Candidato: Nicolò Biancacci 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

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

CERN European Organization for Nuclear Research (1954) Research 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

CERN-SPS L ATTICE parameters Super Proton Synchrotron y BPH BPH s x QF 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) y BPH BPH BPV s x QF QD QF ∆Ф≈ 90⁰

CERN-SPS BEAM parameters Super Proton Synchrotron y’(s) Nb s y(s) 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.

Impedance s EM fields Wake field Impedance y BPV BPV x CERN-SPS Impedance EM fields Wake field Impedance y BPV BPV s x SPS injection kicker MKPA.11936

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

Impedance Local observable Phase adv. beating Global observable CERN-SPS Impedance Local observable Phase adv. beating Global observable Tune shift 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

Detection algorithm HDTL* N Wakes Fourier analysis Tracking data BPH CERN-SPS Impedance Detection Algorithm Wakes Fourier analysis Tracking data BPH BPV HDTL* N MAD-X or FORMULAE Pseudoinverse *HDTL release developed by D.Quatraro and G.Rumolo.

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 (a) s1 (b) s2 (c) (a) Advantages Faster (few sec. Vs 1.5h) Easier add/remove lenses for reconstruction No changes in lattice (b) (c) 180 ⁰ (a) Disadvantages First order model. MAD-X is full non linear. (b) (c) *Details in our thesis report.

Response Matrix Past response matrix. 180 ⁰ phase jumps. 3 CERN-SPS Impedance Detection Algorithm Response Matrix Past response matrix. 180 ⁰ phase jumps. 270 ⁰ 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

Linearity HDTL Z MKPA.11936 at 619 m 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.

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

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

Linearity Increase N or SNR Tune close to 0.5 Complex FFT FFT 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

Conclusions Detection algorithm CERN-SPS Impedance Detection Algorithm Response Matrix 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.

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