Electrostatic Focusing at Relativistic Speeds

Abstract

Power series are derived with which, given data on the electric field, the focal properties of some common electron lenses can be quickly computed even when the speed of the electrons approaches that of light. The expansion is in powers of the ratio of the P.D. across the lens to the sum of the P.D.'s between its electrodes and the cathode (for electrons) or anode (for positive ions), squares of this ratio being neglected in comparison with unity. As an example the focusing properties of two cylinders almost in contact are calculated.