Two-Chicane Compressed Harmonic Generation of Soft X-Rays Page: 3 of 4
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the post-compression energy spread, aua. Even with the
laser focused to a large radius (required for transversely
uniform modulation at large ) function), we need only 6
MW of seed power. In total, we can reach a tunable wave-
length at 3 nm with a fraction of the standard HGHG laser
CHG is most sensitive to errors originating between the
dispersive sections; errors prior to the first chicane are
largely canceled by the second chicane. Here we esti-
mate the effects of incoherent synchrotron radiation (ISR),
broadening from 3D effects, and errors in the second chirp
ISR Induced Energy Spread
Incoherent energy spread, AO(ISR), from ISR between
the two dispersive sections could destroy the fine phase
space structure. To preserve high harmonics, we must limit
the longitudinal broadening, Az(06, from the total energy
spread to less than AL/27rma ~ 0.5 nm. We can estimate
Oz(6) =R5) o6+ R(b) ao-a + R) AO(SR) (5)
where os is the initial energy spread of the beam. The first
two terms are small by design, so for R5b) 20 mm, we
find AO(ISR) _ 10-8 for each bend, achievable with weak
compression chicanes at 1 GeV. Fig. 5 shows bunching
including ISR effects. The accelerator lattice is shown in
Second Order Lattice Effects
The laser modulation must survive transport through two
strong chicanes, and approximately 60 m of accelerator.
Smearing from second order effects (e.g. emittance and
curvature from energy modulation) could broaden the fine
3 nm structure.
The second chirp helps to cancel such effects. An elec-
tron with coordinates X [x, X', y, y' Z, ] acquires a lon-
gitudinal deviation of AZ(T) = XTs1jX, with Tsis the sec-
ond order transport matrix from the modulator to the be-
ginning of the second chirp. The chirp imparts a relative
energy modulation of -9 hAz(), so that following the sec-
ond chicane the particle has a final longitudinal shift of
AZ(F) AZ(T) (T)
The smearing between the two chirps is reduced by the
compression factor, a, with smearing from within the
chirps and second chicane reduced by lesser amounts
(Fig. 3). For our lattice (Fig. 4), the transverse components
of the Tis matrix are dominated by the first chicane, where
we increase the beta function after the small beam radius of
the modulator. The compression from the second chicane
is sufficient to maintain bunching, as seen in elegant simu-
lations (Fig. 5).
-5 0 5 10 15 -5 0 5 10 15
x 10 '
-5 0 5 10 15
z (m) 109
-5 0 5 10 15
z (m) x 109
Figure 3: Elegant simulation demonstrating the emittance
cancelation effect. Starting from a longitudinal delta slice
after the laser modulation, emittance effects increase the
beam size before the second chicane (left, before R56)), but
also introduce a chirp to the beam (bottom left). The chi-
cane then recompresses the bunch by a (right, after R56)).
Bunch head is to the left.
0 50 100 150
Longitudinal Position (in)
Figure 4: Twiss parameters for 3D elegant simulations. We
use L-band structures to decrease wakefield fluctuations,
and a weak second chicane to minimize ISR effects.
RF Phase and Wakefield Stability
RF phase errors, wakefields, and RF curvature alter the
chirp between dispersive sections and degrade the final
bunching. An error in the second, canceling chirp shifts
the unwinding process and leaves the beam either under or
over-compressed. (The first chirp is less problematic be-
cause the two dispersive sections have canceling effects.)
To estimate the sensitivity to a linear chirp error, we re-
peat the earlier analysis, with the addition of an error, E, in
the final chirp. Step three becomes
z3 z2 P3 (P2 - ahz2 - Ez2)/g
Again solving for zf in terms of z,, we find
zf z' + (R56 - R) p2 + AL sin ( Lk t ) (8)
- d- --beta-y \ I -
Ij .-.-.eta-x ! '
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Ratner, Daniel; Huang, Z. & Chao, A. Two-Chicane Compressed Harmonic Generation of Soft X-Rays, article, July 30, 2010; [California]. (https://digital.library.unt.edu/ark:/67531/metadc1014085/m1/3/: accessed March 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.