US LHC Accelerator Research Program bnl fnal lbnl

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US LHC Accelerator Research Program bnl - fnal- lbnl - slac Electron Cloud -

US LHC Accelerator Research Program bnl - fnal- lbnl - slac Electron Cloud - Status and Plans Miguel A. Furman LBNL [email protected] gov LARP CM 10 Danford’s Inn, 23 -25 April 2008 LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 1

Summary NB: some of these activities not LARP funded § Progress • Benchmark code

Summary NB: some of these activities not LARP funded § Progress • Benchmark code WARP vs. HEADTAIL (emittance evolution) • Benchmark code POSINST (2 D) vs. WARP 2 D and 3 D (build-up) • Ecloud build-up simulation of SPS strip detector measurements § SPS • Dipole build-up simulations • Ecloud feedback simulations • SLAC-CERN effort on test chambers at the SPS ecloud chicane § Ecloud detection via microwave transmission • Experiments at PEP-II - through IR 12 straight (Fall 2007) - through the PEP-II ecloud chicane, variable dipole field (March-April 2008) § Ecloud cyclotron resonances • measurements at the PEP-II ecloud chicane § PS 2 and MI upgrade (time permitting) § Plans LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 2

Benchmark: Warp vs. Headtail-1 no synchrotron motion § LHC – =479. 6 – Np=1.

Benchmark: Warp vs. Headtail-1 no synchrotron motion § LHC – =479. 6 – Np=1. 1 1011 – continuous focusing No dipole field • x, y=66. 0, 71. 54 • x, y=64. 28, 59. 31 – – longitudinal motion OFF ne=1012 – 1014 m– 3 ecloud station/turn: Nstn=10 -100 mimic dipole magnetic field by freezing the x-motion of electrons – same initial distribution of macroprotons with initial offset of 0. 1 y LARP CM 10, BNL, Apr. 2008 e- motion frozen in x Electron Cloud - M. Furman 3

Benchmark: Warp vs. Headtail-2 with synchrotron motion, exaggerated parameters § LHC – =479. 6

Benchmark: Warp vs. Headtail-2 with synchrotron motion, exaggerated parameters § LHC – =479. 6 – Np=1. 1 1011 – continuous focusing • x, y=66. 0, 71. 54 • x, y=64. 28, 59. 31 – – – longitudinal motion ON ne=1012 – 1014 m– 3 ecloud station/turn: Nstn=10 -100 field-free region same initial distribution of macro -protons with initial offset of 0. 1 y LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 4

Benchmark: Warp vs. Headtail-3 with synchrotron motion, reasonable parameters § LHC • =479. 6

Benchmark: Warp vs. Headtail-3 with synchrotron motion, reasonable parameters § LHC • =479. 6 • Np=1. 1 1011 • continuous focusing - Warp ne=1012 m-3 ne=1014 m-3 x, y = 66. 0, 71. 54 x, y, z = 64. 28, 59. 31, 0. 0059 = 3. 47 10 -4 p/p = 4. 68 10 -4 chromx, y = 2, 2 ne=1013 m-3 • ne=1011– 1014 m– 3 • Nstn ecloud station/turn=10 -100 • dipole magnetic field effect: frozen xmotion of electrons • same initial distribution of macroprotons with initial offset of 0. 1 y • threshold 2 -particle model for TMCI: ne=1011 m-3 HEADTAIL ne=1012 m-3 ne=1014 m-3 ne=1013 m-3 ne=1011 m-3 ≈ 6. 4 1011 m– 3 LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 5

Benchmark: Warp build-up vs. POSINST Posinst § ILC build-up simulation – E=5 Ge. V

Benchmark: Warp build-up vs. POSINST Posinst § ILC build-up simulation – E=5 Ge. V – Np=2 1010 Warp 2 -D LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 3 -D 6

Benchmarks conclusions § Good agreement between POSINST and WARP in build-up mode • 2

Benchmarks conclusions § Good agreement between POSINST and WARP in build-up mode • 2 D agrees with 3 D when physical model is 2 D (eg. , dipole field) § Good agreement between WARP and HEADTAIL § For LHC, emittance growth negligible up to ~1000 turns when ne < ~1 e 12 m– 3 (below TMCI threshold) § Next steps: • better lattice description (eg. FODO arc cells instead of constant focusing model) • more self-consistency in beam-ecloud dynamics • further understand qualitative features of results • continue benchmarking incoherent emittance growth against CERN calculations LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 7

