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