1. Impact of orbit perturbations on luminosity calibrations
W. Kozanecki
(CEA-Saclay & University of Manchester)
Orbit drifts: why doesn't this beam stay still !?
impact on van der Meer (vdM) scans
impact on length-scale calibrations (LSC)
Hysteresis effects during LSC & vdM scans
Summary

2. Impact of orbit drifts on vdM calibration: 2 (+1) effects
In-plane drift: x [y] during x [y] scan  S x [y]
equivalent to a change in calibration of closed-orbit bump (i.e. in length scale)
+ve {-ve} drift in x [y]  increase {decrease} of S x [y]
Lpeak, x/y unaffected
Peak-to-peak drift [x &/or y]  mpeak, x & y
 beams poorly centered in y during x scan (and/or v-v)  L ➘
Sx/y unaffected
Out-of-plane drift: y [x] during x [y] scan  S x [y] ➘ : in practice, negligible
Pure-gaussian calculation
Pure-gaussian calculation

3. Orbit drifts during vdM scans: the real world
IP1
vdM scan 1
28 Jul 2017
Orbit drifts during vdM scans: the real world
Horiz. separation @ IP1 {mm]
Drift consistent btwn DOROS & Arc BPMs
(this time – but not always!)
Hor. (x) scan
DOROS: "head-on" (!)
DOROS: scanning
Arc BPMS extrap  IP
Beam-beam deflection
+ ??
Vert. separation @ IP1 {mm]
Vertical drift often smaller,
consistent btwn DOROS & Arc BPMs
(this time – but not always!)
Vert. (y) scan
30 mm total span
Apparent x y
coupling?
Beam-beam deflection
Time on 28 Jul 2017

4. Orbit drifts during vdM scans: correction procedure
Parameterize drift in x & y beam separation
DOROS: include only quiescent periods, exclude scanning periods
avoid b-b deflections, apparent x-y coupling, in-scan hysteresis, DOROS length scale
Arc BPMS: include all data
only if knob leakage negligible (not true for all optics!); otherwise as for DOROS
average extrapolations from Left & Right of the IP  eliminate x-y coupling signature
Correct svis for each x-y scan pair separately (all 3 effects)
final vdM calibration is scan-averaged svis value from all head-on scans
OD-related syst. uncertainty: typically Arc-DOROS difference on < svis >
 the tricky part!
Time on 28 Jul 2017
Vert. separation {mm]
IP1
vdM scan 6Y
30 Jun 2018
IP1
vdM scan 1X
28 Jul 2017
Horiz. separation {mm]
DOROS: "head-on" (!)
DOROS: scanning
Arc BPMS extrap  IP
Time on 28 Jul 2017

5. Impact of orbit drifts on absolute L calibration: in numbers
Rule of thumb [± 6 s vdM scan, e ~ 3 mm, b* ~ 19 m, √s = 13 TeV  S ~ 130 mm]
Bias on svis (for one x-y scan pair), if left uncorrected:
In-plane drift: mm total  ~ 1 % on S (per plane, ±)
Peak-to-peak drift: 10 mm  ~ 0.15 % on svis (x or y, always -ve)
Out-of-plane drift: 10 mm total  ~ % on svis (per plane, always +ve)
NB: apparent x-y coupling seen by DOROS ~ 6-7 mm total  negligible impact
Orbit-related systematic uncertainties on absolute L ( , 13 TeV)
Main issue: scan-to-scan consistency of bunch-averaged svis values
Orbit-drift correction critical to reducing these inconsistencies:
1.2 / 0.6 % (2.0 / 1.0 % ) S-to-S inconsistency in 2017/2018 w/ (w/o) orbit-drift correction
Uncertainties on orbit-drift correction
vdM scans: % on scan-averaged svis value ( Sx/y, mpeak, x/y)
LSC scans: ~ 0.3 % on x*y length-scale product (reflected in svis ~ 1/ Sx Sy)
Beam-position jitter: from rapid position jumps within a scan step
evaluated using sample-to sample IP-position jitter (Arc BPMS): Dsvis / svis ~ %

6. Impact of orbit drifts on length-scale calibration
Principle
beams are scanned transversely // to each other over approximately ± 3 sb, while remaining in head-on collision (exc. for mini-scans of the "other" beam)
compare nominal beam displacement (= IP-knob setting) to transverse displacement of the luminous centroid (with the beams perfectly centered)
done separately for the 4 closed-orbit bumps B1X, B2X, B1Y, B2Y
the requirement that beams be perfectly centered is achieved by miniscans of the "other" beam (say B2) around the setting of the bump being calibrated (say B1)
Jul'12 LSC
Time 
Nov'17 LSC
Beam IP1 
B2X ➘
B1X➚
B2Y ➘
No drift
20 mm drift of calibrated beam  apparent change of slope
B1Y➚

