A new 3-D FE procedure for the analysis of TWT gridded electron guns

A new three-dimensional Finite Elements procedure for the analysis of electron guns inside TWT is presented, illustrating its main features. In this procedure cathodic emission is modeled according to Child's law, operating in space charge limited mode. Corrections taking into account cathode geometric shape and relativistic beams are considered allowing us to obtain accurate evaluation of emission currents from the knowledge of the field distribution near the cathode. Electron trajectories are obtained by solving a Vlasov-Poisson system of equations together with the relativistic dynamical equations of motion. This coupled electro-mechanical problem is solved iteratively by assuming stationary conditions. In the analysis an external magnetic field can also be introduced in order to obtain a better focalization of the electron beam.