1. Candidato: Nicolò Biancacci
Transverse Impedance Localization in SPS Ring using HEADTAIL macroparticle simulations
Candidato: Nicolò Biancacci
Correlatore (Roma):
Dr. M.Migliorati
Supervisore (CERN): Dr. B.Salvant
Relatore:
Prof. L.Palumbo

2. CERN European Organization for Nuclear Research (1954) Research
Higgs Boson
Matter / Antimatter
String theory
Neutrino
CP violation
. . .

3. CERN European Organization for Nuclear Research (1954) Research
Higgs Boson
Matter / Antimatter
String theory
Neutrino
CP violation
. . .
Accelerator chain
Linac2 → 50MeV
PS-Booster → 1.4 GeV
PS → 25 GeV
SPS → 450 GeV
LHC → 7TeV

4. CERN-SPS L ATTICE parameters Super Proton Synchrotron y BPH BPH s x QF
Energy: 25 GeV GeV
Length: 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) y
BPH
BPH
BPV s x QF QD QF
∆Ф≈ 90⁰

5. CERN-SPS BEAM parameters Super Proton Synchrotron y’(s) Nb s y(s)
Population Nb :
Bunch length : 14 cm
Transv. Emittance : 11 um Nb s
y(s)
High intensity beams are needed to achieve high luminosities for experiments.
But…
Beams are subject to losses and degradation becouse of different instability sources
Impedance is one of the main sources of instability. Need both global and local monitoring.

6. Impedance s EM fields Wake field Impedance y BPV BPV x
CERN-SPS
Impedance
EM fields
Wake field
Impedance y
BPV
BPV s x
SPS injection kicker MKPA.11936

7. Impedance ≈ s y BPV BPV x MKPA.11936 S T <y> y2 y1 EM fields
CERN-SPS
Impedance y
BPV
BPV s x
MKPA.11936 ≈ S T
<y> y2 y1
EM fields
Wake field
Impedance

8. Impedance Local observable Phase adv. beating Global observable
CERN-SPS
Impedance
Local observable
Phase adv. beating
Global observable
Tune shift
Assumptions:
“Small” tune shift ( < 0.01)
Linear tune shift with Intensity
Local impedances not coupled Z Z
Linear response to the “impedance kick” strength Z
System response matrix

9. Detection algorithm HDTL* N Wakes Fourier analysis Tracking data BPH
CERN-SPS
Impedance
Detection Algorithm
Wakes
Fourier analysis
Tracking data
BPH
BPV
HDTL* N
MAD-X or FORMULAE
Pseudoinverse
*HDTL release developed by D.Quatraro and G.Rumolo.

10. Response Matrix
CERN-SPS
Impedance
Detection Algorithm
Response Matrix
We can compute the response matrix using MAD-X or FORMULAE* we derived.
BPV
BPV Z Z Z s
90 ⁰, 270 ⁰
(a) s1
(b) s2
(c)
(a)
Advantages
Faster (few sec. Vs 1.5h)
Easier add/remove lenses for reconstruction
No changes in lattice
(b)
(c)
180 ⁰
(a)
Disadvantages
First order model. MAD-X is full non linear.
(b)
(c)
*Details in our thesis report.

11. Response Matrix Past response matrix. 180 ⁰ phase jumps. 3
CERN-SPS
Impedance
Detection Algorithm
Response Matrix
Past response matrix.
180 ⁰ phase jumps.
270 ⁰ phase jumps and duplication.
Blank lines (more reconstructors in same place)
Weighted by betatron function 3 1
New response matrix.
Smooth response normalizing on betatron function.
Lenses also in impedance positions (benchmark). 2

12. Linearity HDTL Z MKPA.11936 at 619 m
CERN-SPS
Impedance
Detection Algorithm
Response Matrix
Linearity
HDTL -1 Z
MKPA at 619 m
For the most simple case of one single kick the algorithm presents peaks at the boundary.
MKPA at 619 m
Lenses position (m)
Linearity studies.

13. Linearity MAD-X K FFT Kick 2 BPMs CERN-SPS Impedance
Detection Algorithm
Response Matrix
Linearity
FFT
TUNE
NON LINEARITY
MAD-X K
Kick
2 BPMs

14. Linearity FFT MKPA.11936 MKP all MKPA.11936 x100 CERN-SPS Impedance
Detection Algorithm
Response Matrix
Linearity
FFT
TUNE
NON LINEARITY
MKPA.11936
MKP all
MKPA x100

15. Linearity Increase N or SNR Tune close to 0.5 Complex FFT FFT
CERN-SPS
Impedance
Detection Algorithm
Response Matrix
Linearity
Increase N or SNR
Tune close to 0.5
Complex FFT
FFT
NON LINEARITY
TUNE
Increase Impedance
Beta bump
Set of lenses
Non linear model

16. Conclusions Detection algorithm
CERN-SPS
Impedance
Detection Algorithm
Response Matrix
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.

17. Thanks!!