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E-cloud instability and incoherent emittance growth

CARE HHH Workshop, 7-8 March 2011. E-cloud instability and incoherent emittance growth. Elena Benedetto (NTU-Athens & CERN). Acknowledgments : F. Zimmermann, G. Arduini, E. Metral, G. Franchetti, K. Ohmi, F. Ruggiero, G. Rumolo, D. Schulte. Contents. Introduction

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E-cloud instability and incoherent emittance growth

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  1. CARE HHH Workshop, 7-8 March 2011 E-cloud instability and incoherent emittance growth Elena Benedetto (NTU-Athens & CERN) Acknowledgments: F. Zimmermann, G. Arduini, E. Metral, G. Franchetti, K. Ohmi, F. Ruggiero, G. Rumolo, D. Schulte

  2. Contents • Introduction • Simulations of single-bunch effects • Electron cloud evolution in the bunch potential • In field-free regions and in dipoles • Single-bunch instabilities due to electron cloud • Dependence on beam and machine parameters • Comparison w. analytical models • Incoherent emittance growth • Proposed mechanism • E-cloud wake-field • Conclusions and outlook • CARE-THESIS-06-007, CERN-THESIS-2008-096 CARE-HHH Workshop, 7-8 March 2011

  3. Strong head-tail instability (re > rthresh) Incoherent emittance growth (re < rthresh) re= 3.5 x 1011 m-3 re= 2 x 1011 m-3 re= 1 x 1011 m-3 EC single-bunch effects • Single-bunch effects below & above EC instability threshold • Strong head-tail instability, coherent tune shift, head-tail motion and associated emittance growth. • During bunch passage, e-go toward beam center (pinch). • e-follow perturbations of beam: • If displacement between head and tail, tail feels wake force. • Effective short-range wake field: • Single-bunch TMC Instability. • Incoherent emittance growth and long-term beam losses (simulations for LHC @ injection) CARE-HHH Workshop, 7-8 March 2011

  4. y y x x z z (Nk=3) s2 s1 R y z s3 x Simulations – HEADTAIL code HEADTAIL→ CERN, 2002, G. Rumolo, F. Zimmermann, et al. • EC localized in a finite number Nk of interaction points (IPs) around the ring. • EC density as input. • The cloud is thin(2D). • Bunch divided in slices, which enter into the EC at subsequent time steps. • At each time step,2D interaction computed with PIC module: • Matrix to transport protons between IPs: • e- perturbed by p+ field • p+ get a kick Du by e- field (by G.Rumolo) CARE-HHH Workshop, 7-8 March 2011

  5. Studies of electron cloud effects Electron cloud evolution CARE-HHH Workshop, 7-8 March 2011

  6. y x z sEC R s=0 t=tend t=0 Bunch HEAD Bunch TAIL z Electron cloud evolution • EC “pinch” in the transverse plane, during the passage of a bunch Log (re) 20 10 x/sb 0 Log(re) -10 -20 y/sy EC density in the horizontal plane vs. time LHC @ inj, field-free region x/sx CARE-HHH Workshop, 7-8 March 2011

  7. t t=tend t=0 Bunch TAIL Bunch HEAD z Electron cloud evolution • EC evolution at the centre of the bunch (x,y)=(0,0) • peaks (“linear” e-) • density increase (“non linear” e-) 300 r(t)/r0 |r=0 EC phase space at different times: t0=beginning, t1=first peak, t2=first valley, t3=second peak 1 → EC density function of longitudinal & transverse position in the bunch CARE-HHH Workshop, 7-8 March 2011

  8. t=0 t=0 t [ns] t [ns] t=tend t=tend Bunch TAIL Bunch TAIL Bunch HEAD Bunch HEAD z z Electron cloud evolution • EC evolution in dipole regions of LHC (@ inj energy) Horizontal plane Vertical plane y/sy x/sx CARE-HHH Workshop, 7-8 March 2011

  9. Studies of electron cloud effects Head-tail instability CARE-HHH Workshop, 7-8 March 2011

  10. t = 0 ms t = 20 ms t = 40 ms Head-tail instability Vertical centroid motion and emittance growth in the the first 14 ms, at the onset of the strong head-tail instability. • During the bunch passage, e-are accumulated around beam center • If offset between head and tail: • tail feels transverse electric field created by head • effective short-range wake field (simulations for LHC @ inj. energy, re=6 x 1011 m-3,Q’=2,field free region) Snapshot of the vertical bunch profile (bunch centroid and rms size) at different time steps. CARE-HHH Workshop, 7-8 March 2011

