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11 - Beam-Wave Interaction

Published online by Cambridge University Press:  27 April 2018

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

Under small-signal conditions the r.f. properties of a linear, magnetically focused, electron beam can be represented by a pair of normal modes (space-charge waves). The fast space-charge waves carries positive power and has a phase velocity slightly greater than the electron velocity. The slow space-charge waves carries negative power and has a phase velocity slightly less than the electron velocity. An important parameter is the reduced plasma frequency of the beam which depends upon the space-charge density and the boundary conditions. Space-charge wave theory can be used to understand the interaction between an electron beam and the r.f. field of a surrounding electromagnetic structure. The theory of small-signal gain in klystrons and TWTs is discussed in detail. In periodic slow-wave structures the beam can interact with a space-harmonic wave having negative group velocity leading to the possibility of backward-wave gain or oscillation. In large-signal models of electron beams the equations of motion of sample electrons in d.c. and r.f. electromagnetic and space-charge fields are integrated numerically. Results from a model of this type are discussed. Simple models for the exchange of energy between the r.f. field of a gap and modulated and unmodulated electron beams are introduced.

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Microwave and RF Vacuum Electronic Power Sources , pp. 375 - 432
Publisher: Cambridge University Press
Print publication year: 2018

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  • Beam-Wave Interaction
  • Richard G. Carter, Lancaster University
  • Book: Microwave and RF Vacuum Electronic Power Sources
  • Online publication: 27 April 2018
  • Chapter DOI: https://doi.org/10.1017/9780511979231.012
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  • Beam-Wave Interaction
  • Richard G. Carter, Lancaster University
  • Book: Microwave and RF Vacuum Electronic Power Sources
  • Online publication: 27 April 2018
  • Chapter DOI: https://doi.org/10.1017/9780511979231.012
Available formats
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Save book to Google Drive

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  • Beam-Wave Interaction
  • Richard G. Carter, Lancaster University
  • Book: Microwave and RF Vacuum Electronic Power Sources
  • Online publication: 27 April 2018
  • Chapter DOI: https://doi.org/10.1017/9780511979231.012
Available formats
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