Les lentilles quadrupolaires electrostatiques

Abstract

The expression for the potential Φ ( x , y , z ) within the useful zone of a quadrupole lens has been established not only when the excitation potentials are symmetrical with respect to earth, but also when these potentials are asymmetrical. New terms arise as a result of this asymmetry, which have a pronounced effect upon both the sense and the size of the aperture aberration. In the second part we recapitulate the first order optical properties and the results of an experimental study, the object of which is to determine the equivalent length of the lenses and to establish the quantitative behaviour of a doublet. Next the results of research which has been devoted to measuring and correcting the aperture aberration are given, and several methods of correcting this aberration which are equally valid in stigmatic and in astigmatic operation are suggested. Finally the so-called “third-order” equations of motion have been established for excitations of both kinds and with the aid of these equations we can calculate the spherical aberration in any system of electrostatic quadrupole lenses. For a doublet this calculation has been performed numerically, and the values obtained agree well with the experimental results.