Differential algebraic description and analysis of trajectories in vacuum electronic devices including space-charge effects

A new method is presented to obtain transfer maps describing trajectories in vacuum electronic devices to arbitrary order. The method is based on differential algebraic techniques and is well suited for a combination with many field-generating codes. Also, internal space-charge fields in two or three dimensions can be treated in a straightforward manner based on the method of regular Gaussian subbeams. Contrary to the very unstable numerical differentiation techniques, all nonlinearities of the transfer map describing the trajectories will be obtained to an accuracy limited only by the discretization error of the field computation program