  11. Agrees with a 2-particles model analytical estimate of the threshold density for TMC type instability: r = 3 x 1012 m-3 r = 9 x 1011 m-3 Vertical Emittance [m] r = 6 x 1011 m-3 r = 4 x 1011 m-3 r = 3.5 x 1011 m-3 r = 3 x 1011 m-3 Time [s] Simulation of head-tail instability • Dependence of beam blow-up on EC density value (studies for LHC @ injection) Vertical emittance vs. time, for different EC densities;chromaticity Q’=2 E. Benedetto, G. Rumolo, D. Schulte, F. Zimmermann, PRST-AB 8, 124402 (2005) CARE-HHH Workshop, 7-8 March 2011

  12. Simulation of head-tail instability • Dependence on bunch intensity • At half nominal bunch intensity (green curve) → below threshold of the fast head-tail Vertical emittance vs. time, varying bunch intensity;(LHC @ inj), re=6 x 1011 m-3,chromaticity Q’=2 CARE-HHH Workshop, 7-8 March 2011

  13. Q’ Q’=2 Q’=15 Q’=10 Q’=20 Vertical Emittance [m] Q’=25 Q’=30 re [x 1012 m-3] Q’=40 Time [s] Simulation of head-tail instability Vertical emittance vs. time, for different chromaticities (re= 6 x 1011 m-3 ) Chromaticity vs. e- density, needed to cure head-tail instability. • Chromaticity cures head-tail instability (in agreement w. observations) • Incoherent emittance growth below head-tail instability threshold • numerical noise or physical effect ? CARE-HHH Workshop, 7-8 March 2011

  14. Simulation of head-tail instability (Simulations for LHC @ inj. energy, 10 kicks/turn, Q’=2) • Dipole field regions • Field free regions Relative emittance growth [s-1] • Clear threshold in both planes. • Emittance growthbelow threshold. • Clear threshold in the vertical plane. • No instability in the horizontal plane. CARE-HHH Workshop, 7-8 March 2011

  15. Studies of electron cloud effects Emittance growth below density threshold CARE-HHH Workshop, 7-8 March 2011

  16. Incoherent emittance growth • HEADTAIL-ws (“weak-strong” or “Frozen cloud” approx) • EC potential (z-dependent) computed only at 1st interaction • Used for successive turns • Speeds-up simulations • Valid for study of incoherent effects only! Emittance growth rate vs. # of macroparticles, for 1 (top) and 10 kicks/turn (bottom lines); Simulation results for dynamic (blue) and frozen cloud (magenta) are compared. • dependence # kicks/turn! CARE-HHH Workshop, 7-8 March 2011

  17. Incoherent effects • Non-monotonic dependence on # of kicks 8 1 10 17 Horizontal emittance growth vs # kicks CARE-HHH Workshop, 7-8 March 2011

  18. Incoherent emittance growth • Persisting emittance growth below threshold TMCI • NOT ONLY numerical noise • resonance crossing and trapping or scattering • Combined effect of : • Synchrotron motion • Incoherent tune shift induced by EC (with pinch effect) • Resonances, excited by external nonlinearities or e-cloud itself (in the simulations depend on e-cloud “kicks” number and position) Bunch intensity and bunch length vs. time for the first (red) and last (green) bunch in a train. Measurements in SPS with LHC-type bunch, MDs (coast) 26th Aug’04. (G.Rumolo, CARE-HHH Workshop, March’06, GSI) KEKB, Vertical beam size vs. beam Intensity (H.Fukuma, ECLOUD’02) CARE-HHH Workshop, 7-8 March 2011

  19. 59.4 Qy 59.2 64.4 64.2 Qx Incoherent emittance growth • Tune shiftfunction of z Protons at high synchrotron amplitude can cross a resonance back and forward. z HEAD TAIL • Synchrotron motion Qs≈ 0.006 z’ z HEAD TAIL CARE-HHH Workshop, 7-8 March 2011