7. Impact of orbit drifts on length-scale calibration (2)
Measured B1 displacement [mm]
Elapsed time [arbitrary units]
Elapsed time [arbitrary units]
Measured B2 displacement [mm]
Calibrate B1X knob
Calibrate B1Y knob
B1Y (DOROS)
B2Y (DOROS)
B2X (DOROS)
B1Y (Arcs)
~ 20 mm
B2X (Arcs)
B2Y (Arcs)
B1X (DOROS)
B1X (Arcs)
Typical impact: rule of thumb
e ~ 3 mm, b* = 19.2 m, √s = 13 TeV
sb ~ 91 mm, LSC scan over ± 2.5 sb :
10 mm drift (1 beam, 1 plane) / D = 450 mm * ½ [bec. vdM scans antisymmetric: length-scale = (B1+B2)/2]
= 1.1% bias on L scale (if uncorrected)

8. Observation of hysteresis effects in length-scale scans
Principle
Compare nominal beam displacement (= IP-knob setting) to the single-beam displacements recorded by DOROS BPM
linear? reproducible? sensitive to scan direction?
The tricky parts – in order of increasing pain
beam-beam deflection
0 (or negligible) if consider only mini-scan steps with nominalSeparation == 0
orbit drifts/jumps, real or instrumental: the curse!
exacting requirements on the relative calibration of the DOROS wrt IP knobs
LSC scans typically over ± 220 m  1% error on DOROS-knob intercalibration mimics a ~ 4 m (total) non-linearity
Time 
Nov'17 LSC
Beam IP1 
Beam IP1 
Time 
B1DXSet
B1Xmeas
B2Xmeas
B2 ➘
B1➚

9. Residual displacement: B1,2X_res = s * B1,2X_DOROS – B1,2X_nom
Out-of-plane scans masked
Out-of-plane scans included
After DOROS-knob intercalibration
Residual displacement: B1,2X_res = s * B1,2X_DOROS – B1,2X_nom
DOROS B1X calibration: s = 0.971
DOROS B2X calibration: s = 0.973
Nov'17 LSC
DOROS B1X calibration: s = 0.966
DOROS B2X calibration: s = 0.976

10. Hysteresis effects in LSC: sign sensitivity
Out-of-plane scans masked
Hysteresis effects in LSC: sign sensitivity
Time 
Beam IP1 
Time 
Beam IP1 
B1➚
B2 ➘
B1➚
B2 ➚
Nov'15 LSC
Nov'17 LSC
The B2 miniscans affect the reproducibility of the B2 displacement
B2➚
B2 ➚
B2 ➘
B2➚
The sign of the orbit distortion flips with the scanning direction

11. Residual (= measured-nominal) beam displacement in vdM scans
Nov'15 vdM (scans 1-3)
B1X
B1Y
Residual beam displacement [m]
Residual beam displacement [m]
nom. sep. = 0
scanning
Time [a.u.]
Time [a.u.]
Beam-beam deflection (corrected for) & hysteresis (not corrected for) add up in Dx, y = B1x, y - B2x, y  bias on Sx, y ?
B2X
B2Y
Residual beam displacement [m]
Residual beam displacement [m]
Time [a.u.]
Time [a.u.]

12. Summary Orbit drifts (OD) Hysteresis effects
drifts as large as 20 mm/beam were observed during both vdM & LSC scans
consistency between Arc & DOROS BPMs varies scan-to-scan:  multiple sources?
main impact is scan-to-scan reproducibility of vdM calibrations [~ O (1-1.5%) ]
vdM (LSC) uncertainty on OD correction ~ 0.2 % (0.3%) (partial cancellations!)
Hysteresis effects
Unambiguous evidence for small magnetic non-linearity of IP knobs
independently from DOROS BPMs (LSC & vdM) & luminous-region data (LSC)
The sign of the non-linearity is correlated, and flips, with the scan direction (ascending or descending), for both beams/both planes
the characterization of the shape of the non-linearity (best attempted in LSC scans (b-b deflections!) is limited by the quality of the data (limited # points, orbit drifts)
Implications
essential to apply consistent + reproducible scan protocols in vdM & LSC scans
reproducibility of magnetic non-linearity in consecutive vdM scans to be analyzed
associated systematics on LSC & vdM calibrations to be quantified for final Run-2 L
Orphan topics: beam-position jitter & apparent x-y coupling
Help needed from our LHC colleagues to identify the sources!
Systematic characterization during Run 3 needed (easy!)