SPS strip detector measurements (data from M. Jiménez et al. , Proc. ECLOUD’ 04)

SPS strip detector measurements (data from M. Jiménez et al. , Proc. ECLOUD’ 04) Dipole field Field free 80 e. V Dipole field Heat load efficiency = HLE e-HLE(DF)= 1. 7 × e-HLE(FF) Ee->180 e. V located in the centre faster beam conditioning observed 180 e. V LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 8

SPS chicane strip detector simulation § Conclusions: • Qualitative agreement in e– intensity (dipole

SPS chicane strip detector simulation § Conclusions: • Qualitative agreement in e– intensity (dipole > FF) • Ditto in spatial distib. • Not in energy spectrum § More detailed work desirable (needed? ) LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 9

Ecloud in SPS § E-Cloud in SPS has detrimental effects on LHC injection §

Ecloud in SPS § E-Cloud in SPS has detrimental effects on LHC injection § SPS emittance blowup and intensity limits translate directly to LHC intensity limits • Nominal LHC beams in SPS at edge of e-cloud stability (with chromaticity at maximum) § Future injector upgrade scenarios raise intensity well beyond stability threshold § Possible remedies for SPS E-Cloud instabilities • Vacuum chamber coating to reduce SEY - potentially expensive and requires significant shutdown • Beam scrubbing - Is it enough? • High chromaticity operation - Significant beam losses (reduction in dynamic aperture) - effectiveness uncertain at higher intensities • Active damping - damps coherent component of instability - damping vertical single bunch instability is challenging LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 10

Feedback damper of ecloud instability for SPS § § § SLAC-LBNL NI proposal made

Feedback damper of ecloud instability for SPS § § § SLAC-LBNL NI proposal made at CM 9 (J. Fox and J. Byrd) We are beginning to form a collaboration SLAC: J. Fox, M. Pivi, L. Wang LBNL: J. Byrd, M. Furman, J. -L. Vay BNL: R. de Maria CERN: F. Zimmermann, W. Höfle, E. Chapochnikova LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 11

SPS simulations-1 arc dipole § Assume peak SEY=~1. 3 -1. 4 (based on MI

SPS simulations-1 arc dipole § Assume peak SEY=~1. 3 -1. 4 (based on MI experience) § Then ne~(5 -10)e 11 m– 3 at Nb=1. 1 e 11 LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 12

Preliminary simul. study of SPS EC feedback-1 beam distribution after 300 turns (J. -L.

Preliminary simul. study of SPS EC feedback-1 beam distribution after 300 turns (J. -L. Vay) Feedback cutoff 0. 8 GHz (1/turn) Y (cm) No feedback Y-centroid (cm) centroid Time (ns) Power (a. u. ) Time (ns) LARP CM 10, BNL, Apr. 2008 Frequency (Gz) Electron Cloud - M. Furman Frequency (Gz) 13

Preliminary simul. study of SPS EC feedback-2 § SPS at injection (Eb=26 Ge. V)

Preliminary simul. study of SPS EC feedback-2 § SPS at injection (Eb=26 Ge. V) – =27. 729 – Np=1. 1 1011 – continuous focusing • x, y= 33. 85, 71. 87 • x, y= 26. 12, 26. 185 • z= 0. 0059 – Nstn ecloud station/turn=100 – Initial EC dist. From Posinst LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 14

Preliminary simul. study of SPS EC feedback-3 present conclusions § Idea seems, in principle,

Preliminary simul. study of SPS EC feedback-3 present conclusions § Idea seems, in principle, to work well • Damping the coherent vertical motion has beneficial impact on emittance growth § What next: • Better modeling of the feedback system (bandwidth, gain, noise, separate pickup from kicker, …) • Longer runs • Look at horizontal motion • … LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 15

Electron Cloud Studies for the SPS and LHC 1. GROOVE TESTS IN THE SPS:

