The Bell System Technical Journal 



Vol. XVIII January, 1939 No. 1 



Electrostatic Electron-Optics 



By FRANK GRAY 



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 

 difTerential 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 electron- 

 optics, thin lenses, thick lenses, aberration, the reduction of aberra- 

 ration, apertured plates, and concentric tubes. A list of symbols 

 and lens equations is also included at the end of the article. 



TN certain types of modern vacuum tubes, a beam of electrons is 

 -*■ brought to a focus by an electrostatic field whose action on the 

 beam is analogous to that of an optical lens on a beam of light. An 

 electrostatic field which acts in this manner is called an electron lens. 

 Such lenses are rapidly finding applications in amplifier tubes, tele- 

 vision and oscillograph tubes, electron microscopes, and various types 

 of experimental apparatus. As the extent of their application widens, 

 the theory of these lenses naturally assumes a corresponding 

 importance. 



The first articles on the new science of electron-optics were published 

 by Bush ^ in 1926-1927, and the next important step in its develop- 

 ment was taken by Davisson and Calbick ^ and by Briiche and 

 Johannson ^ working independently in 1931-1932. The following 

 years marked an increased interest in the subject, with comprehensive 

 articles by various authors, and its literature expanded rapidly. An 



1 H. Bush, Ann. d. Physik, 81, 974, 1926 and Arch. f. Elecktrotech., 18, 583, 1927. 

 2C. J. Davisson and C. J. Calbick, Phys. Rev., 38, 585, 1931 and Phys. Rev., 

 42, 580, 1932. 



^ E. Bruche and N. Johannson, Ann. d. Physik, 15, 145, 1932. 



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