Evolution of long pulses in a tapered wiggler free-electron laser Page: 3 of 11
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Evolution of long pulses in a tapered wiggler free-electron laser
John C. Goldstein
Los Alamos National Laboratory
X-l, MS E531, Los Alamos, New Mexico 87545
The evolution of a long pulse (pulse length much greater than the slippage distance) in
a tapered wiggler Tree-electron laser is studied by numerical solution of the 1-D theoreti-
cal model for a realistic 3et of magnet, electron beam, and optical resonator parameter
values. Single-pass gain curves are calculated for low and high light intensity. We find
that an initial, low-amplitude, incoherent pulse grows into a coherent pulse whose growth
rate agrees with the calculated small signal gain. The transient evolution of coherent
pulses is calculated for several different cavity lenqth det'.nings, and a quasi steady-
state desynchronism curve is given. The frequency changing behavior of the optical pulse
is shown to occur through sideband generation associated with synchrotron oscillations.
Pulse evolution with an ideal intracavity high-pass optica) filter is calculated.
In this work the evolution of a long optical pulse in a tapered wiggler free-electron
laser (FEL) oscillator is studied by numerical solution of the 1-D theoretical model for a
realistic set of magnet, electron beam, and optica)-resonator parameter values. The theo-
retical model used here is one developed by Colson, l*J although other equivalent models1"5
have been developed. The model is solved first for a series of single-pass gain curves.
These curves, which show the amplification of cv coherent light at low and high intensity,
are obtained by neglecting all finite pulse effects. They are, nonetheless, reasonable
first estimates for the rate of growth of the actual finite optical pulse because, for the
physical parameters of the laser system considered here, the slippage distance is much
shorter than the pulse length. However, the initial low intensity light in the resonator
is not coherent--it is Incoherent spontaneous emission. We have studied the development of
coherence of such an initially incoherent pulse and find that after ^100 to 150 passes
through the resonator, the optical pulse has achieved a narrow spectrum, with reasonably
smooth electric f;'eld amplitude and phase functions, and is growing at a rate predicted by
the cw single pass small signal gain curve. Results of this calculation, which should be
taken only as an approximate indication of the build-up of light from spontaneous emission,
are pres< nted.
The transient evolution of a coherent optical pulse, from lov intensity small signal
gain conditions to high intensity saturated oain conditions, is then calculated for
several different optical resonator lengths and a quasi steady-state desynchronism curve is
obtained. A comparison of various optica) pulse and electron characteristics at different
points alonq the desynchronism curv* is made. The trequency changinq behavior ("chirping")
of the optical pulse durinq its evolution is characterized by a discontinuous step noted
when strong modulation of the electric field envelope is present with a period about, equal
to the slippage distance. Finally, the effect of an ideal intracavity optical filter on
the evolution of the liqht is presented.
Ga_i_n_curves and the development of coherence
The laser system to be modeled is a linear accelerator driven FEL, with parameter values
qiven in Table 1, in which a pulse of electrons is maqnetically guided into the optical
resonator where it interacts with a pulse of light while transiting the wiggler magnet.
The electron pulse is then dunped out of the resonator while the light pulse reflects from
the mirrors and meets a new electron pulse from the linac when it re-enters tht< wiggler.
The axial variation of the wrvelenqth and maqnetlc field strength of the wiqgler are shown
in Figure 1. The 1-D mathematical model used to analyze this FEL system ii upecified in
Table'2. Note That we are tea’inq with a plane polarized wiggler, which accounts for the
coupling constant G, hut we noqlect all hiqher haimonlcs of the emitted radiation. A Gaus-
sian mode variation or the on-axis electric field amplitude and phase is taken into account
hut in not explicitly shown in Table 2.
The cw qain vs optical wavrlenqth for this las^r system, ignoring finite pulse effects,
is shown in Fiqure 2. Note that these curves are for an idealized mon^enerqetic electron
beam. The small signal qiin is in Fiqure 2a and the larqe signal gain is in Fiqure 2b.
Notr that the wavelength of peak qair. shifts with increasing liqht intensity: this leads
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Goldstein, J.C. Evolution of long pulses in a tapered wiggler free-electron laser, article, January 1, 1983; New Mexico. (digital.library.unt.edu/ark:/67531/metadc1103697/m1/3/: accessed January 18, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.