Electron spectrograph with a hyperbolic electrostatic field

The electron-optical properties of an energy analyzer representing a parallel-plate capacitor with a linear distribution of the potential on the upper plate are studied. It is shown that first-order focusing conditions in this analyzer do not depend on the particle energy and the linear dispersion is proportional to the square root of the energy. Such an analyzer can simultaneously record an electron spectrum in a wide energy range, that is, operate as a spectrograph. Double focusing conditions in a box-type analyzer are found, which allows the relative aperture of the spectrograph to be raised several-fold.