Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T02:54:57.288Z Has data issue: false hasContentIssue false

7 - Linear Electron Beams

Published online by Cambridge University Press:  27 April 2018

Richard G. Carter
Richard G. Carter
Affiliation:
Lancaster University
Get access

Summary

The flow of electrons between the cathode and the anode of a diode can be controlled by introducing permeable electrodes (grids). The properties of triodes can be understood using an electrostatic model in which space-charge is neglected. The influence of the anode voltage on the electric field at the cathode is described by the penetration factor. The effects of space-charge can be included using the concept of an equivalent diode whose properties are determined by considering limiting cases. Good agreement with experimental results is obtained in this way. When the control grid is close to the cathode the emission from the cathode becomes non-uniform (island formation) and the penetration factor varies with position. It is shown that the current in a triode generally obeys the 3/2 power law but varies from this near cut-off if there is island formation. The current intercepted by the grid can be estimated by calculating electron trajectories. Similar methods can be applied to the modelling of a tetrode by reducing it to an equivalent triode. The effects of space-charge in the region between the screen grid and the anode can be understood by regarding it as a diode with injected current.
Type
Chapter
Information
Microwave and RF Vacuum Electronic Power Sources , pp. 250 - 286
Publisher: Cambridge University Press
Print publication year: 2018

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

Srivastava, V. and Carter, R. G., ‘Effect of boundaries on the space charge potential in coupled cavity travelling wave tubes’, IEE Proceedings I: Solid-State and Electron Devices, vol. 133, pp. 185–188, 1986.Google Scholar
Lawson, J. D., The Physics of Charged-Particle Beams. Oxford: Oxford University Press, 1977.Google Scholar
Tsimring, S. E., Electron Beams and Microwave Vacuum Electronics. Hoboken, NJ: John Wiley & Sons, 2006.CrossRefGoogle Scholar
Kleen, W. J., Electronics of Microwave Tubes. New York: Academic Press, 1958.Google Scholar
Bleaney, B. I. and Bleaney, B., Electricity and Magnetism. London: Oxford University Press, 1957.Google Scholar
Ramo, S. et al., Fields and Waves in Communication Electronics. New York: Wiley, 1965.Google Scholar
Gittins, J. F., Power Travelling-Wave Tubes. London: English Universities Press, 1965.Google Scholar
Smith, M. J. and Phillips, G., Power Klystrons Today. Taunton, England: Research Studies Press Ltd., 1995.Google Scholar
Brillouin, L., ‘A theorem of Larmor and its importance for electrons in magnetic fields’, Physical Review, vol. 67, pp. 260–266, 1945.CrossRefGoogle Scholar
Neugebauer, W., ‘Equlibrium solutions for partially immersed relativistic electron beams’, IEEE Transactions on Electron Devices, vol. ED-14, pp. 686–693, 1967.CrossRefGoogle Scholar
Neugebauer, W., ‘Equlibrium solutions for partially immersed relativistic electron beams’, IEEE Transactions on Electron Devices, vol. ED-15, p. 43, 1968.CrossRefGoogle Scholar
Beck, A. H. W., Space-Charge Waves and Slow Electromagnetic Waves. London: Pergamon Press, 1958.Google Scholar
Ash, E. A., ‘Compression and reflection of Brillouin beams’, Journal of Electronics and Control, vol. 15, pp. 401–417, 1963.CrossRefGoogle Scholar
Gandhi, O. P. and Vaidya, N. C., ‘Behavior of electron beams under magnetic compression’, Proceedings of the IEEE, vol. 52, pp. 1052–1053, 1964.CrossRefGoogle Scholar
Vaidya, N. C. and Gandhi, O. P., ‘Performance of magnetically compressed O-type electron beams emitted from nonshielded cathodes’, IEEE Transactions on Electron Devices, vol. 13, pp. 453–458, 1966.CrossRefGoogle Scholar
Amboss, K., ‘Studies of a magnetically compressed electron beam’, IEEE Transactions on Electron Devices, vol. 16, pp. 897–904, 1969.CrossRefGoogle Scholar
Seeger, J. A., ‘Magnetic compression of axially symmetric Brillouin-focused electron beams’, IEEE Transactions on Electron Devices, vol. 16, pp. 1–5, 1969.CrossRefGoogle Scholar
