Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-18T03:18:24.775Z Has data issue: false hasContentIssue false
  • English
  • Français

27.—The Quantum Theory of the Klystron and the Modulation of Electron Beams at Optical Frequencies*

Published online by Cambridge University Press:  14 February 2012

P. S. Farago  and
R. M. Sillitto
P. S. Farago
Affiliation:
Department of Physics, University of Edinburgh
R. M. Sillitto
Affiliation:
Department of Physics, University of Edinburgh
Get access Rights & Permissions [Opens in a new window]

Synopsis

The relationship between the modulation of electron beams at optical frequencies (the Schwarz-Hora effect) and at microwave frequencies is discussed. At optical frequencies the interaction between the modulating field and the electron beam must be described quantum mechanically, although the field itself may be described classically; in the microwave case the process may be described entirely classically. The interaction modifies the state functions of the individual electrons, but the observable modulation of the total electron beam results from the coherence of the modulating field. The main features of the Schwarz-Hora effect result from ‘single photon’ processes, but the beam modulation in the klystron is a ‘multi-photon’ process.

The exponential decay of the depth of modulation with distance from the interaction region, observable in the optical frequency case but not in the klystron, is not an inherently quantal effect. The periodic variation of the depth of modulation with distance along the beam, observed in the optical frequency case, is an essentially quantum mechanical effect, and is different, in its origins and in its dependence on the modulation frequency, from the space-charge waves which are observed on a klystron beam.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 71 , Issue 4 , 1974 , pp. 305 - 321
Copyright
Copyright © Royal Society of Edinburgh 1974

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

References to Literature

Becchi, C. and Morpurgo, G., 1971. Phys. Rev., D, 4, 288–294.Google Scholar
Campbell, N. R., 1909. Proc. Camb. Phil. soc., 15, 117–136, 310–328.Google Scholar
Chang, C. S. and Stehle, P., 1972. Phys. Rev., A, 5, 1928–1941.CrossRefGoogle Scholar
Farago, P. S., 1970. Free Electron Physics. London: Penguin.Google Scholar
Favro, L. D., Fradkin, D. M., and Kuo, P. M., 1971 a. Phys. Rev., D, 3, 2934–2937.Google Scholar
Favro, L. D., Fradkin, D. M., Kuo, P. M., and Rolnick, W. B., 1971 b. Appl.Phys. Lett, 18, 352–354.CrossRefGoogle Scholar
Gibbon, J. D. and Bullogh, R. K., 1972. J. Phys., C: Solid St. Phys., 5, L80–84.Google Scholar
Gradshteyn, I. S. and Ryzhik, I. M., 1965. Table of Integrals, Series & Products. New York: Academic Press.Google Scholar
Hadley, R., Lynch, D. W., Stanek, E. and Rossauer, E. A., 1971. Appl. Phys. Lett., 19, 145–147CrossRefGoogle Scholar
Hora, H., 1970. Physica Status Solidi, 42, 131–136.CrossRefGoogle Scholar
Hora, H., 1971. In Light Scattering in Solids (Ed. Balkanski, M.). Pergamon, 128–132.Google Scholar
Salat, A., 1970. J. Phys. C: Solid St. Phys., 3, 2509–2515.CrossRefGoogle Scholar
Schwarz, H., 1968. Bull. Am. Phys. soc., 13, 897.Google Scholar
Schwarz, H., 1971 a. Trans. N.Y. Acad. Sci., 33, 159–162.CrossRefGoogle Scholar
Schwarz, H., 1971 b. In Light Scattering in Solids (Ed. Balkanski, M.). Pergamon, 123–127.Google Scholar
Schwarz, H. and Hora, H., 1969. Appl. Phys. Lett., 15, 349–351.CrossRefGoogle Scholar
Van Zandt, L. L. and Meyer, J. W., 1970. J. Appl. Phys., 41, 4470.CrossRefGoogle Scholar
Varshalovich, A. D. and D'Yakonov, M. I., 1970. ZhetfPis'ma v Redaktsiyu, 11, 594. (Sov. Phys,- JETP Lett. 11, 411–114.)Google Scholar
Varshalovich, A. D. and D'Yakonov, M. I., 1971. Zh. Eksp. Teor. Fiz., 60, 90–101. (Sov. Phys. JETP. 33, 51–57.)Google Scholar