1 / 48

Emittance growth induced by electron cloud in proton storage rings

Dottorato in Energetica, XVIII ciclo. Emittance growth induced by electron cloud in proton storage rings. Elena Benedetto. PhD coordinator: Prof. Bruno Panella. Tutors: Prof. Gianni Coppa, Dr. Frank Zimmermann. Torino, 7 th April 2006. Contents. Introduction

fleur-hooper
Download Presentation

Emittance growth induced by electron cloud in proton storage rings

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Dottorato in Energetica, XVIII ciclo Emittance growth induced by electron cloud in proton storage rings Elena Benedetto PhD coordinator: Prof. Bruno Panella Tutors: Prof. Gianni Coppa, Dr. Frank Zimmermann Torino, 7th April 2006

  2. Contents • Introduction • The Electron Cloud issue for LHC • Electron cloud evolution in the bunch potential • Single-bunch instabilities due to electron cloud • Incoherent emittance growth • Conclusions and outlooks Emittance growth induced by electron-cloud in proton storage rings

  3. CERN accelerator complex • The LHC (Large Hadron Collider) at CERN (Geneva), will provide proton-proton collisions at 14 TeV energy. • LHC injector chain: • Duoplasmatron source → 100keV • linear accelerator LINAC2 → 50 MeV • PS-Booster → 1.4 GeV • PS (Proton Synchrotron) → 26 GeV • SPS (Super Proton Synchrotron): • C= 6.911 km • 26 GeV → 450 GeV • 2 beams in separated vacuum chambers • collisions in 4 points • C= 26.659 km • 450 GeV → 7 TeV • Measurements are done in SPS Emittance growth induced by electron-cloud in proton storage rings

  4. The beam is not continuous, but it is made ofBUNCHES. Intro - Accelerator components • Dipoles: bend protons on the curved trajectory • Quadrupoles: focus the beam. • RF cavities: accelerate and bunch the beam. Emittance growth induced by electron-cloud in proton storage rings

  5. R u = x,y y x s z’ z HEAD TAIL Intro – Particles motion in a circular accelerator • Betatron motion (transverse plane): • induced by the quadrupoles ~ harmonic oscillations around the ideal orbit Qu= Betatron tune = # oscillations /turn~ 60 (LHC) • Synchrotron motion (longitudinal plane): • bunch particles mix longitudinally due to the RF voltage characteristics Qs=Synchrotron tune≈ 0.006 (LHC) Emittance growth induced by electron-cloud in proton storage rings

  6. x’ einit einit x’ x x efinal Intro - Keywords • Instabilities due to collective effects: • Interactions between cloud electrons and beam protons treated via their electro-(magnetic) fields • Emittance growth: • the emittance (beam dimensions in the transverse phase space) in an ideal machine is invariant (with time and position in the ring) • Interactions with electron cloud (EC) induce emittance growth Need to keep beam emittance small Aellipse= pe ebeam emittance smaller beam size higher collision rate (luminosity) Emittance growth induced by electron-cloud in proton storage rings

  7. The Electron Cloud issue • In a proton (positron) accelerator vacuum chamber • Build-up of electron cloud (EC) • from “a few” primary e- (e.g. photoelectrons, from residual gas ionization…) • p+ bunch accelerate e- • e- impact on the wall and extract secondary e- • avalanche production • up to a saturation level (Courtesy F.Ruggiero) (depends on surface properties, beam intensity, bunch spacing,…) Concern for beam stability and heat deposition on the beam screen Emittance growth induced by electron-cloud in proton storage rings

  8. The Electron Cloud issue • Instabilities, beam loss and beam-size blow-up due to electron cloud observed at CERN PS and SPS, KEKB LER, and PEP II; a concern for LHC KEKB, Vertical beam size vs. Beam Intensity (H.Fukuma, ECLOUD’02) First bunches Last bunches Beam losses after few ms in SPS, affecting last bunches of a batch (G.Arduini, ‘03) Emittance growth induced by electron-cloud in proton storage rings

  9. Studies of electron cloud effects HEADTAIL code Emittance growth induced by electron-cloud in proton storage rings

  10. Simulations – HEADTAIL code HEADTAIL(written at CERN in 2002, by G.Rumolo and F.Zimmermann) • EC localized in a finite number Nk of interaction points (IPs) around the ring. y y x x z z (Nk=3) s2 s1 R y • EC density as input. z s3 x • 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 a PIC module: • Matrix to transport protons between IPs: • e- perturbed by p+ field • p+ get a kick Du by e- field Emittance growth induced by electron-cloud in proton storage rings

