Chapter 12
Free-Electron Lasers
12.1 Concepts
In our description of undulator radiation, we saw the enormous gains that could be
achieved if radiation from separate magnetic poles were added coherently. As a
reminder, when N equal sources are added coherently, the produced intensity I varies
as N
2 , compared to intensity gains of only N when the sources are added incoherently. In a conventional undulator, radiation from N p individual poles is coherent;
hence I / N p
2 . However, electrons within a given bunch still radiate incoherently
with respect to each other, so the intensity varies linearly with the number of
electrons N e . (One exception is long wavelength synchrotron radiation—if the
wavelength is long compared to the bunch length, in the far-IR or THz regimes,
then coherent synchrotron radiation can be observed) [553].
The key feature of a “free-electron laser” or “FEL” is the restructuring of the
electron bunch into equally spaced “microbunches,” so that the electrons also radiate
coherently. Since the number of electrons N e in a bunch is on the order of 10
8 , the
potential for additional intensity from N e
2 vs. N e is enormous. This is true for average
brightness, but especially true for peak brightness, as illustrated in Fig. 12.1.
12.2 Peak Brightness vs. Average Brightness: A New
Figure of Merit
Back in Chap. 1 when we defined the X-ray spectral brightness, we referred to the
average over time, and we ignored the bunch structure of the storage ring source:
B S ¼
number of photons
s
ð Þ mm 2
ð
Þ mrad
2
À
Á
0:1%ΔE=E
ð
Þ
ð12:1Þ
© Springer Nature Switzerland AG 2020
S. P. Cramer, X-Ray Spectroscopy with Synchrotron Radiation, Biological and Medical
Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-030-28551-7_12
295
Free-Electron Lasers
12.1 Concepts
In our description of undulator radiation, we saw the enormous gains that could be
achieved if radiation from separate magnetic poles were added coherently. As a
reminder, when N equal sources are added coherently, the produced intensity I varies
as N
2 , compared to intensity gains of only N when the sources are added incoherently. In a conventional undulator, radiation from N p individual poles is coherent;
hence I / N p
2 . However, electrons within a given bunch still radiate incoherently
with respect to each other, so the intensity varies linearly with the number of
electrons N e . (One exception is long wavelength synchrotron radiation—if the
wavelength is long compared to the bunch length, in the far-IR or THz regimes,
then coherent synchrotron radiation can be observed) [553].
The key feature of a “free-electron laser” or “FEL” is the restructuring of the
electron bunch into equally spaced “microbunches,” so that the electrons also radiate
coherently. Since the number of electrons N e in a bunch is on the order of 10
8 , the
potential for additional intensity from N e
2 vs. N e is enormous. This is true for average
brightness, but especially true for peak brightness, as illustrated in Fig. 12.1.
12.2 Peak Brightness vs. Average Brightness: A New
Figure of Merit
Back in Chap. 1 when we defined the X-ray spectral brightness, we referred to the
average over time, and we ignored the bunch structure of the storage ring source:
B S ¼
number of photons
s
ð Þ mm 2
ð
Þ mrad
2
À
Á
0:1%ΔE=E
ð
Þ
ð12:1Þ
© Springer Nature Switzerland AG 2020
S. P. Cramer, X-Ray Spectroscopy with Synchrotron Radiation, Biological and Medical
Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-030-28551-7_12
295