A New Self-Consistent Unbounded Magnetic Field 3-D FE Computation for Electron Guns

An innovative 3-D Finite Element approach for the computation of the self-consistent unbounded magnetic field of electron beams is presented for the analysis of electron guns. The solution of the whole problem is obtained by solving iteratively a Vlasov-Maxwell equation assuming stationary conditions together with the relativistic dynamical equations of motion. The self-consistent unbounded magnetostatic field is computed by using an edge elements curl-curl formulation for the magnetic vector potential. A fictitious boundary iterative algorithm is adopted to overcome the problem of boundary conditions assignment. An accuracy test concerning the spread of a relativistic beam and the simulation of a complex gridded electron gun are shown in order to validate and better illustrate the procedure.