Abstract
The schematic setup of a low-gain FEL is shown in Fig. 3.1.
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Notes
- 1.
In Chap. 4 the inhomogeneous wave equation will be used to compute the energy exchange between the electron beam and the FEL wave.
- 2.
The shifted phase \(\phi \) is only needed for our comparison between FEL and pendulum. It will not be used in the other chapters.
- 3.
This is the traditional definition of the gain function in FEL theory. In the terminology of electronic amplifiers as well as of standard laser physics the gain should be defined as \(gain \equiv G+1\) because unity gain means that the output signal is equal to the input signal.
- 4.
In the FEL literature the modified undulator parameter is often written in the form \(K\cdot JJ\) or \(K \cdot A_{JJ}\).
References
K. Wille, The Physics of Particle Accelerators. An Introduction (Oxford University Press, Oxford, 2001)
J.M.J. Madey, Relationship between mean radiated energy, mean squared radiated energy and spontaneous power spectrum in a power series expansion of the equation of motion in a free electron laser. Nuovo Cimento 50B, 64 (1979)
M. Abramowitz, I.A. Stegun (eds.), Handbook of Mathematical Functions (Dover Publications, New York, 1965)
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Schmüser, P., Dohlus, M., Rossbach, J., Behrens, C. (2014). Low-Gain FEL Theory. 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_3
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