The dispersion relation for a cylindrical Cherenkov free electron maser

We have constructed a Cherenkov maser oscillator designed to operate at 16.9 GHz with a solid electron beam accelerated to 70 kV, using an alumina tube, fitted into a copper pipe. Although we achieved nearly 100% transmission of a 100 mA electron beam, no microwave output was observed despite the theoretical small signal gain being >300%. To resolve this problem, we have measured the dispersion curves of various dielectrically loaded structures and have observed a marked discrepancy between the theoretical and experimentally measured data in the case of alumina. This was sufficiently large to explain the non-operation of the FEM. After considering possible causes, we concluded that the small gap between the alumina liner and the copper waveguide (only 1% of the diameter of the guide), was responsible for the difference.