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Principles of Free-Electron Lasers pp 153–244Cite as

Coherent Emission: Nonlinear Theory

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Abstract

The self-consistent nonlinear theory of the free-electron laser describes the interaction through the linear regime and includes the saturation of the growth mechanism. Saturation can occur through a variety of mechanisms. For an ideal beam which is both monoenergetic and with a vanishing pitch-angle spread, saturation occurs by means of electron trapping in the ponderomotive potential. In the thermal regime, saturation occurs by a different process. In this case, the axial energy spread of the beam (which can arise due to either a distribution in the total energy of the beam electrons or pitch-angle spread) gives rise to a broad-band emission spectrum. As a result, a quasilinear saturation mechanism is operative in which the beam undergoes turbulent diffusion in momentum space. Since the growth rate in this regime is proportional to the slope of the distribution function, the turbulent diffusion acts to form a plateau in momentum space which flattens out the distribution of the beam. As a result, the axial energy spread of the beam increases, and the instability is quenched when the slope of the distribution falls to zero. As might be expected, however, the saturation efficiency in the thermal regime is much reduced relative to that found for a sufficiently cold beam in which saturation occurs through the particle-trapping mechanism. As a consequence, we shall focus attention on the latter ca se in this chapter.

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Authors and Affiliations

  1. Science Applications International Corporation, McLean, Virginia, USA

    H. P. Freund

  2. University of Maryland, College Park, Maryland, USA

    T. M. Antonsen Jr.

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© 1992 H. P. Freund and T. M. Antonsen, Jr

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Freund, H.P., Antonsen, T.M. (1992). Coherent Emission: Nonlinear Theory. In: Principles of Free-Electron Lasers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2316-7_5

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  • DOI: https://doi.org/10.1007/978-94-011-2316-7_5

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  • Print ISBN: 978-94-010-5023-4

  • Online ISBN: 978-94-011-2316-7

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