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Transverse Impedance Localization in SPS Ring using HEADTAIL macroparticle simulations

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. Introduction to CERN and CERN-SPS. OUTLINE.

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Transverse Impedance Localization 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. Introduction to CERN and CERN-SPS OUTLINE • CERN experiments and accelerator chain • SPS: lattice and beam parameters Impedance and wake fields • Impedance and wake fields in transverse plane Detection algorithm • Derived formulae for response matrix construction • Response matrix studies • Linearity and accuracy limits in the algorithm Outlook

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

  4. 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

  5. CERN-SPS Super Proton Synchrotron Beam Position Monitor L ATTICE parameters ∆Ф y BPM • 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) CERN-SPS s QF QF QD x Defocusing quadrupole Focusing quadrupole Beta function Equation of particle motion

  6. 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 number of collision events in experiments. But… Beams are subject to losses and degradation because of different instability sources Coupling Impedance is one of the main sources of instability. Need both global and local monitoring.

  7. CERN-SPS Impedance EM fields Wake field Impedance Beam current Maxwell’s equations Impedance L q2 q1 y2 y1 s ‘’Angle kick’’ Dipolar wake and quadrupolar wake (V/mm pC) Exampleofcharged beam excitinge.m.fieldspassingbydiscontinuities. (courtesyofB.Salvant)

  8. CERN-SPS Impedance Impedance y s BPV x SPS injection kickerMKPA.11936

  9. CERN-SPS Impedance Impedance y s BPV x SPS injection kickerMKPA.11936 • Impedance acts like a defocusing thin lens (in vertical plane). • This effect is also proportional to the number of particles in the beam. Nb ∆y(s) ∆Ky

  10. Impedance CERN-SPS Impedance Courtesy of H.Burkhardt, B.Salvant We can measure: Assumptions: with μ(s)=φ(s)/2π “Small” tune shift ( < 0.01) Linear tune shift with Intensity Local impedances not coupled From linear optics: • Linear response with ∆k variation

  11. Detection algorithm CERN-SPS Impedance Detection Algorithm Wakes Fourier analysis HDTL* N MAD-XorFORMULAE Pseudoinverse *HDTL release developed by D.Quatraro and G.Rumolo.

  12. 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 (c) (a) (b) s1 s2 (a) (b) (c) 180 ⁰ (a) (b) (c) *Details in our thesis report.

  13. Response Matrix CERN-SPS Impedance Detection Algorithm Response Matrix Past response matrix. BPM pair 180 ⁰ phase jumps. 270 ⁰ phase jumps and duplication. Blank lines: more reconstructors in same place and/or different response because of smaller beta function 2 s lenses 1 New response matrix. Smooth response normalizing on betatron function. Lenses also in impedance positions (benchmark). 3

  14. Linearity & Accuracy CERN-SPS Impedance Detection Algorithm Response Matrix Linearity & Accuracy 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 and accuracy studies.

  15. Linearity & Accuracy CERN-SPS Impedance Detection Algorithm Response Matrix Linearity & Accuracy DFT TUNE NON LINEARITY MAD-X K Kick 2 BPMs

  16. Linearity & Accuracy CERN-SPS Impedance Detection Algorithm Response Matrix Linearity & Accuracy DFT TUNE NON LINEARITY MKP all MKPA.11936 x100 MKPA.11936

  17. Linearity & Accuracy CERN-SPS Impedance Detection Algorithm Response Matrix Linearity & Accuracy • Increase N or SNR • Tune close to 0.5 • Complex DFT DFT NON LINEARITY TUNE • Increase Impedance • Beta bump Z

  18. Outlook CERN-SPS Impedance Detection Algorithm Response Matrix Linearity & Accuracy Outlook Detection algorithm • The algorithm was made fully working again. • Main assumptions behind it were analyzed. Responsematrix • 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.

  19. Thanks for your attention!

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