transverse impedance l ocalization in sps ring using headtail macroparticle simulations
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Transverse Impedance Localization in SPS Ring
using HEADTAIL macroparticle simulations
Candidato:Nicolò Biancacci
Relatore:
Prof. L.PalumboCorrelatore (Roma):
Dr. M.Migliorati
Supervisore (CERN):Dr. B.Salvant
CERNCERN European Organization for Nuclear Research (1954)
• Higgs Boson• Matter / Antimatter• String theory• Neutrino• CP violation• . . .
Research
CERNCERN European Organization for Nuclear Research (1954)
• Higgs Boson• Matter / Antimatter• String theory• Neutrino• CP violation• . . .
• Linac2 → 50MeV• PS-Booster → 1.4 GeV• PS → 25 GeV• SPS → 450 GeV• LHC → 7TeV
Accelerator chain
Research
CERN-SPSCERN-SPS Super Proton Synchrotron
• Energy: 25 GeV - 450 GeV
• Length: 6911.5038 m
• 100 Defocusing quads (QD)
• 102 Focusing quads (QF)
• 105 Horizontal Beam
Position Monitors (BPH)
• 93 Vertical Beam
Position Monitors (BPV)
• ∆Ф≈90⁰ Phase advance per cell
(FODO)
• (Qx, Qy) ≈ (26.13, 26.18)
L ATTICE parameters
QF QDx
y
s
QF
BPH BPHBPV
0β
∆Ф≈ 90⁰
CERN-SPSCERN-SPS Super Proton Synchrotron
BEAM parameters
• Population Nb :
• Bunch length : 14 cm
• Transv. Emittance : 11 um
But…
Impedance is one of the main sources of instability. Need both global and local monitoring.
111015.1
S
yx,
y’(s)
S
s y(s)
Nbyx,
High intensity beams are needed to achieve high luminosities for experiments.
Beams are subject to losses and degradation becouse of different instability sources
ImpedanceCERN-SPS Impedance
ImpedanceWake field
x
y
s
BPV
EM fields
BPV
SPS injection kickerMKPA.11936
ImpedanceCERN-SPS Impedance
x
y
s
BPVBPV
MKPA.11936
ImpedanceWake fieldEM fields
0β
T S
y2 y1<y>
BEAT0
≈
ImpedanceCERN-SPS Impedance
1. “Small” tune shift ( < 0.01)
2. Linear tune shift with Intensity3. Local impedances not coupled
4. Linear response to the “impedance kick” strength
Assumptions:
Local observable
Phase adv. beating
Global observable
Tune shift
ZZ
ZSystem response matrix
HDTL*
Pseudoinverse
Wak
es
MAD-Xor
FORMULAE
Tracking data
BPH BPV
Fourieranalysis
N
*HDTL release developed by D.Quatraro and G.Rumolo.
Detection algorithmCERN-SPS Impedance Detection Algorithm
Response MatrixCERN-SPS Impedance Response MatrixDetection Algorithm
We can compute the response matrix using MAD-X or FORMULAE* we derived.
*Details in our thesis report.
Z Z Z s
BPV BPV
Advantages
Faster (few sec. Vs 1.5h)
Easier add/remove lenses for reconstruction
No changes in lattice
Disadvantages
First order model. MAD-X is full non linear.
(a) (b) (c)
(a)
(b)
(c)
(a)
(b)
(c)
s1 s290 ⁰, 270 ⁰
180 ⁰
1
3
2
Response MatrixCERN-SPS Impedance Response MatrixDetection Algorithm
Past response matrix.
1. 180 ⁰ phase jumps.2. 270 ⁰ phase jumps and
duplication.3. Blank lines (more
reconstructors in same place)
4. Weighted by betatron function
New response matrix.
1. Smooth response normalizing on betatron function.
2. Lenses also in impedance positions (benchmark).
LinearityCERN-SPS Impedance Response MatrixDetection Algorithm Linearity
MKPA.11936 at 619 m
Lenses position (m)
Z
MKPA.11936 at 619 m
HDTL -1
For the most simple case of one single kick the algorithm presents peaks at the boundary.
Linearity studies.
2 BPMs Kick
MAD-X K
LinearityCERN-SPS Impedance Response MatrixDetection Algorithm Linearity
FFT TUN
E
NO
N LIN
EARITY
FFT TUN
E
NO
N LIN
EARITY CERN-SPS Impedance Response MatrixDetection Algorithm Linearity
Linearity
MKPA.11936 MKP all MKPA.11936 x100
CERN-SPS Impedance Response MatrixDetection Algorithm Linearity
Linearity
FFT
TUN
E
• Increase N or SNR
• Increase Impedance• Beta bump• Set of lenses Non linear model
NO
N LIN
EARITY
• Tune close to 0.5• Complex FFT
ConclusionsCERN-SPS Impedance Response MatrixDetection Algorithm Linearity Conclusion
Detection algorithm The algorithm was made fully working again. Main assumptions behind it were analized.
Response matrix Thin lens reconstruction was implemented. Analytical formulae derived to make reconstructing faster. Improved understanding between lattice and corresponding response matrix.
Linearity
Main limits in FFT accuracy. • Increase accuracy with higher N of turns, complex FFT, higher SNR with larger beam displacement or tune close to half an integer.• Increase artificially the impedance to the detectable area. • Develop a non linear model for high impedance reconstruction.
Thanks!!
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