Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Amplitude detuning measurements
Ewen H.Maclean
1 Detuning with amplitude2 Measurement with kicked beams3 Measurement with driven oscillations 4 Alternative measurements5 Conclusions
Many thanks to the Optics Measurement and Corrections team
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Detuning with amplitude→ dependence of tune on action (Jx,y ) or CS-invariant (ǫx,y = 2Jx,y )
→ N [σnominal] =q
2Jǫnominal
Qz(ǫx , ǫy ) = Qz0 +“
∂Qz
∂ǫxǫx + ∂Qz
∂ǫyǫy
”
+
+ 12!
“
∂2Qz
∂ǫ2x
ǫ2x + 2 ∂2Qz
∂ǫx ∂ǫyǫxǫy + ∂2Qz
∂ǫ2y
ǫ2y
”
+ ...
Order Source (3 = sextupole)
∂Q∂ǫ
(K3)2, K4
∂2Q∂ǫ2 (K3)
4, (K3)2K4, (K4)
2, K3K5, K6
∂Qx
∂ǫx→ “Direct term”
∂Qy
∂ǫx→ “Cross term”
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Amplitude detuning from an octupole
Hn = 1Bρ
Re[
1n
[Bn(s) + iAn(s)] (x + iy)n]
Normal octupole → H4 = 14!K4L (x4
− 6x2y2 + y4)
In action-angle coordinates (x , y =√
2Jx,yβx,y cos φx,y)
H4 = 14!K4L (4J2
x β2x cos4 φx − 24JxJy cos2 φx cos2 φy + 4J2
y β2y cos4 φy )
Qx = 12π
∂〈H〉∂Jx
= 116π
K4L(
Jxβ2x − 2Jyβxβy
)
∂Qx
∂ǫx= 1
32πβ2
xK4L∂Qx
∂ǫy= −
116π
βxβyK4L∂Qy
∂ǫy= 1
32πβ2
yK4L
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Equivalence of detuning cross terms
1st order detuning: ∂Qx
∂Jy= 1
2π
∂2〈H〉∂Jy∂Jx
=∂Qy
∂Jx
2nd order detuning:
∂2Qy
∂J2x
= 12π
∂3〈H〉∂J2
x ∂Jy= ∂2Qx
∂Jx∂Jy
∂2Qx
∂J2y
= 12π
∂3〈H〉∂Jx∂J2
y=
∂2Qy
∂Jx∂Jy
Terms like ∂2
∂Jx ∂Jymeasured directly with diagonal kicks in H-V plane
but from cross term equivalence actually determine all second order termswith pure H or V measurements
Cross term equivalence gives good sanity check for data/fit quality
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Traditional detuning measurement uses single kicks
Dipole kicker ramped up/down within single turn
observe free betatron oscillations with turn-by-turn BPM data
-3
-2
-1
0
1
2
0 500 1000 1500
x [m
m]
Turn
BPM.30L1.B2
Oscillations do not decay
Oscillations decohere
Measurement is destructive
Fresh beam for every kick
BPM data post processed by Singular Value Decomposition (SVD)R.Tomas & R.Calaga, Statistical analysis of RHIC beam position monitors performance,
Phys.Rev.ST.AB,7,042801
Identifies malfunctioning BPMs
Removes uncorrellated noise from BPM signals
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Action determined from mean peak-to-peak TbT data over BPMs
2Jx,y =
P
BPMs
( 12
Peak−to−Peak)2
βx,y
NBPMs
Various sources of uncertainty:beta-beat, coupling, BPM-scaling, BPM-nonlinearity, phase-spacedistortion from resonances
Tune determined via spectral analysis of TbT data
Spectral analysis done via SUSSIX (interpolated FFT)R.Bartolini & F.Schmidt, CERN SL/Note 98-017(AP),
‘SUSSIX: a computer code for frequency analysis of non-linear betatron motion’
Decoherence limits number of turns available for spectral analysis
Beams kicked to varying amplitudes for several angles in H-V plane(at least pure kicks in H and V)
Limited by kicker strength, or machine / dynamic apertures
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Traditional detuning measurements performed at injection in 2012
E.H.Maclean, R.Tomas, F.Schmidt, T.H.B.Persson. Phys.Rev.ST.AB,18,081002(2014)Measurement of nonlinear observables in the Large Hadron Collider using kicked beams
Nominal injection optics (Landau octupoles on)
Landau octupoles off + beam-based correction of Q′′ & Q′′′
0.25
0.26
0.27
0.28
0.29
0.0 0.2 0.4 0.6 0.8 1.0
Qx
2Jx [µm]
4σ 6σ 8σ 10σ
0.29
0.30
0.31
0.32
0.33
0.0 0.2 0.4 0.6 0.8 1.0
Qy
2Jx [µm]
4σ 6σ 8σ 10σ
0.25
0.26
0.27
0.28
0.29
0.0 0.2 0.4 0.6 0.8 1.0
Qx
2Jy [µm]
4σ 6σ 8σ 10σ
0.29
0.30
0.31
0.32
0.33
0.0 0.2 0.4 0.6 0.8 1.0
Qy
2Jy [µm]
Nominal injection settingsMO depowered + NL-chroma corrections
4σ 6σ 8σ 10σ
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Beam-based correction also reduced decoherence and increased DA
-3
-2
-1
0
1
2
3
0 500 1000 1500 2000
x [m
m]
Turn no.
