# 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

power.

FEASIBILITY

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

strength.

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)

9

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

Fig. 4.

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)

9AZ(T) /a

(6)

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, wherewe 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).

x103 10-

0Y 0

-1 _

-5 0 5 10 15 -5 0 5 10 15

x109 -109

xlOxl19x 10 '

10

-5 0 5 10 15

z (m) 109x 10

10

-5 0 5 10 15

z (m) x 109Figure 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.100

A 50

00 50 100 150

Longitudinal Position (in)200

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 becomesz3 z2 P3 (P2 - ahz2 - Ez2)/g

(7)

Again solving for zf in terms of z,, we find

zf z' + (R56 - R) p2 + AL sin ( Lk t ) (8)- -

--ueta-x

- 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.