13. Supplementary material

14. Residual displacement during LSC scan: B1X, B2X, collision point
Out-of-plane scans masked
Out-of-plane scans included
After DOROS-knob intercalibration
Residual displacement during LSC scan: B1X, B2X, collision point
B1X_res
B2X_res
DOROS B1X calibration: s = 0.971
DOROS B2X calibration: s = 0.973
Nov'17 LSC
B2X LSC (Jul'12)
Collision point ~ (B1X_res + B2X_res) / 2
Only antisymmetric component can impact LS

15. x-y coupling in vdM-scanning knobs: apparent or real?
IP1
vdM scan 5
28 Jul 2017
x-y coupling in vdM-scanning knobs: apparent or real?
DOROS: scanning
DOROS: head-on
B1X during Y scan
B1Y during X scan
Candidates:
BPM rotation?
coupling in optics?
tilted X/YCORs?
elx cross-talk??
2.5 m / 1160 m = + 2 mrad
~ + 4 mrad
Same sign & magnitude
 cancel in Dx = B1X - B2X
Opposite sign  enhanced in Dy = B1Y - B2Y
Is it real?
Compare to luminous-centroid displacement in LSC
B2X during Y scan
B2Y during X scan
~ + 2 mrad
~ mrad
If real:
impact on svis from out-of plane drift
~ %

16. A few examples of orbit-drift symptoms during vdM scans
vdM Fill 6868
30 Jun-1 Jul 2018
Global orbit: 1 h before S2
B1X
B1Y
B2X
B2Y

17. A few examples of orbit-drift symptoms during vdM scans
vdM Fill 6868
30 Jun-1 Jul 2018
Global orbit: during S4X
B1X
B1Y
B2X
B2Y

18. Examples of orbit-drift symptoms during vdM scans (2)
Beam IP1: reoptimization following a long drift after S6
vdM Fill 6868
30 Jun-1 Jul 2018
S6X
S6Y

19. Examples of orbit-drift symptoms during vdM scans (3)
Beam IP1: manual recentering between S4X & S4Y
vdM Fill 6868
30 Jun-1 Jul 2018

20. A few examples of orbit-drift symptoms during vdM scans (4)
IP1-orbit & L glitches during S2X
vdM Fill 6868
30 Jun-1 Jul 2018

21. A few examples of orbit-drift symptoms during vdM scans (5)
Inconsistency in peak L btwn S3Y & S5Y (off-axis  more sensitive)
vdM Fill 6868
30 Jun-1 Jul 2018
S3X
S3Y
S5X
S5Y

22. Impact of orbit drifts on vdM calibration: 2 (+1) effects
In-plane drift: x [y] during x [y] scan  S x [y]
Lpeak, x/y unaffected
Peak-to-peak drift [x &/or y]  mpeak, x & y
Sx/y unaffected
Out-of-plane drift: y [x] during x [y] scan  S x [y] : typically negligible
Pure-gaussian calculation
Assumed orbit drift
Pure-gaussian calculation
Assumed orbit drift

23. Observation of hysteresis effects in length-scale & vdM scans
Nov 2015
Principle
beams are scanned transversely // to each other over approximately ± 3 sb, while remaining in head-on collision (exc. for mini-scans of the "other" beam)
compare nominal beam displacement (= IP-knob setting) to displacement recorded by (i) DOROS BPM (single beams) & (ii) luminous centroid)
linear? reproducible? sensitive to scan direction?
The tricky parts – in order of increasing pain
beam-beam deflection
0 (or negligible) if consider only mini-scan steps with nominalSeparation == 0
orbit drifts/jumps, real or instrumental: the curse!
exacting requirements on the relative calibration of the DOROS wrt IP knobs
LSC scans typically over ± 220 m  1% error on DOROS calibration mimics a ~ 4 m (total) non-linearity
Time 
Nov'15 LSC
Beam IP1 
Beam IP1 
Time 
B1DXSet
B1Xmeas
B2Xmeas
B1➚
B2 ➚

24. DOROS calibration by the consistency method: B1X
Out-of-plane scans not shown
Nov 2015
LSC
DOROS calibration by the consistency method: B1X
B1X_res = .981* B1X_meas - B1DXSet
B1X_res = .991 * B1X_meas - B1DXSet
B1X_res = .971 *B1X_meas - B1DXSet

25. Comparison of nominal & measured displacements: X (Nov 2015 LSC)
Out-of-plane scans not shown
After DOROS-knob intercalibration
Comparison of nominal & measured displacements: X (Nov 2015 LSC)

26. Comparison of nominal & measured displacements: Y (Nov 2015 LSC)
Out-of-plane scans not shown
After DOROS-knob intercalibration
Comparison of nominal & measured displacements: Y (Nov 2015 LSC)

27. Sensitivity to relative DOROS-knob calibrations?
Nominal calibration
Nominal - 0.4%
Nominal +0.4%
Beams in head-on collision
B1X
A hard way to make a living…
B2X