BPM.30L1.B2
additional Q’’, Q’’’ correction applied.MO off and MCO residual field zeroed.
Nominal injection settings.
Decoherence used as onlinecheck b4 corrections worked
In general Q′′ correction wont
correct detuning & DA
Implies local correction
60
70
80
90
100
0 2 4 6 8 10
Sur
vivi
ng In
tens
ity 3
0s a
fter
kick
[%]
σx [σnominal]
nominal injection optics (meas)MO off + Q′′ ,Q′′′ correction (meas)
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Comparison to LHC model
0.25
0.26
0.27
0.28
0.29
0.0 0.2 0.4 0.6 0.8 1.0
Qx
2Jx [µm]
MeasurementModel
4σ 6σ 8σ 10σ
0.29
0.30
0.31
0.32
0.33
0.0 0.2 0.4 0.6 0.8 1.0
Qy
2Jx [µm]
4σ 6σ 8σ 10σ
[unit] Meas’ ± err Model ± err
∂Qx∂ǫx
[103m-1] −29 7 −27.0 0.8
∂Qy∂ǫx
19 3 21 2
∂Qx∂ǫy
24 4 21 2
∂Qy∂ǫy
−32.8 0.4 −30.5 0.9
∂2Qx∂ǫ2
x[109m-2] −60 30 −14 4
∂2Qy
∂ǫ2x
34 10 18 9
Good agreement of 1st order detuning
Qualitatively similar 2nd order
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
When comparing model and measurement must account for linear coupling
-28
-26
-24
-22
0.0 0.5 1.0 1.5 2.0
δQx/
δεx
[1
03 m-1
]
Coupling phase [π]
14
16
18
20
22
0.0 0.5 1.0 1.5 2.0
δQx/
δεy
[1
03 m-1
]
Coupling phase [π]
-32
-30
-28
-26
0.0 0.5 1.0 1.5 2.0
δQy/
δεy
[1
03 m-1
]
Coupling phase [π]
|C-|
0.002
0.0025
0.003
0.0035
0.004
0.0045
0.005
0.0055
0.006
0.0065
14
16
18
20
22
0.0 0.5 1.0 1.5 2.0
δQy/
δεx
[1
03 m-1
]
Coupling phase [π]
In simulation linear coupling significantly affects the detuning...even far from the coupling resonance
Not only δQmin that’s important: also phase of RDT
Best option is a good correction at start of measurement
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Coupling effect may also impinge upon detuning measurements
Detuning with Jy moved tunes together
Tune separation saturates
Kicks at large Jy couple significantly into H-plane
Observed in real LHC and simulation
0.00
0.02
0.04
0.00 0.20 0.40
| Qx
- Q
y |
2Jy [µm]
Measured tune splitModel tune split
0.00
0.20
0.40
0.60
0.00 0.20 0.40 0.60
ε y M
AX
[µm
]
εx MAX [µm]
Measured kicksModelled H-kicksModelled V-kicks
Behaviour associated with transverse planes becoming strongly coupled
Still very far from measured |C−| = 0.0036
Implies existance of amplitude dependent δQmin
Coupling stopband will distort detuning......but may have a nonlinear contribution
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Single kick detuning measurements not possible at top energy in LHC
Require new fill for every kick (destructive measurement)
Machine protection
LHC is equiped with AC-dipole kickers
Sinosoidally driven dipole kicker
Driving frequency close (but not on!) natural tunes generates largeresponse with little power, even at high energy
If ramped up/down adiabatically kicks are non-destructive
Routinely used for linear optics measurements throughout cycle
-1.0
-0.5
0.0
0.5
1.0
0 2000 4000 6000 8000 10000
x [m
m]
Turns
AC-dipole provides a tool to measureamplitude detuning at high energy
Actually rely on non-perfect adiabaticity
to excite natural tune lines in spectrum
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
AC-dipole modifies solutions to equations of motion:
x (s) =√
2Jxβx (s) cos φx (s)
→ xD (s) =√
2Jxβx (s) cos φx (s) +p
2Axβ′x (s) cos φD (s)
· A, φD (s) are action angle variables of the driven oscillation
· β′
is beta-function modified by the AC-dipole (β′ ≈ β)
Alters action-angle Hamiltonian & Q, eg octupole tune shift:
Qx = 12π
∂〈H〉∂Jx
= 116π
K4L`
Jxβ2x − 2Jyβxβy
´
→ 116π
K4L`
Jxβ2x + 2Axβ
′xβx − 2Jyβxβy
´
Jx << Ax → direct detuning 2× expectation for free oscillations
Detuning cross term unnaffected
Similar result for Qy
In general:Direct detuning terms from n
th order are n2
larger when measured withAC-dipole than free oscillations. Cross terms are unnaffected.
