Zur Elektronenoptik elektrostatischer Beschleuniger im relativistischen Bereich

Abstract

The properties of electrostatic lenses for relativistic particles are described by means of transfer matrices. Using GANS' polygon-method, the matrices are calculated by integrating the equation of motion of relativistic particles in electric fields that have rotational symmetry. These general results are used for calculating the first-order approximations of the characteristic data for two-cylinder lenses. Numerical evaluation shows that the lens properties at a fixed V2/V1 vary only slowly with increasing energy (V1 and V2 being the potentials of the lens). The results are compared with those calculated by TIMM for the nonrelativistic case, which can be seen in our results as a special case. The easiest way of applying the derived formulas to the case of multistage accelerator tubes is discussed.