Herrmannsfeldt, W. B., ‘Numerical design of electron guns and space charge limited transport systems’, Nuclear Instruments and Methods in Physics Research, vol. 187, pp. 245–253, 1981.CrossRefGoogle Scholar
Spangenberg, K. R., Vacuum Tubes. New York: McGraw-Hill, 1948.Google Scholar
Pierce, J. R., ‘Spatially alternating magnetic fields for focusing low-voltage electron beams’, Journal of Applied Physics, vol. 24, p. 1247, 1953.CrossRefGoogle Scholar
Clogston, A. M. and Heffner, H., ‘Focusing of an electron beam by periodic fields’, Journal of Applied Physics, vol. 25, pp. 436–447, 1954.CrossRefGoogle Scholar
Mendel, J. T. et al., ‘Electron beam focusing with periodic permanent magnet fields’, Proceedings of the I.R.E., vol. 42, pp. 800–810, 1954.Google Scholar
Harker, K. J., ‘Periodic focusing of beams from partially shielded cathodes’, IRE Transactions on Electron Devices, vol. ED-2, pp. 13–19, October 1955.CrossRefGoogle Scholar
Mendel, J. T. et al., ‘Electron beam focusing with periodic permanent magnet fields’, Proceedings of the Institute of Radio Engineers, vol. 42, pp. 800–810, 1954.Google Scholar
Chang, K. K. N., ‘Stability of periodic-field beam focusing’, Journal of Applied Physics, vol. 27, pp. 1527–1532, 1956.CrossRefGoogle Scholar
Ura, K. and Terada, M., ‘Equivalence of periodic magnetic field to uniform magnetic field in electron beam focusing’, IEEE Transactions on Electron Devices, vol. ED-13, pp. 930–934, 1966.CrossRefGoogle Scholar
Buck, D. C., ‘Stability of a cylindrical electron beam in nonsinusoidal periodic magnetic-focusing fields’, IRE Transactions on Electron Devices, vol. 4, pp. 44–49, 1957.CrossRefGoogle Scholar
Datta, S. K. et al., ‘Stability analysis for electron beam transport in double-periodic permanent magnet focusing structure’, in Eighth IEEE International Vacuum Electronics Conference, Kitakyushu, Japan, pp. 357–358, 2007.Google Scholar
Burke, P. F. C., ‘Compensated reversed field focusing of electron beams’, Proceedings of the IEEE, vol. 51, pp. 1653–1659, 1963.CrossRefGoogle Scholar
Siekanowicz, W. and Cash, J. Jr, ‘Focusing of Brillouin electron beams by use of long-period magnetic fields’, in 1964 International Electron Devices Meeting, pp. 88–90, 1964.CrossRefGoogle Scholar
Schindler, M. J., ‘The magnetic field and flux distributions in a periodic focusing stack for TWTs’, RCA Review, vol. 21, pp. 414–436, 1960.Google Scholar
Kory, C. L., ‘Effect of geometric azimuthal asymmetries of PPM stack on electron beam characteristics [TWTs]’, IEEE Transactions on Electron Devices, vol. 48, pp. 38–44, 2001.CrossRefGoogle Scholar
Carter, R. G. and MacGregor, A., ‘Effect of imperfections on periodic permanent magnet focusing of electron beams’, in 2nd IEEE International Vacuum Electronics Conference, Noordwijk, The Netherlands, pp. 211–213, 2001.Google Scholar
MacGregor, A., ‘Periodic permanent magnet focusing of electron beams’, PhD, Engineering Department, Lancaster University, Lancaster, UK, 1986.Google Scholar
Moats, R. R., ‘Calculations of beam trajectories under non-ideal conditions of PPM focusing’, in 1976 International Electron Devices Meeting, pp. 515–519, 1976.CrossRefGoogle Scholar
Minakovic, B., ‘Effect on an electron beam of variations in periodic permanent-magnet focusing systems’, Electrical Communication, vol. 38, pp. 415–424, 1963.Google Scholar
Tien, P. K., ‘Focusing of a long cylindrical electron stream by means of periodic electrostatic fields’, Journal of Applied Physics, vol. 25, pp. 1281–1288, 1954.CrossRefGoogle Scholar
McLachlan, N. W., Bessel Functions for Engineers. Oxford University Press, 1954.Google Scholar
Priestland, P. B. and Hartnagel, H. L., ‘Theory of periodic electrostatic focusing of electron beams’, IEEE Transactions on Electron Devices, vol. 15, pp. 915–935, 1968.CrossRefGoogle Scholar
Priestland, P. B. and Hartnagel, H. L., ‘A further contribution to the theory of electrostatic focusing’, IEEE Transactions on Electron Devices, vol. 16, pp. 803–812, 1969.CrossRefGoogle Scholar
Cutler, C. C., ‘Instability in hollow and strip electron beams’, Journal of Applied Physics, vol. 27, pp. 1028–1029, 1956.CrossRefGoogle Scholar
Nguyen, K. T. et al., ‘Intense sheet electron beam transport in a uniform solenoidal magnetic field’, IEEE Transactions on Electron Devices, vol. 56, pp. 744–752, 2009.CrossRefGoogle Scholar
