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. 2011 Mar;18(Pt 2):101-8.
doi: 10.1107/S090904951004896X. Epub 2011 Jan 8.

A simplified description of X-ray free-electron lasers

G Margaritondo  1 , Primoz Rebernik Ribic
Affiliations

A simplified description of X-ray free-electron lasers

G Margaritondo et al. J Synchrotron Radiat. 2011 Mar.

Abstract

It is shown that an elementary semi-quantitative approach explains essential features of the X-ray free-electron laser mechanism, in particular those of the gain and saturation lengths. Using mathematical methods and derivations simpler than complete theories, this treatment reveals the basic physics that dominates the mechanism and makes it difficult to realise free-electron lasers for short wavelengths. This approach can be specifically useful for teachers at different levels and for colleagues interested in presenting X-ray free-electron lasers to non-specialized audiences.

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Figures

Figure 1
Figure 1
Mechanism of a free-electron laser for X-rays. (a) The optical amplification is produced by relativistic electrons in an accelerator and is activated by a periodic array of magnets (undulator). (b) The first waves emitted by the electrons trigger the formation of microbunches. (c) and (d) Contrary to non-microbunched electrons (c), the emission of electrons in microbunches (d) separated from each other by one wavelength is correlated. (e) This causes an exponential intensity increase with the distance that continues until saturation is reached as discussed in the text [experimental data from Emma et al. (2010 ▶)].
Figure 2
Figure 2
Why are the emitted wavelengths in the X-ray range? Relativity provides the answer. (a) The relativistic electron approaches the periodic B-field of the undulator. (b) In the electron reference frame the undulator period L is Lorentz-contracted to L/γ and the B-field is accompanied by a transverse E-field perpendicular to it: the two fields resemble an electromagnetic wave. (c) This wave stimulates the electron to oscillate and emit waves of equal wavelength. (d) The (relativistic) Doppler effect further reduces the wavelength in the laboratory frame, bringing it to the X-ray range.
Figure 3
Figure 3
The speed difference (c − u) between waves and electrons makes microbunching possible. Top: in this situation the longitudinal Lorentz forces caused by the wave B-field B W and to the electron transverse velocity v T push the electrons towards microbunching. Bottom: after the electron travels over one-half undulator period, its transverse velocity is reversed. The wave travels ahead of the electron by one-half wavelength: its B-field is also reversed, the Lorentz force keeps its direction and microbunching continues.
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References

    1. Altarelli, M. (2010). From Third- to Fourth-Generation Light Sources: Free-Electron Lasers in the UV and X-ray Range, in Magnetism and Synchrotron Radiation, edited by E. Beaurepaire, H. Bulou, E. Scheurer and J. K. Kappler. Berlin: Springer.
    1. Bonifacio, R. & Casagrande, S. (1985). J. Opt. Soc. Am. B, 2, 250–258.
    1. Bonifacio, R., De Salvo, L., Pierini, P., Piovella, N. & Pellegrini, C. (1994). Phys. Rev. Lett. 73, 70–73 - PubMed
    1. Bonifacio, R., Pellegrini, C. & Narducci, L. M. (1984). Opt. Commun. 50, 373–378.
    1. Brau, C. A. (1990). Free-Electron Lasers. Oxford: Academic Press.

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