  11. Vertical emittance vs. time, for different number of IPs 5 IPs 3 IPs Vertical emittance [m] 2 IPs 7 IPs 6 IPs 1 IP 4 IPs 8 IPs Time [s] Simulations – HEADTAIL code • Implemented new features: • Electrical boundary conditions of a perfect conductor. • Position of the IPs and beam-size variation at the IP. • Initial electron tranverse distribution • non-uniform (Gaussian profile, stripes,…) • ‘Frozen cloud’ model • same EC over successive turns • for studies of incoherent effects • HEADTAIL–FODO • real accelerator structure • Sensitivity studies. • Successful benchmark with other codes Emittance growth induced by electron-cloud in proton storage rings

  12. Studies of electron cloud effects • Electron cloud evolution during a bunch passage • Effects on the beam below & above EC density threshold “Strong head-tail instability” for e- cloud (re > rthresh) re= 3.5 x 1011 m-3 Incoherent emittance growth (re < rthresh) re= 2 x 1011 m-3 re= 1 x 1011 m-3 (studies for LHC @ injection) Emittance growth induced by electron-cloud in proton storage rings

  13. Studies of electron cloud effects Electron cloud evolution Emittance growth induced by electron-cloud in proton storage rings

  14. y x z sEC R s=0 Electron cloud evolution • EC density evolution in the transverse plane, during the passage of a bunch click on the picture to see animation Electrons accumulate (“pinch”) in the bunch centre. Emittance growth induced by electron-cloud in proton storage rings

  15. t=0 t t=tend Bunch TAIL Bunch HEAD z 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 sb Position vs. time of e- at different initial amplitude (0.5sb,…,3sb). we depends on the initial amplitude. x [m] Emittance growth induced by electron-cloud in proton storage rings

  16. t=tend t=0 Bunch HEAD Bunch TAIL z t t=tend t=0 Bunch TAIL Bunch HEAD z Electron cloud evolution Log [re(x,z) [m-3]] • EC evolution at the center of the bunch (x,y)=(0,0) • peaks (linear e-) • density increase (e- at x >> sx) x/sb re(t)|r=0 EC density in the horizontal plane vs. time Emittance growth induced by electron-cloud in proton storage rings

  17. Electron cloud in dipoles • ~80% of SPS circumference covered by dipoles • more e- multipacting than in field free regions • expect similar situation for LHC @ injection The EC behavior in dipoles determines the instability characteristics • typically in a dipole, electrons populate 2 vertical stripes Horizontal axis Electron flux in a strip detector installed in a dipole magnet during the MD 26Aug 04, with LHC type Coast beam @26GeV Time [s] Emittance growth induced by electron-cloud in proton storage rings

  18. 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 in dipole regions of SPS y/sy x/sx Emittance growth induced by electron-cloud in proton storage rings

  19. Studies of electron cloud effects Head-tail instability Emittance growth induced by electron-cloud in proton storage rings

  20. Head-tail instability • During the bunch passage, electrons are accumulated around beam center • If there is offset between head and tail: • tail feels transverse electric field created by head • tail become unstable • Particles mix longitudinally →also head can become unstable (above threshold) (Courtesy G.Rumolo) t = 0 s t = 0.02 s t = 0.04 s Head-tail motion and emittance growth y [m] Head-tail instability, from simulations: Snapshot of the vertical bunch profile (bunch centroid and rms size) at different time steps. z [m] Emittance growth induced by electron-cloud in proton storage rings

  21. 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 Emittance growth induced by electron-cloud in proton storage rings

  22. Q’ Q’=2 Q’=15 Q’=10 Vertical Emittance [m] Q’=20 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. electron density, to cure head-tail instability. CHROMATICITY: machine parameter, introduces spread in the particles betatron tune. • Chromaticity cures head-tail instability (in agreement w. observations) • Incoherent emittance growth below head-tail instability threshold • numerical noise or physical effect ? Emittance growth induced by electron-cloud in proton storage rings

  23. 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 E.Benedetto et al. , Phys. Rev. ST Accel. Beams 8, 124402 (2005) Time [s] • Study of conventional head-tail instability using HEADTAIL code Emittance growth induced by electron-cloud in proton storage rings

  24. Simulation of head-tail instability • Simulations in dipole field regions(for LHC at inj) Emittance doubling time 1s Relative emittance growth [s-1] 1min 1h • Clear threshold (in the vertical plane). • No instability in the horizontal plane. • Slow emittance growth below instability threshold. Emittance growth induced by electron-cloud in proton storage rings

  25. Studies of electron cloud effects Emittance growth below density threshold Emittance growth induced by electron-cloud in proton storage rings

