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 GeV Length: m Phase advance ∆Ф: 90⁰ or 180⁰ or 270⁰ (β QD, β QF )≈(20m, 100m) (Qx, Qy) ≈ (26.13, 26.18) L ATTICE parameters QFQD x y s QF BPM ∆Ф∆Ф Equation 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. y’(s) s y(s) NbNb 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 Wake fieldEM fields Beam current Maxwell’s equations Example of charged beam exciting e.m. fields passing by discontinuities. (courtesy of B.Salvant) y2y2 y1y1 s L q1q1 q2q2 Dipolar wake and quadrupolar wake (V/mm pC) ‘’Angle kick’’ 7/18

CERN-SPS Impedance x y s BPV SPS injection kicker MKPA /18

CERN-SPS Impedance x y s Impedance acts like a defocusing thin lens (in vertical plane). This effect is also proportional to the number of particles in the beam. SPS injection kicker MKPA NbNb ∆y(s) ∆K y BPV 9/18

CERN-SPS Impedance 1.“Small” tune shift ( < 0.01) 2.Linear tune shift with Intensity 3.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 Wakes Tracking data BPHBPV N *HDTL release developed by D.Quatraro and G.Rumolo. CERN-SPS Impedance Detection Algorithm Fourier analysis 11/18

CERN-SPS Impedance Response Matrix 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 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) s1s1 s2s2 90 ⁰, 270 ⁰ 180 ⁰ 12/18

1 2 3 CERN-SPS Impedance Response Matrix Detection Algorithm Past response matrix ⁰ phase jumps 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 at 619 m Lenses position (m) Z MKPA at 619 m For the most simple case of one single kick the algorithm presents peaks at the boundary. Linearity and accuracy studies. CERN-SPS Impedance Response Matrix Detection Algorithm Linearity & Accuracy 14/18

2 BPMs Kick K DFT TUNENON LINEARITY CERN-SPS Impedance Response Matrix Detection Algorithm Linearity & Accuracy 15/18

DFT TUNENON LINEARITY MKPA MKP allMKPA x100 CERN-SPS Impedance Response Matrix Detection Algorithm Linearity & Accuracy 16/18

CERN-SPS Impedance Response Matrix Detection Algorithm Linearity & Accuracy DFT TUNE Increase Impedance Beta bump NON LINEARITY 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 Matrix Detection Algorithm Linearity & Accuracy 18/18 Outlook