  20. Ts Horizontal emittance [x 10-9 m] Time [s] Incoherent emittance growth • When a particle cross a resonance… …its oscillation amplitude varies (cfr. random walk) netincrease of beam rms size and emittance Horizontal action vs. time of a proton at large synchrotron amplitude (from HEADTAIL simulations) E. Benedetto, G. Franchetti, F. Zimmermann, PRL 97, 3, 034801 (2006) CARE-HHH Workshop, 7-8 March 2011

  21. Studies of electron cloud effects EC “wake field” CARE-HHH Workshop, 7-8 March 2011

  22. EC wake field • Wake field depends on pinch effect Wake fields averaged on the transverse beam cross section Wake fields calculated on the axis Different bunch sections at z = 0, at z ≈ 0.4 and at z ≈ 0.8 transversely displaced to compute wake field induced on the following part of the bunch. CARE-HHH Workshop, 7-8 March 2011

  23. Simulation of head-tail instability • Broadband impedance model for the electron cloud K.Ohmi, F.Zimmermann, E.Perevedentsev, Phys. Rev. E 65, 016502 (2002). CARE-HHH Workshop, 7-8 March 2011

  24. Simulation of head-tail instability • Broadband impedance model for the electron cloud Emittance vs. time for different EC densities: comparison between resonator model (dotted line) and HEADTAILPIC module (full line). r = 9x 1011 m-3 r = 3 x 1012 m-3 Vertical emittance [m] r= 6 x 1011 m-3 r = 4 x 1011 m-3 • Fair agreement at the onset of the instability only Time [s] CARE-HHH Workshop, 7-8 March 2011

  25. Studies of electron cloud effects Conclusions CARE-HHH Workshop, 7-8 March 2011

  26. Conclusions • Single-bunch instabilities and emittance growth induced by EC • Simulations above the strong instability threshold • Dependence on different parameters • Thresholdin agreement with analytical models • Chromaticity as a cure for EC-TMC Instability (in agreement with measurements) • Dipole field • Comparison w. broad-band resonator model (agrees at the onset) • Slow emittance growth mechanism • not only numerical noise • resonance crossing and trapping or scattering mechanism • HEADTAIL(weak-strong) and e-MICROMAP successfully benchmarked • Very important to model: • Electron cloud pinch inducing incoherent tune shift • Accelerator lattice, non-linearities and e-cloud location in the ring CARE-HHH Workshop, 7-8 March 2011

  27. Studies of electron cloud effects Back-up Slides CARE-HHH Workshop, 7-8 March 2011

  28. sb Electron cloud evolution • e-motion during the passage of a proton bunch (Gaussian shape): • x << sxharmonic oscillations (~ 2) • x >> sxnon-linear oscillations (x > 12sx, e- perform less then ¼ oscillat.!!!) 3sb 2sb x [m] t=0 t t=tend z Bunch TAIL Bunch HEAD EC phase space at different times: t0=beginning, t1=first peak, t2=first valley, t3=second peak Position vs. time of e- starting from different initial amplitudes. CARE-HHH Workshop, 7-8 March 2011

  29. Parameters LHC @ injection (simulations ‘06) eN=3.75 mm CARE-HHH Workshop, 7-8 March 2011

  30. rmax, DQmax re=0 HEAD (-2 sz) TAIL (-2 sz) Benchmark with space charge code • Benchmark between: HEADTAIL-ws(CERN): field computed with PIC module e-MICROMAP (GSI space-charge code): analytical expression to compute the field • approximate EC distribution • PIC noise avoided • real EC distribution CARE-HHH collaboration w. G.Franchetti, GSI • Simplified model • circular symmetry • Gaussian beam (sb) • EC Gaussian distribution (se= fsb) • EC density linearly increasing in z • linearized synchrotron motion CARE-HHH Workshop, 7-8 March 2011

  31. Benchmark with space charge code • Benchmark with simplified model Relative emittance vs. number of turns, for 2 different EC densities (different DQmax) se= 0.5sb , DQmax=0.04 se= 1sb , DQmax =0.1 e-MICROMAP HEADTAIL HEADTAIL e-MICROMAP • very good agreement ! CARE-HHH Workshop, 7-8 March 2011

  32. Benchmark with space charge code • Analytical model approx: • longitudinally: real EC-density • transversely: Gaussiancloud • sEC(t=0)= sbeam • r pR2 = const • DQmax=0.13 • Benchmark withEC “pinch” Under-estimation of electron charge !!! • qualitatively good agreement CARE-HHH Workshop, 7-8 March 2011

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