Transverse Impedance Localization in SPS Ring using HEADTAIL macroparticle simulations

Transverse Impedance Localization in SPS Ring

using HEADTAIL macroparticle simulations

Candidato:Nicolò Biancacci

Relatore:Prof. L.Palumbo

Correlatore (Roma):Dr. M.Migliorati

Supervisore (CERN):Dr. B.Salvant

2/18

• CERN experiments and accelerator chain• SPS: lattice and beam parameters

• Impedance and wake fields in transverse plane

• Derived formulae for response matrix construction• Response matrix studies• Linearity and accuracy limits in the algorithm

Outlook

Introduction to CERN and CERN-SPS

Impedance and wake fields

Detection algorithm

CERN European Organization for Nuclear Research (1954)

• Higgs Boson• Matter / Antimatter• String theory• Neutrino• CP violation• . . .

Research

3/18

CERN 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

4/18

CERN-SPS Super Proton Synchrotron

• Energy: 25 GeV - 450 GeV

• Length: 6911.5038m

• Phase advance ∆Ф:

90⁰ or 180⁰ or 270⁰

• (βQD, βQF)≈(20m , 100m)

• (Qx, Qy) ≈ (26.13, 26.18)

L ATTICE parameters

QF QDx

y

sQF

BPM

)(s

∆Ф

))(cos()()( 0 sssyEquation of particle motion

Focusing quadrupole

Defocusing quadrupole

Beam Position Monitor

Beta function

5/18

CERN-SPS Super Proton Synchrotron

BEAM parameters

• Population Nb :

• Bunch length : 14 cm

• Transv. Emittance : 11 um

But…

Coupling 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 number of collision events in experiments.

Beams are subject to losses and degradation because of different instability sources

6/18

CERN-SPS Impedance

ImpedanceWake fieldEM fieldsBeam current

v

Maxwell’s equations

Example of charged beam exciting e.m. fields passing by discontinuities. (courtesy of B.Salvant)

y2y1

s

Lq1q2

Dipolar wake and quadrupolar wake (V/mm pC)

‘’Angle kick’’

7/18

CERN-SPS Impedance

x

y

sBPV

SPS injection kickerMKPA.11936

8/18

CERN-SPS Impedance

BEAT0

x

y

s

BEAT0

• Impedance acts like a defocusing thin lens (in vertical plane). • This effect is also proportional to the number of particles in the beam.

)(')(

1)(01

)(')(

1

1

2

2

sysy

Nksysy

by

SPS injection kickerMKPA.11936

Nb ∆y(s) ∆Ky

BPV

9/18

CERN-SPS Impedance

1. “Small” tune shift ( < 0.01)

2. Linear tune shift with Intensity3. Local impedances not coupled

4. Linear response with ∆k variation

Assumptions:

Local observablePhase advance beating slope

Global observableTune shift slope

From linear optics:

10/18

We can measure:

with μ(s)=φ(s)/2π

Courtesy of H.Burkhardt, B.Salvant

Pseudoinverse

Tracking data

BPH BPV

N

*HDTL release developed by D.Quatraro and G.Rumolo.

CERN-SPS Impedance Detection Algorithm

Fourier analysis

11/18

CERN-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

Response with formulae

Faster (few sec)

Easier add/remove lenses for reconstruction

No changes in lattice

Response with MAD-X

Slower (1.5h)

Non linear model

(a) (b) (c)

(a)

(b)

(c)

(a)

(b)

(c)

s1 s290 ⁰, 270 ⁰

180 ⁰

12/18

1

2

3

CERN-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 and/or different response because of smaller beta function

New response matrix.

1. Smooth response normalizing on betatron function.

2. Lenses also in impedance positions (benchmark).

13/18

s

BPM pair

lenses

MKPA.11936 at 619 m

Lenses position (m)

Z

MKPA.11936 at 619 m

-1

For the most simple case of one single kick the algorithm presents peaks at the boundary.

Linearity and accuracy studies.

CERN-SPS Impedance Response MatrixDetection Algorithm Linearity & Accuracy

14/18

2 BPMs KickK

DFT TUN

E

NO

N LIN

EARITY CERN-SPS Impedance Response MatrixDetection Algorithm Linearity & Accuracy

15/18

DFT TUN

E

NO

N LIN

EARITY

MKPA.11936 MKP all MKPA.11936 x100

mMmMZ j /20,/2)Im(

CERN-SPS Impedance Response MatrixDetection Algorithm Linearity & Accuracy

16/18

CERN-SPS Impedance Response MatrixDetection Algorithm Linearity & Accuracy

DFT

TUN

E

• Increase Impedance• Beta bump

NO

N LIN

EARITY

• Increase N or SNR• Tune close to 0.5• Complex DFT

Z

17/18

Detection algorithm The algorithm was made fully working again. Main assumptions behind it were analyzed.

Response matrix Thin lens reconstruction was implemented. Analytical formulae derived to make reconstructing faster. Improved understanding between lattice and corresponding response matrix.

Linearity and accuracy

Main limits in DFT accuracy. • Increase accuracy with higher N of turns, complex DFT, higher SNR with larger beam displacement or tune close to half an integer.• Increase artificially the impedance to the detectable area.

CERN-SPS Impedance Response MatrixDetection Algorithm Linearity & Accuracy

18/18

Outlook