The effect of a gap between dielectric and waveguide on the dispersion relation of the Čerenkov device

We present a method for calculating efficiently the dispersion curve of a cylindrical Čerenkov device having a small gap between the dielectric liner and the guide wall. In any practical realisation, such a gap cannot be avoided and the results obtained here indicate that the dispersion curve is very sensitive to its thickness. Using a liner with a higher dielectric constant increases the sensitivity of the dispersion to the size of the gap. If a very high-energy electron beam is employed, having an electron velocity almost equal to c (speed of light in a free space) then synchronism occurs close to the intersection of the dispersion curve and the vacuum light line where the effect of the gap is small; in fact, a large gap could be left between the dielectric liner and the waveguide if this was advantageous for construction purposes. However, at lower electron energies, typical of those used in microwave devices, the effect of even a relatively small gap can be considerable on the synchronism condition.