Adjoint Approach to Analysis of External Circuit Effects in Vacuum Electronic Devices

We expand the adjoint approach to optimization and sensitivity analysis of beam-wave interaction in any vacuum electronic device (VED) that consists of a circuit interacting with a linear beam through a series of gaps. The method is based on the conservation of symplectic area for two perturbed solutions of the Hamiltonian form of the equations and was originally used for electron optics sensitivity analysis [1] and expanded to the RF beam-wave interaction in [2] , [3] . When the adjoint solution is obtained using a simulation code, it may be used to evaluate the multidimensional derivatives needed for efficient optimization and for sensitivity analysis. The adjoint approach has been implemented in 1D approximation using CHRISTINE-Z code [4] where the external circuit effects are described in terms of the generalized impedance matrix. We focused on numerical implementation and study of the effects of external circuit variations what expressed as variation of gap-to-gap distances, gap size and impedance matrix of the external structure. To study the effects of multi parameter variations of the external circuit we introduced a transmission line model based on fitting of local elements of the line by using calculated by 3D EM codes dispersion curves and coupling coefficients. Realistic terminations of the circuit are mimicked by adding directly calculated by 3D EM codes frequency dependent impedance matrices of terminating cells. The transmission line model shown excellent agreement with the results of direct calculations by 3D EM codes.