“…In fact a focusing magnetic field is usually present in the electron gun to obtain electron beam laminar and with a specific radius, in the interaction region to reduce the spread of the beam avoiding electrons' impinging on SWS, and in the collector to obtain a better distribution of the electrons on the electrodes and to reduce backstreaming current, due also to the secondary electron. Specialized 3D simulators, mostly based on finite element (FE) approach, are currently used by TWT designers to analyze and test new high efficiency devices, including the effect of self‐consistent magnetic field, the one generated from electron beam, and of the externally applied focusing magnetic field (Coco et al , 2006). Unfortunately, automatic optimization techniques in the design process of these devices are rarely used (Ghosh and Carter, 2007; Petillo et al , 2007; Vaden et al , 2002), because of the high computational cost of the simulation and of the high number of parameters from which the operation of this device depends: the geometry and the voltages of the electrodes and the applied focusing magnetic field, etc.…”