I. Introduction
RF cavities have long been used to accelerate charged particles to achieve high electric field strengths and because of the wide availability of high power RF sources. However, special care must always be taken to match the phase velocity of the wave in the RF structure (whether it be traveling or standing) to the velocity of the particle to be accelerated. This constraint prohibits empty straight waveguides and cavities from being used, because the phase velocity in such structures is always greater than . Dielectrics can sometimes be used to circumvent this problem, but dielectrics introduce difficulties of their own, such as outgassing and dielectric breakdown. In practice, corrugated structures are almost always used to achieve slow wave operation, since these structures tend to have high accelerating electric field and can also be used in a superconducting regime.