A Mechanical Theory of Electron-Image Formation

The formation of an electron image and its optical constants, such as magnification and position, is predicted from the simple assumption of transversal deflection in true proportion to the radial distance off the axis. The treatment is mechanical, rather than optical. Investigation of the electron trajectory is avoided. At first, the deflecting forces are supposed to act only in a negligible portion of the electron path. It is found that there exists for this case a "thin-lens law" which differs from the optical analogy only in that the distances are replaced by transit times. The resulting expression for electron-optical magnification is a ratio of transit times. Applications of these deductions are made for some particular electron tubes. The mechanical treatment is then used in connection with an extended field with a variable deflection constant all along the axis. The constants of thick lenses, either electric, magnetic, or combined fields, are expressed in terms of three integrals of the deflection with respect to transit time. The first of these integrals gives the focal length, the second the magnification, and the third the positions of corresponding object and image planes. All results are available in a graph of a family of hyperbolas for various operation parameters. The plane accelerating field, which forms a virtual rather than a real electron image, is studied in the same manner. Appendix A gives the mathematical proof of convergence of the series of functions used for approximation.