Theory for cylindrical, open ended, complex cavities supporting all TE0n modes: Gyrotron application

A theory is developed to accurately determine the resonant frequencies and quality factors in good conducting, open-ended cylindrical structures with step changes and weakly irregular changes in wall radius, supporting all TE_0n modes. Analytical expressions are obtained which avoid the need to solve the complicated boundary value problem. Inadequacies in experimental quality factors are discussed and new definitions are developed which consider mode coupling effects. The theory is applied to complex cavity gyrotron structures. Very good agreement is shown with existing experiments. Linear and quadratic phase shifts result from slight tapers. Small changes in the open-ended cavity geometry significantly changes the quality factor of the desired mode. The theory is applicable in overmoded structures with a dense frequency spectrum as a consequence of the high accuracy in determining the resonant frequency