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LCLS Conceptual Design Report - Stanford Synchrotron Radiation ...

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β (m)<br />

120<br />

100<br />

80<br />

60<br />

40<br />

20<br />

0<br />

Q24701<br />

WIGGLER<br />

L C L S C O N C E P T U A L D E S I G N R E P O R T<br />

QM21<br />

B21<br />

CQ21<br />

B22<br />

β<br />

x<br />

β<br />

y<br />

η<br />

x<br />

400 405 410<br />

S (m)<br />

415 420<br />

Figure 7.26 Dispersion and beta functions through BC2 chicane for R 56 ≈ −22.5 mm. The energy<br />

spread profile monitor is indicated by a small circle at the center of the chicane in<br />

schematic at top. The two quadrupoles inside the chicane are for dispersion correction<br />

and are nominally switched off. The superconducting wiggler is located at S ≈ 397 m.<br />

7.4.2.2 Momentum Compaction<br />

The momentum compaction (R56) for a chicane is given by Eq. (7.12). The second order<br />

momentum compaction is T566 ≈ –3R56/2 (as in BC1). A beam delay as described in Eq. (7.13) is<br />

also necessary for the L3 rf phase. The L3 rf phase needs to be delayed, with respect to the<br />

chicane-off phase, by dφ/dR56 ≈ π/λ ≈ 1.72°/mm (or 38.7° with the nominal BC2 R56 value of<br />

−22.5 mm).<br />

7.4.2.3 Incoherent <strong>Synchrotron</strong> <strong>Radiation</strong> (ISR)<br />

Horizontal emittance dilution will occur if significant energy spread is generated anywhere<br />

within the chicane (or the wiggler). <strong>Synchrotron</strong> radiation within the dipoles generates energy<br />

spread, which breaks the linear achromaticity of the chicane and therefore dilutes the horizontal<br />

emittance. Using a typical symmetric beta function through a single chicane with its maximum,<br />

βmax, at start and end of the chicane and its minimum, βmin, in the middle, and using symbols<br />

defined in Table 7.14, then<br />

max min<br />

B23<br />

CQ22<br />

B24<br />

QM22<br />

Q24901<br />

0.35<br />

0.3<br />

0.25<br />

0.2<br />

0.15<br />

0.1<br />

0.05<br />

β = 2β= 4L + 2∆<br />

L+∆L<br />

. (7.21)<br />

B c<br />

The additive ISR emittance dilution [29] can then be approximated, for ∆ε/ε 0

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