  26. Qy Qx Incoherent emittance growth • NOT only numerical noise, BUT resonances crossing or trapping • transverse motion ~ harmonic oscillator • Qx(y) oscillations per turn • Need to avoid resonance lines EC (and other collective effects) can induce proton tune shift and touch resonances Tune diagram, with resonances up to 5th order. In red, LHC working point (Qx=64.28, Qy=59.31) Emittance growth induced by electron-cloud in proton storage rings

  27. DQu= tune shift 59.4 Qy 59.2 Qx 64.4 64.2 Incoherent emittance growth EC induced tune shift: • transverse motion (~ harmonic oscillator) + linear force (or linearized) in u: • perturbed motion described by oscillator with tune: • EC force (from Gauss theorem) TUNE SHIFT proportional to EC density (function of z) Emittance growth induced by electron-cloud in proton storage rings

  28. 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 (longitudinal) particles motion Qs≈ 0.006 z’ z HEAD TAIL Emittance growth induced by electron-cloud in proton storage rings

  29. Ts Incoherent emittance growth • When a particle cross a resonance… …its oscillation amplitude varies (cfr. random walk) netincrease of beam rms size and emittance Horizontal oscillation amplitude vs. time of a proton at large synchrotron amplitude (from HEADTAIL simulations) E.Benedetto et al., submitted to Phys. Rev. Lett. (feb ‘06) Emittance growth induced by electron-cloud in proton storage rings

  30. Incoherent emittance growth • Effect of synchrotron motion • without synchrotron motion emittance growth stops • dependence on # IPs(excited different resonances) Horizontal emittance [x 10-9 m] Emittance vs. time, from simulations, w. and w/o synchrotron motion 7.82 Time [s] • Successfully benchmarked with code for space-charge studies (where a similar phenomenon was firstly discussed) Emittance growth induced by electron-cloud in proton storage rings

  31. Studies of electron cloud effects Conclusions Emittance growth induced by electron-cloud in proton storage rings

  32. Conclusions • Single-bunch instabilities and emittance growth induced by EC studied by means of simulations and analytical approach • HEADTAIL codebenchmarked and new features added • Electron evolution in bunch potential studied • Simulations above the strong instability threshold • dependence on different parameters • thresholdin agreement with analytical models • chromaticity as a cure for EC (in agreement with measurements) • comparison w. broad-band resonator model (agrees at the onset) • behavior of electron cloud in dipole field regions • accelerator structure modeled Emittance growth induced by electron-cloud in proton storage rings

  33. Conclusions • Slow emittance growth mechanism understood • not only numerical noise • resonance crossing and trapping mechanism • benchmarked with analytical code • Modeling real machine and EC characteristics • important both above & below instability threshold • HEADTAIL-FODO has been developed (for incoherent effects studies) Emittance growth induced by electron-cloud in proton storage rings

  34. Acknowledgements CERN/AB/ABP, in particular: G.Rumolo HEADTAIL code development and simulations F.Ruggiero electron cloud studies D.Schulte code development and simulations G.Arduini measurements and observations in SPS E.Metral TMC Instabilities H.Burkhardt observations in SPS and TMC Instabilities G.Franchetti (GSI)Incoherent effects, resonance crossing mechanism E-CLOUD community, in particular: K.Ohmi (KEK)code benchmark, incoherent & coherent emittance growth A.Gahlam, T.Katzouleas (USC & UCLA)plasma simulations, code benchmark Emittance growth induced by electron-cloud in proton storage rings

  35. Studies of electron cloud effects Additional material Emittance growth induced by electron-cloud in proton storage rings

  36. EC build-up • EC Build-up (Courtesy D.Schulte) Simulations of EC build-up along 2 bunch trains of LHC-beam in SPS dipole regions. (SEY=1.3, r = 1, nominal bunch spacing = 25ns, gap of 225ns between the trains). Emittance growth induced by electron-cloud in proton storage rings

  37. Strategies to cure EC • Reduce primary electrons • Improved vacuum • Antechambers or “sawtooth surface” • Reduce electron Secondary Emission Yield • Surface coating with low SEY films • Grooved surface • Scrubbing process • circulating beam induces multipacting and clean the surface • Modify beam structure (e.g., superbunches) • Reduce EC build-up • Reduce beam intensity • Increase bunch spacing • Solenoids to avoid e- to reach the beam center (at KEK) • Clearing electrodes • Cure head-tail instability • Increase chromaticity, octupoles, synchrotron tune; build ultrafast feedback • Cure incoherent emittance growth • Change working point (Qx, Qy) Emittance growth induced by electron-cloud in proton storage rings