S.White, R.Tomas, E.H.Maclean, ‘Direct amplitude detuning measurement with ac dipole’,Phys.Rev.ST.AB,16,071002(2013)
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Effect of AC-dipole on observed detuning was verified experimentally atinjection
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Measurement of natural tune variation with AC-dipole action is morechallenging than with free oscillations
FFT of driven oscillations for different SVD cuts
Natural tune not a strong signal
Need agressive SVD cleaning
Additonal resonancesaQx + bQy = z
→ aQx + bQy + pQACx + qQACy = z
“Tune” identified by SUSSIX in ∼500 LHC BPMs
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Particle loss
Peak-to-Peakx
Peak-t
o-P
eaky
Watch out for dynamic aperture!
In general DA smallerthan un-driven motion
Kicking to DA will causeblow up and particle loss
DA depends on QAC
S.Monig et. al. Short term dynamic aperture with AC dipoles. CERN-ACC-NOTE-2015-0027
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
AC-dipole detuning measurements performed successfully at top energy
Measured @ 6.5 TeV, β∗ = 0.4 m during 2015 MD
Comparison of to MAD-X tracking simulations, including AC-dipole
red = measurement
blue = model
green = model+b4 corr IR1+5
Amplitude detuning measurements by A.Langner, comparison to simulation by S.Monig
For 0.4 m detuning dominated by b4 errors in IR1+IR5(negligible contribution of arcs, which dominate Q′′)
Implies ∼ 12
expected b4 of IR1 + IR5
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Amplitude detuning is not the only probe available for NL-errors
With AC-dipole detuning measurements gain spectral info for free
Studied for Wire Excitation experiments in SPS
U.Dorda et. al. Wire excitation experiments in the CERN SPS, EPAC’08
Sextupole coupling line Qx + Qy
Predict change in amplitude for change in beam-wire separation
Qualitative agreement with observed spectrum
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Traditional DA measurement with single kicks used at injection→ Not viable at top energy
Alternative method is blow up emittance with transverse damper→ study long term DA via intensity loss & scaling laws→ Demonstrated at injection, viable at top energy→ being considered for optimization of NL-correctors in IR
0
20
40
60
80
100
02:25 02:30 1.4
1.45
1.5
1.55
1.6
Oct
upol
e co
rrec
tor
curr
ent [
A]
Inte
nsity
[cha
rges
× 1
010]
Time [ 25/06/2012 ]
Bunch intensity vs time for Ioctupole correctors=+90 [A]
MCO currentBeam intensity
6
6.5
7
7.5
8
8.5
9
9.5
0 1 2 3 4 5
DA
(N)
σno
min
al
Turn [106]
Extrapolated 108 turn DA = 4.85σnominal
possibilities for short-term DA measurement with AC-dipole
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Currently study NL-errors in low-β∗ IRs via feed-down
E.H.Maclean, R.Tomas, M.Giovannozzi, T.H.B.Persson. Accepted to Phys.Rev.ST.ABFirst measurement and correction of nonlinear errors in the experimental insertions of the CERN LHC
0.000
0.002
0.004
0.006
-300 -200 -100 0 100 200 300
|C- |
LHCB2, IR1 β*=0.4mModel
Measurement
0.316
0.318
0.320
-300 -200 -100 0 100 200 300
Qy
Vertical crossing angle in IR1 [µrad]
ModelMeasurement
e.g. IR1 @ 0.4 m, 4 TeV
b3 + a4 feed-down to|C−|
a3 + b4 feed-down to Qy
Potentially quite useful in conjunction with other observables
Amp’detuing
Singlekicks
AC-dipole
Othermethod
Summary
Simulations and Measurements of Long Range Beam-Beam Effects in the LHC, Lyon, 1st December 2015
Conclusions
Traditional detuning measurement → single kicks
1st & 2nd order detuning measured @ 450GeV with single kicks
Traditional measurement not viable at LHC top energy
AC-dipole measurment possible at LHC top energy
Theory predicts driven oscillations have different detuning
Verified experimentally @ 450GeV
AC-dipole measurement tougher than single-kick
Demonstrated at top energy → now routine
Various additional methods also available
long-term DA (ADT), short-term DA (AC-dipole), feed-down, spectra
