its construction; by tailoring the size and shape, cavities can be designed to support particular modes at defined frequencies. These modal frequencies can be determined with high accuracy, and low losses can be achieved, leading to high quality factors, features that make them good candidates for frequency-determining components where precision is critical. This is particularly so at high frequencies, where cavity sizes are reducing, and the performance of competing lumped element components has degraded.
Resonant cavities can be filled with dielectric materials, which serve to reduce the resonant frequency of a given cavity. However, if left hollow, it is possible to interact with the internal fields. This finds application in, for example, particle beam devices, where a charged particle beam propagates through the cavity. Such devices are used for the generation and amplification of RF signals – in which the beam gives up energy resonantly to the field – and in particle accelerators, where, conversely, the field gives up energy to the beam. This application note will concentrate on the last of these, and will illustrate the relevant attributes of Opera’s electromagnetic eigenvalue solver, Modal HF, in the analysis of a typical accelerator cavity. It should be noted that cavities of the general type discussed here may be used for a number of different tasks, such as beam bunching and deceleration. However, they will be termed collectively as ‘accelerator cavities’.