Theory of multibeam electron-optical systems

In this work we discuss the calculational methods which exclude the brutal application on numerical algorithms in 3-space trajectory analysis programs for multibeam systems of interacting microstreams. There are the theory of non-relativistic system with large-scale ruling grid; the theory of relativistic injector with triode-type potential distribution at the axis in the absence of external magnetic field; the theory of one-layer relativistic systems in arbitrarily oriented magnetic field. The guaranteed accuracy of asymptotic theory and the probability of optimization due to variation of potential distribution distinguish this approach from 3-space numerical models which have all systematic shortcomings of 2-space programs so their accuracy can´t be evaluated adequately.