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Transverse Impedance L ocalization in SPS Ring using HEADTAIL macroparticle simulations

Transverse Impedance L ocalization in SPS Ring using HEADTAIL macroparticle simulations. Candidato : Nicolò Biancacci. Correlatore (Roma): Dr. M.Migliorati Supervisore (CERN): Dr. B.Salvant. Relatore : Prof. L.Palumbo. CERN. E uropean O rganization for N uclear R esearch (1954).

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Transverse Impedance L ocalization in SPS Ring using HEADTAIL macroparticle simulations

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

  3. CERN European Organization for Nuclear Research (1954) Research CERN • 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 Super Proton Synchrotron L ATTICE parameters • 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) CERN-SPS y BPH BPH BPV s x QF QF QD ∆Ф≈ 90⁰

  5. CERN-SPS Super Proton Synchrotron BEAM parameters y’(s) CERN-SPS • 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. CERN-SPS Impedance EM fields Wake field Impedance Impedance y BPV BPV s x SPS injection kickerMKPA.11936

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

  8. Impedance CERN-SPS Impedance 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 CERN-SPS Impedance Detection Algorithm Wakes Fourieranalysis HDTL* N MAD-XorFORMULAE 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 90⁰, 270 ⁰ (c) (b) (a) s1 s2 (a) (b) (c) 180 ⁰ (a) (b) (c) *Details in our thesis report.

  11. Response Matrix CERN-SPS Impedance Detection Algorithm Response Matrix Past response matrix. 180⁰ phase jumps. 270⁰ 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 CERN-SPS Impedance Detection Algorithm Response Matrix Linearity HDTL -1 Z MKPA.11936 at 619 m For the most simple case of one single kick the algorithm presents peaks at the boundary. MKPA.11936 at 619 m Lenses position (m) Linearity studies.

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

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

  15. Linearity 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 CERN-SPS Impedance DetectionAlgorithm ResponseMatrix Linearity Conclusion Detection algorithm • The algorithm was made fully working again. • Main assumptions behind it were analized. Responsematrix • 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!!

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