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!!