LCLS Conceptual Design Report - Stanford Synchrotron Radiation ...

〈∆E/E 0 〉 /%
I pk /I pk0
0.1
0
−0.1
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
E = 14.346 GeV, tol=46 %
0
0.2
−0.2
−4 −2 0 2 4
1.1
1.05
1
0.95
tol=5.6 %
0.9
−4 −2 0
∆Q/Q /%
0
2 4
(∆E/E 0 ) rms /%
〈∆t f 〉 /psec
0.08
0.06
0.04
0.02
−0.1
0
−4 −2 0 2 4
0.2
0.1
0
−0.2
−4 −2 0 2 4
∆Q/Q /%
0
Figure 7.9 Same plots as Figure 7.8, but versus relative charge jitter, ∆Q/Q0, at the gun. A 5.6%
charge jitter causes a 12% peak current jitter. The beam energy is, for all practical
purposes, insensitive to charge.
The sensitivities listed in Table 7.4 are used to generate a tolerance budget based on
summing random, uncorrelated effects:
2
⎛ ptol
⎞
<
n
∑ ⎜ ⎟ 1 . (7.9)
⎝ p ⎠
i= 1 sen
i
The tolerance to be chosen for each parameter is ptol, and the weighting value taken from Table
7.4 for each sensitivity is psen. For this budget, only the first fourteen (n = 14) sensitivities from
Table 7.4 are applied. If ptol = psen for all i, then the summation produces n 1/2 , or √14-times larger
peak-current or beam energy jitter than the 12% and 0.1%, respectively, used to calculate the
above sensitivities. If the tolerances are chosen such that, ptol < psen, for all i, a budget is formed
where the less challenging tolerances (e.g., chicane bend power supplies) are pushed very much
below their sensitivities, and the more challenging tolerances (e.g., L1 rf phase) are only slightly
reduced. Table 7.5 lists two possible tolerance budgets. If the first budget (column 3, titled
|∆I/I0| < 12%) is used, the relative peak-current fluctuations in the undulator will be held to