Evolution of long pulses in a tapered wiggler free-electron laser Page: 7 of 11
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T
oa-
caU
0/4 -
LO ~
900 1000 1900
NUMBER OF PASSES
2000
20 -16 -12 -a -4 0 4 6
cavity length change
Figure 4. Optical pulse energy vs pass
number.
Figure 5. Desynchronism curve
Figure 6 compares some quasi steady-state optical and electron pulse characteristics for
two different cavity length detunings. Figures 6a and 6b show the light intensity vs axial
location z at the end of the wiggler for resonator length detuning of -18 urn and -0.5 urn,
respectively. Figures 6c and 6d show the optical spectra of these pulses, and Figures 6e
and 6f show the corresponding electron spectra (the initial electron beam is monoeneraetic
with y0 ■ 40.7932). Figure 6f corresponds to a 2.5% energy-extraction efficiency from the
electron beam and exhibits the double-peaked spectrum characteristic of a tapered wiggler.
As is evident fiom Figure 2, the location of maximum single-pass gain shifts to longer
wavelengths with increasing light intensity. Hence, the optical pulse also changes its
spectrum (chirps) as the light intensity builds up. The principle mechanism for chirping
appears to be the generation of sidebands due to the electrons' synchrotron motion. This
in turn implies that the shift in the optical spectrum to longer wavelengthF is not contin-
uous with increasing light intensity, but rather occurs in discontinuous steps. Figure 7
illustrates such a step for the -0.5-um-cavity-length detuning case. The evolution of
the spectrum after 925 panues to the final shape--which is shown in Figure 6d--is more com-
plicated and less clearly a stepwise process.
Th generation of sidebands at high light intensity occurs because the electrons execute
synchrotron oscillations,15 characterized by a period hSy, in the ponderomotive poten-
tial wells. LSy depends on the light intensity and is given by
This means that the periodicity of the electrons' orbits is given not by the wiggler wave
vector Kw hut by Kw i KSy, where K„y ■ 2n/LBy. Hence, cue might expect that this motion
would couple to a shifted optical wavelength ls« through a modified resonance condition:
(14)
(15)
or
r
Xn(] > VS,y)
(16)
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Goldstein, J.C. Evolution of long pulses in a tapered wiggler free-electron laser, article, January 1, 1983; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc1103697/m1/7/: accessed April 20, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.