Abstract
The possibility to generate a stimulated emission of the FEL type by means of a crystalline undulator is discussed. The considered range of photon energies, \(10^2\)–\(10^3\) keV, is inaccessible in conventional FELs. Three different schemes of achieving the lasing effect are presented: (a) a gamma-amplifier based on the use of a single CU; (b) a gamma-klystron which utilizes the sequence of two (or more) CUs; (c) a Crystalline Undulator Laser. We demonstrate, that despite a number of parasitic effects, present technologies are nearly sufficient to achieve the conditions needed to achieve the emission stimulation by means of CU. It is shown, that the brilliance of CUL radiation can be as high as \(10^{28}\)–\(10^{32}\) \(\mathrm {photons/s/mrad}^{2}/\mathrm {mm}^{2}/0.1\,\%\,\mathrm {BW}\) in the sub-Angstrøm range of the emitted photon wavelengths.
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Notes
- 1.
To be specific, we assume the emission in the forward direction. This is why the longitudinal coordinate, i.e., the one along the undulator axis, plays the key role.
- 2.
- 3.
In accordance with the general theory of FEL (e.g., [208]) the emission stimulation in an undulator occurs only at the frequencies corresponding to the harmonics of the spontaneous undulator radiation. As it is written, (8.16) defines the wavenumber of the fundamental harmonic \(k=\omega _1/c\). In what follows, for the sake of simplicity, we consider the emission in the first harmonic only.
- 4.
The lowest value presented in the table, \({n_{{{\mathrm {ch}}},\, 0}} \sim 10^{21}\) cm\(^{-3}\) is two orders of magnitude larger than that available in modern colliders, see Table 5.2.
- 5.
See also the historic survey [190] on the early stage of the evolution of ideas related to the theory of undulators and FELs.
- 6.
X-rays with energy less than a few tens of keV are strongly absorbed in crystals, see Sect. 4.3.2. This introduces a lower limit on the photon energies generated in the CU based devices.
- 7.
The minimum wavelength of X-rays, achievable in the currently operational or under construction XFELs is \(\sim \)1 Å [215], which corresponds to the emitted photon energy \(\hbar \omega \approx 12.4\) keV.
- 8.
Note that in conventional FELs this ratio is of the order of 10\(^{-3}\)–10\(^{-4}\) [190, 248]. As a result, these FELs are very demanding to the quality of the electron beam in terms of the energy spread.
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© 2014 Springer-Verlag Berlin Heidelberg
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Korol, A.V., Solov’yov, A.V., Greiner, W. (2014). Stimulated Emission from CU. In: Channeling and Radiation in Periodically Bent Crystals. Springer Series on Atomic, Optical, and Plasma Physics, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54933-5_8
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DOI: https://doi.org/10.1007/978-3-642-54933-5_8
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