Quadrupole Magnet Vibrations and RF StabilityPaul Emma
LCLS-II Physics Meeting
June 18, 2014
2No CSR here
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RF Stability Requirements and Consequences (1)
LCLS-II FAC Review, July 1-3, 2014
Longitudinal sensitivities where each entry in the DE/E0-column causes a 0.01% energy error, in the DI/I0-column causes a 4% peak current error, and in the Dtf -column causes a 20-fs bunch arrival time error.
L0 RF phase error of ±0.048 degL causes ±4% peak current change (and 44 more such linear fits fill out the table).
L0 RF phase sensitivity (LiTrack)
±0.048 degL
±4%
Scale down such that quadrature sum of all errors just reaches beam stability limit for each columnBeam-based feedback covers jitter slower than ~10 Hz
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RF Stability Requirements and Consequences (2)
LCLS-II FAC Review, July 1-3, 2014
ENERGY
PEAKCURRENT
ARRIVALTIME
Target final energy, peak current, and timing stabilityHold to ~0.01-deg & ~0.01% tols**
Assume uncorrelated RF jitter (cavity to cavity)Include bunch charge, laser, & chicane power supplies
* The gun timing error is compressed by 3.85, from gun to 100 MeV, due to velocity compression.
Jitter Simulations in LiTrack
** If correlated errors, would then achieve 0.01%, 4%, and 20 fs stability
Quadrupole Magnet Vibration Tolerances (1)
LCLS-II FAC Review, July 1-3, 2014
HXR (SXR not shown)
Linac to split ,
Introduce the normalized trajectory oscillation amplitude, Ax (or Ay),
with Dx'i the kick angle of the ith quadrupole due to its displacement.
For N uncorrelated kicks along the accelerator…
𝐴𝑥2=∑
𝑖=1
𝑁
(∆ 𝑥′𝑖)2𝛽𝑖 /𝜖 𝑖 ,
𝐴𝑥2= 1
1 02 [∑𝑖=1
𝑁 1 (∆ 𝑥′𝑡 1
∆ 𝑥′𝑠𝑖 )2
+ ∑𝑗=𝑁 1+1
𝑁 2 (∆ 𝑥′𝑡 2
∆ 𝑥′𝑠𝑗 )2
+ ∑𝑘=𝑁2+1
𝑁 3 ( ∆ 𝑥′𝑡 3
∆𝑥 ′𝑠𝑘 )2]
Budget is formed by grouping tolerances into a few discrete levels and setting Ax = 10%...
where N1 + N2 + N3 = N.
Vibration sensitivity of each magnet: Dx's 285 quadrupole magnets
(includes undulators)
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Quadrupole Magnet Vibration Tolerances (2)
LCLS-II FAC Review, July 1-3, 2014
tol. bin:
500 nm
(rms)
120 nm
(rms)
50 nm
(rms)
sx 51 153 81
sy 47 152 86
Divide tolerances into 3 bins (500, 120, & 50 nm rms)…rms vib. sensitivities: Linac to LTU-Split (x & y)
rms vib. sensitivities: HXR (SXR not shown)
x & y tol.’s listed for each quad.
Number of quads/bin (x & y)
285 quadrupole magnets