Functional Analysis Method for Nonlinear Theory of Gyrotrons

This paper proposes an analyzing method for the nonlinear theory of gyrotrons based on the functional analysis theory. This method is computationally efficient and highly practical, and the results have good accuracy as that of the self-consistent theory. Moreover, the stability of the gyrotron can be easily analyzed by the trajectory of the mapped efficiency space based on the fixed point of the functional analysis theory. The validity and effectiveness of the presented method are verified by the results of self-consistent theory and experiments presented in the references, such as typical examples of gyrotrons working at various frequencies and modes.