Abstract
In the first part of this chapter we want to exploit the third-order differential equation for the amplitude of the FEL wave in order to obtain a deeper understanding of the properties and peculiarities of high-gain free-electron lasers.
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Notes
- 1.
In reality the Gaussian is not centered at \(\eta =0\) but shifted to slightly positive values. This shift is due to the energy dependence of the coefficients \(c_j(\eta )\) and can be ignored here because it has a negligible effect on the bandwidth. The term “\(-\)1” in Eq. (5.3) can be dropped in the high-gain regime where \(|\tilde{E}_x(\eta ,z)|^2 /E_{\mathrm {in}}^2 \gg 1\).
References
J.B. Murphy, C. Pellegrini, Introduction to the physics of the free electron laser, in Laser Handbook, ed. by W.B. Colson, C. Pellegrini, A. Renieri, Vol. 6 (North Holland, Amsterdam, 1990), p. 11
W.B. Colson, Classical free electron laser theory, Laser Handbook (North Holland, Amsterdam, 1990), p. 115
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Schmüser, P., Dohlus, M., Rossbach, J., Behrens, C. (2014). Applications of the High-Gain FEL Equations. In: Free-Electron Lasers in the Ultraviolet and X-Ray Regime. Springer Tracts in Modern Physics, vol 258. Springer, Cham. https://doi.org/10.1007/978-3-319-04081-3_5
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DOI: https://doi.org/10.1007/978-3-319-04081-3_5
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