Calculation of DC space-charge fields in a traveling-wave amplifier in the large signal regime

A fully two-dimensional (2-D) dc space charge model has been implemented in a large-signal traveling-wave amplifier code. The simulation algorithm takes an iterative approach by alternately solving the Poisson equation and the beam trajectory equations to converge toward a self-consistent steady-state solution. This approach is similar to that employed in steady-state gun codes. However, it is well known from gun simulations that the iterative algorithm can be slow to converge. We have found the slow convergence is due to a convective numerical instability. To speed up convergence, we implemented and tested stabilization schemes based on mixing one-dimensional and 2-D Poisson potentials during the iteration cycles. These schemes are shown to accelerate convergence considerably. The fully 2-D dc space-charge model permits accurate treatment of the axial dc space-charge field in the computation of the large signal gain and efficiency, taking into account the fast variation of beam parameters along the device axis. Therefore, it can be applied to a mismatched beam with large scalloping motion. The methodology of incorporating dc space charge is general and could be incorporated in other large signal codes.