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7 - Linear Electron Beams

Published online by Cambridge University Press:  27 April 2018

Richard G. Carter
Richard G. Carter
Affiliation:
Lancaster University
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Summary

The electron velocity in a linear, cylindrical (pencil), electron beam is determined by the potential difference between the cathode and the beam tunnel, taking space-charge potential depression into account. The effect of space-charge forces is to cause the beam radius to expand and static electric and magnetic fields can act as electron lenses. Beam spreading can be opposed by a uniform axial magnetic (solenoid) field if the beam is rotating. The conditions for stable flow are established using Busch’s theorem. The beam radius varies periodically (scalloping) if the initial conditions are incorrect. Increasing the current density increases the equilibrium beam radius to an extent controlled by the fraction of the magnetic flux linking the cathode (the beam stiffness). A pencil beam can also be collimated by a periodic array of converging magnetic lenses in periodic permanent magnet (PPM) focusing. Its properties are similar to those of a solenoid-focused beam with the addition of a periodic ripple in the radius. The design of practical focusing systems is described and the effects of imperfections including thermal velocities and trapped ions are discussed. Brief consideration is given to periodic electrostatic focusing and to the control of annular and sheet electron beams.

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Microwave and RF Vacuum Electronic Power Sources , pp. 250 - 286
Publisher: Cambridge University Press
Print publication year: 2018

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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

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  • 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/10.1017/9780511979231.008
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  • 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/10.1017/9780511979231.008
Available formats
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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/10.1017/9780511979231.008
Available formats
×