Cylindrical Capacitor as an Analyzer. II. Relativistic Part

Abstract

The study of the dynamic and optical properties of the cylindrical capacitor as an analyzer for charged particles is extended to the relativistic region. The proposed analyzer is found to be absolutely unrestricted by the relativistic effect, the latter introducing some changes which do not however impair the analytical features of the device. The emission angle for which there is a second order focus is energy‐dependent, shifting from θ₀=42°18.5′ in the nonrelativistic case to θ₀=55° in the ultrarelativistic case. It is shown that the usual derivation of the relativistic formulae from the nonrelativistic ones by replacing the nonrelativistic potential difference by an ``effective relativistic potential difference'' is incorrect for electrostatic devices, unless this quantity is given a specifically ``electrostatic'' form, distinct from the magnetic one. The figures of merit of the analyzer concerning resolution and luminosity are comparable with those of the best magnetic spectrometers. The analyzer seems to be simpler and cheaper than the magnetic type, but calls for very high deflecting voltages, which may be a disadvantage in operation.