Full 2D Model for DC Space Charge Fields in the Large-Signal Code TESLA

Abstract

Summary form only given. The strong bunching process in klystron-type devices can cause beam electrons to slow down and reverse direction. For these particles the role of DC space-charge forces is important. Here we investigate an improved model for the calculation of such DC forces in TESLA. In the first approximation the space-charge density distribution can be considered as slowly varying along the device axis, and the Poisson equation can be reduced to a 1D version taking into account only the radial dependence of the potential. This allows for a fast solution for the potential "on the fly" at every cross-section of the device. With this approach the longitudinal electric field component can be found as the difference of solutions for potential at neighboring cross-sections. However, the 1D approximation becomes strained in devices where the space-charge density varies rapidly in the longitudinal direction. This will happen when particles are dramatically slowed down in the vicinity of the output cavity, or when the electron beam develops scallops with small axial period. In these cases the capability to provide a full 2D solution for the space charge potential becomes very important. The large-signal code TESLA was extended by the addition of a fully 2D Poisson solver, which allow to model more general cases with increased accuracy. The new Poisson solver was applied to cases with a large fraction of slow particles, whose contribution to the space-charge density was found to be significant. To cover the whole device the 2D solver was also extended inside the cavity for each gap region to provide an accurate solution. The main features and results of the new 2D solver are discussed in detail.