PHYSICAL LIMITATIONS IN ELECTRON BALLISTICS 321 



well. As it is, if we make a tube for given power smaller and smaller, using 

 the most refractory materials available we eventually reach a size of tube 

 which will, despite our best efforts, melt, thaw, and resolve itself into a dew. 



CONCLUSION 



Perhaps after these somewhat gloomy words concerning physical lim- 

 itations in electron ballistics, you may wonder how it is at all possible to 

 surmount the difficulties mentioned. It certainly is not easy; all electronic 

 devices represent compromises of one sort or another between fundamental 

 physical limitations of electron flow on the one hand and structural com- 

 plications on the other. In working with vacuum tubes one is perhaps 

 troubled more by physical limitations, difficulties of construction, inade- 

 quacy of materials and the lack of quantitative agreement between compli- 

 cated phenomena and relatively simple theories than in any other part of 

 the electric art. It is for this reason that a friend of mine twisted an old 

 aphorism into a new one and said, "Nature abhors a vacuum tube". 



References 

 Electron Microscopes 



1. James Hillier and A. W. Vance: "Recent Developments in the Electron Micro- 



scope," Proc. I.R.E. 29, pp. 167-176, April, 1941. 



2. L. Marton and R. G. E. Hutter: "The Transmission Type of Electron Microscope 



and Its Optics," Proc. I.R.E. 32, pp. 3-11, Jan. 1944. 



Thermal Velocities 



3. D. B. Langmuir: "Theoretical Limitations of Cathode-Ray Tubes," Proc. I.R.E 



25, pp. 977-991, Aug., 1937. 



4. J. R. Pierce: "Limiting Current Densities in Electron Beams," Jour. App. Phys., 



10, pp. 715-724, Oct., 1939. 



5. J. R. Pierce: "After Acceleration and Deflection," Proc. I.R.E. 29, pp. 28-31, 



Jan., 1941. 



6. R. R. Law: "Factors Governing the Performance of Electron Guns in Cathode- 



Ray Tubes," Proc. I.R.E. 30, pp. 103-105, Feb., 1942. 



7. J. R. Pierce: "Theoretical Limitation to Transconductance in Certain Types of 



Vacuum Tubes," Proc. I.R.E. 31, pp. 657-663, Dec, 1943. 



Space Charge 



8. C. E. Faj^ A. L. Samuel and W. Shockley: "On the Theory of Space Charge 



Between Parallel Plane Electrodes," Bell Sys. Tech. Jour. 17, pp. 49-79, 1938. 



9. I. Langmuir and K. Blodgett: "Currents Limited by Space Chargeb etween Coaxial 



Cylinders," Phys. Rev. 22, pp. 347-356, 1923. 



10. I. Langmuir and K. B. Blodgett: "Currents Limited by Space Charge between 



Concentric Spheres," Phys. Rev. 24, pp. 49-59, 1924. 



11. J. R. Pierce: "Rectilinear Electron Flow in Beams," Jour, of App. Phys. 11, pp. 



548-554, Aug., 1940. 



12. B. J. Thompson and L. B. Headrick: "Space Charge Limitations on the Focus of 



Electron Beams," Proc. I.R.E., 28, pp. 318-324, July, 1940. 



13. C. J. Calbick: "Energy Distribution of Electrons within Dense Electron Beams," 



Bull. Am. Phys. Soc, 19, No. 2, p. 14 (April 28, 1944). 



14. J. R. Pierce: "Limiting Stable Current in Electron Beams in the Presence of Ions," 



Jour. App. Phys. 15, No. 10, pp. 721-726 (1944). 



15. A. L. Samuel, "Some Notes on the Design of Electron Guns," Proc. IRE 33, pp. 233- 



240, April, 1945. 