  38. Log [re(x,z) [m-3]] x/sb HEAD TAIL z x [m] re(z)|r=0 z/sz HEAD TAIL z/sz Electron cloud evolution e- motion during the passage of a Gaussian bunch: • x < ~ sxharmonicoscillations (~ 4) • x >> sxnon-linear oscillations (x >12sx, e- perform less then ¼ oscillat.) EC density at (x,y=0,0) Position vs. time of e- at different initial amplitude (0.5sb,…,3sb). we depends on the initial amplitude. re,r=0 =re(z)→ EC density at the bunch center is a function of the longitudinal position in the bunch. Emittance growth induced by electron-cloud in proton storage rings

  39. Benchmark codes • PEHTS(KEK) • macroparticles • single kick approximation • QuickPIC(USC, UCLA +CERN collaboration) • originally PIC code for plasma accelerators • adapted to stydy of EC in circular rings • parallel capability • can deal with >2000 “kicks”/turn and/or perform long-term simulations Emittance growth induced by electron-cloud in proton storage rings

  40. Benchmark with QuickPIC Horizontal (right)and vertical(left)beam size vs. time. For purpose of comparison in both HEADTAIL and QuickPIC the electron cloud has been modeled using 1 IP per turn. Collaboration with Ali Ghalam and Tom Katsouleas QuickPIC HEADTAIL Horizontal Beam Size [m] HEADTAIL Vertical Beam Size [m] QuickPIC Time [s] Time [s] Emittance growth induced by electron-cloud in proton storage rings

  41. Benchmark with PEHTS Horizontal emittance vs. time, for LHC at injection (re= 6 x 1011 m-3). Comparison of HEADTAIL and PEHTS results for various grid sizes, considering a single IP. Emittance growth induced by electron-cloud in proton storage rings

  42. x 10-7 re= 9 x 1011 m-3 re= 6 x 1011 m-3 e-c in field free regions re= 9 x 1011 m-3 e-c in dipole regions re= 6 x 1011 m-3 Simulation of head-tail instability Simulations of EC in a dipole field • e-follow vertical field lines (→ strong field approximation), horizontal motion is frozen • e- concentrated in two vertical stripes (from measurement) (for SPS w. LHC type beam @26GeV) Emittance vs. time. The electron cloud is assumed to be in field free region (uniform distribution) or in the dipoles (stripes). Emittance growth induced by electron-cloud in proton storage rings

  43. Incoherent emittance growth • “resonance crossing” DIPENDENCE ON # IPs with 10 IPs along the ring (blu and purple) less emittance growth 10 IPs excite fewer low order resonance HEADTAIL simulations. Emittance vs. time, with and w/o synchrotron motion Emittance growth induced by electron-cloud in proton storage rings

  44. rmax, DQmax • HEADTAIL*: • field computed with PIC module • . • . • real EC distribution re=0 HEAD (-2 sz) TAIL (-2 sz) • GF CODE (G.Franchetti, GSI): • analytical expression to compute the field • . • . • simplified EC distribution • PIC noise avoided Incoherent emittance growth • 2 codes Benchmark: • Simplified model • circular symmetry • Gaussian beam (sb) • linearized synchrotron motion • EC Gaussian distribution (se= f sb) • EC density linearly increasing in z * To spead up simulations in HEADTAIL, “weak-strong” approximation implemented: • EC potential (z-dependent) computed only during 1° bunch passage • used for subsequent interactions • OK! for low EC densities (only incoherent effects) Emittance growth induced by electron-cloud in proton storage rings

  45. se= 1 sb DQmax =0.1 se= 0.5 sb DQmax =0.04 Crescita “lenta” di emittanza – Simulazioni - • Benchmark with simplified model Relative emittance vs. number of turns, for 2 different EC densities (different DQ) GF-CODE HEADTAIL GF-CODE HEADTAIL Very good agrement!!! Emittance growth induced by electron-cloud in proton storage rings

  46. F D F D F F O O O O FODO lattice implementation • 8 e- kicks / cell • transport matrices forQuad(F,D) or Drift / Bends(O) • 108 FODO cells of SPS • Computing time → Weak-strong HEADTAIL Emittance growth induced by electron-cloud in proton storage rings

  47. Simulations with the FODO lattice Only a few ms (~250 turns) • Slow emittance growth depends on the e- density ZOOM Emittance growth induced by electron-cloud in proton storage rings

  48. Incoherent emittance growth ??? • Bunch shortening due to EC Bunch intensity vs. time for the first (red) and last (green) bunch in a train Bunch length vs. time for the first (red) and last (green) bunch in a train. Measurements in SPS with LHC-type bunch during Aug’04 MDs (in coasting mode), Courtesy G.Rumolo Emittance growth induced by electron-cloud in proton storage rings

More Related