Electrostatic electron-optics

Certain types of electrostatic fields may be used as lenses to focus electron beams. The theory of these lenses is developed for electric fields that are symmetrical about a central axis. The introduction of two velocity functions exactly reduces the partial differential equations of electron motion to a series of ordinary differential equations. The first equation describes the action of a lens for electron paths near the axis; the remaining equations determine the higher order aberration terms. Sections on the following subjects are included: the general equations of electronoptics, thin lenses, thick lenses, aberration, the reduction of aberraration, apertured plates, and concentric tubes. A list of symbols and lens equations is also included at the end of the article.