Pasour, J. et al., ‘Demonstration of a 100-kW solenoidally focused sheet electron beam for millimeter-wave amplifiers’, IEEE Transactions on Electron Devices, vol. 58, pp. 1792–1797, 2011.CrossRefGoogle Scholar
Booske, J. H. et al., ‘Stability and confinement of nonrelativistic sheet electron beams with periodic cusped magnetic focusing’, Journal of Applied Physics, vol. 73, pp. 4140–4155, 1993.CrossRefGoogle Scholar
Booske, J. H. and Basten, M. A., ‘Demonstration via simulation of stable confinement of sheet electron beams using periodic magnetic focusing’, IEEE Transactions on Plasma Science, vol. 27, pp. 134–135, 1999.CrossRefGoogle Scholar
Wang, Z. L. et al., ‘The conditions for stable sheet electron beams transport in periodic permanent magnet fields’, Journal of Infrared Millimeter and TeraHertz Waves, vol. 31, pp. 649–658, June 2010.Google Scholar
Kyhl, R. L. and Webster, H. F., ‘Breakup of hollow cylindrical electron beams’, IRE Transactions on Electron Devices, vol. 3, pp. 172–183, 1956.CrossRefGoogle Scholar
Pierce, J. R., ‘Instability of hollow beams’, IRE Transactions on Electron Devices, vol. 3, pp. 183–189, 1956.CrossRefGoogle Scholar
Demmel, E. K., ‘Some studies on a high-perveance hollow-beam klystron’, IEEE Transactions on Electron Devices, vol. 11, pp. 66–73, 1964.CrossRefGoogle Scholar
Dohler, G., ‘On the stability of hollow beams in PPM focused TWTs’, IEEE Transactions on Electron Devices, vol. 28, pp. 602–604, 1981.CrossRefGoogle Scholar
Lau, Y. Y., ‘A unified theory of the diocotron, cyclotron maser, and negative-mass instabilities’, IEEE Transactions on Electron Devices, vol. ED-31, pp. 329–337, 1984.CrossRefGoogle Scholar
Szabo, A., ‘Thermal velocity effects in magnetically confined beams’, IRE Transactions on Electron Devices, vol. 5, pp. 183–185, 1958.CrossRefGoogle Scholar
Palmer, J. L. and Susskind, C., ‘Effects of transverse velocities in magnetically focused cylindrical electron beams’, in Third International Congress on Microwave Tubes, Munich, pp. 456–460, 1960.Google Scholar
Kirstein, P. T., ‘On the effects of thermal velocities in two-dimensional and axially symmetric beams’, IEEE Transactions on Electron Devices, vol. 10, pp. 69–80, 1963.CrossRefGoogle Scholar
Hechtel, J. R., ‘Magnetic focusing of electron beams in the presence of transverse velocity components’, IEEE Transactions on Electron Devices, vol. 28, pp. 473–482, 1981.CrossRefGoogle Scholar
Herrmann, G., ‘Optical theory of thermal velocity effects in cylindrical electron beams’, Journal of Applied Physics, vol. 29, pp. 127–136, 1958.CrossRefGoogle Scholar
Jepsen, R. L., ‘Ion oscillations in electron beam tubes; ion motion and energy transfer’, Proceedings of the IRE, vol. 45, pp. 1069–1080, 1957.CrossRefGoogle Scholar
Sutherland, A. D., ‘Relaxation instabilities in high-perveance electron beams’, IRE Transactions on Electron Devices, vol. 7, pp. 268–273, 1960.CrossRefGoogle Scholar
Thorington, C. B., ‘Computer simulation of ion trapping and detrapping in a PPM focused traveling wave tube’, IEEE Transactions on Electron Devices, vol. 48, pp. 56–61, 2001.CrossRefGoogle Scholar
Tighe, W. et al., ‘Transient ion disturbances in traveling wave tubes’, IEEE Transactions on Electron Devices, vol. 48, pp. 82–87, 2001.CrossRefGoogle Scholar
Carter, R. G. and Newton, R. H. C., ‘An experimental study of charge densities and radio-frequency propagation characteristics in an ion beam/plasma system’, J. Phys. D, vol. 7, pp. 1670–1676, 1974.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Linear Electron Beams
  • Richard G. Carter, Lancaster University
  • Book: Microwave and RF Vacuum Electronic Power Sources
  • Online publication: 27 April 2018
  • Chapter DOI: https://doi.org/10.1017/9780511979231.007
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Linear Electron Beams
  • Richard G. Carter, Lancaster University
  • Book: Microwave and RF Vacuum Electronic Power Sources
  • Online publication: 27 April 2018
  • Chapter DOI: https://doi.org/10.1017/9780511979231.007
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Linear Electron Beams
  • Richard G. Carter, Lancaster University
  • Book: Microwave and RF Vacuum Electronic Power Sources
  • Online publication: 27 April 2018
  • Chapter DOI: https://doi.org/10.1017/9780511979231.007
Available formats
×