transverse impedance localization in sps ring using headtail macroparticle simulations candidato:...
TRANSCRIPT
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 CERN European Organization for Nuclear Research (1954)
• Higgs Boson• Matter / Antimatter• String theory• Neutrino• CP violation• . . .
Research
3/18
CERN 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 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 sssy
Equation of particle motion
Focusing quadrupole
Defocusing quadrupole
Beam Position Monitor
Beta function
5/18
CERN-SPS 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 CERN-SPS Impedance 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 CERN-SPS Impedance Impedance
x
y
sBPV
SPS injection kickerMKPA.11936
8/18
CERN-SPS CERN-SPS Impedance 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
sy
sy
Nksy
sy
by
SPS injection kickerMKPA.11936
Nb ∆y(s) ∆Ky
BPV
9/18
CERN-SPS CERN-SPS Impedance 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 observable
Phase advance beating slope
Global observable
Tune 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 CERN-SPS Impedance Impedance Detection Algorithm Detection Algorithm
Fourier analysis
11/18
CERN-SPS CERN-SPS Impedance Impedance Response MatrixResponse MatrixDetection Algorithm Detection 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 CERN-SPS Impedance Impedance Response MatrixResponse MatrixDetection Algorithm Detection 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 CERN-SPS Impedance Impedance Response MatrixResponse MatrixDetection Algorithm Detection Algorithm Linearity & AccuracyLinearity & Accuracy
14/18
2 BPMs KickK
DFT TU
NE
NO
N LIN
EARITY CERN-SPS CERN-SPS Impedance Impedance Response MatrixResponse MatrixDetection Algorithm Detection Algorithm Linearity & AccuracyLinearity & Accuracy
15/18
DFT TU
NE
NO
N LIN
EARITY
MKPA.11936 MKP all MKPA.11936 x100
mMmMZ j /20,/2)Im(
CERN-SPS CERN-SPS Impedance Impedance Response MatrixResponse MatrixDetection Algorithm Detection Algorithm Linearity & AccuracyLinearity & Accuracy
16/18
CERN-SPS CERN-SPS Impedance Impedance Response MatrixResponse MatrixDetection Algorithm Detection Algorithm Linearity & AccuracyLinearity & 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 CERN-SPS Impedance Impedance Response MatrixResponse MatrixDetection Algorithm Detection Algorithm Linearity & AccuracyLinearity & Accuracy
18/18
OutlookOutlook