Electron Cloud Studies for the SPS and LHC 1. GROOVE TESTS IN THE SPS: A number of electron cloud mitigation test chambers are in preparation for installation in a new dedicated 4 -magnet chicane in the SPS. We are manufacturing groove insertions to fit in one of the test chamber. Collaboration: M. Venturini, M. Furman (LBNL), M. Pivi, L. Wang (SLAC) G. Arduini, E. Chapochnikova, M. Taborelli (CERN). CERN Contact: G. Arduini, E. Chapochnikova. 2. SINGLE-BUNCH INSTABILITY SIMULATIONS: code benchmarking and long term runs for the SPS and LHC. Simulation support for FDBK system (item 3 below) Collaboration: J. -L. Vay (LBNL), M. Pivi, L. Wang (SLAC), F. Zimmermann, W. Höfle (CERN), R. De Maria (BNL) CERN Contact: F. Zimmermann 3. RF MICROWAVE TRANSMISSION: Measurement of the electron cloud density in sections of the SPS by measuring the phase shift of microwave transmitted through the beam line, as recently done at SLAC and CERN. Collaboration: S. De Santis, J. Byrd (LBNL), M. Pivi (SLAC), F. Caspers, T. Kroyer (CERN) CERN Contact: F. Caspers 4. FEEDBACK SYSTEM IN THE SPS: to mitigate electron cloud. See J. Fox & J. Byrd proposal. Balance of FY 08 FY 09 0. 4 0. 6 M&S 29 k$ 40 k$ Travel 7. 5 k$ 12. 5 k$ FTEs (simulation and experimental efforts) LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 16

Electron Cloud Studies for the SPS and LHC § CERN has a chicane at

Electron Cloud Studies for the SPS and LHC § CERN has a chicane at the SPS for ecloud tests § Goal is to have 4 types of chamber tests: • St. chamber (reference) • Clearing electrodes • Carbon coating • NEG (Ti. Zr. V) coating § There is a joint CERN-SLAC effort to manufacture 1 -mm grooved liner to insert in the chicane chamber § SLAC already manufactured a 2 -mm Al grooved chamber (backup option for tests) § No SLAC $$$ allocated for this project • But EMEGA Corp. has offered to do it if we pay for the tools § Goal is 1 prototype St. grooved insertion 20” long • Ready in July 2008, installed summer 2008 LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 17

SPS grooves requirements Triangular Grooves Groove Width 0. 35 mm Groove Depth 1 mm

SPS grooves requirements Triangular Grooves Groove Width 0. 35 mm Groove Depth 1 mm Overall Depth 2 mm Groove Length 0. 5 m Taper Angle 20 deg Radius at Top & Bottom 0 (< 80 mm) LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 18

Manufacturing option for 1 mm depth: metal folding Metal Folding: Form multiple folds. [EMEGA

Manufacturing option for 1 mm depth: metal folding Metal Folding: Form multiple folds. [EMEGA Company, USA] LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 19

Aluminum triangular groove, SLAC. Depth 1. 9 mm, Opening angle 20 o, radius top

Aluminum triangular groove, SLAC. Depth 1. 9 mm, Opening angle 20 o, radius top 95 um, radius valley 144 um Tip Valley • 1 mm depth stainlees steel groove insertion under development: CERN/SLAC • Back-up for SPS: 2 mm Aluminum+coating triangular grooves (pictures above), manufactured by SLAC. Extrusion manufacturing limited by the groove sharpness requirements. LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman Lanfa Wang, SLAC 20

Manufacturing options for 1 mm depth: razor blades LARP CM 10, BNL, Apr. 2008

Manufacturing options for 1 mm depth: razor blades LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 21

Manufacturing options for 1 mm depth: razor blades Brazed-up Assembly: Use individual razor type

Manufacturing options for 1 mm depth: razor blades Brazed-up Assembly: Use individual razor type foil blades LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 22

Mfg. Options § Extrusion: Very small radii at top & bottom of grooves are

Mfg. Options § Extrusion: Very small radii at top & bottom of grooves are difficult to mfg § Machining: Mill multiple slots in solid material § Metal Folding: Form multiple folds § EDM: Small radii are beyond normal tolerances § Brazed-up Assembly: use individual razor type foil blades § Isostatic Pressing or Metal Injection Molding: uses powdered metal & binders which would probably would not be suitable for vacuum usage. Also have difficulty in forming small radii LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 23

Microwave Transmission Through an Electron Cloud § Original idea from Caspers and Kroyer (CERN)

Microwave Transmission Through an Electron Cloud § Original idea from Caspers and Kroyer (CERN) • Initially tried at the SPS § Experiment recently carried out twice at PEP-II: • SLAC-LBNL-CERN collaboration: • Through IR 12 straight section (L~50 m) (fall 2007) - De Santis, Byrd, Caspers, Krasnykh, Kroyer, Pivi and Sonnad, PRL 100, 094801 (7 March 2008) • Through the ecloud chicane, with adjustable dipole field (March 2008) - Paper in progress § Fundamental idea: ecloud causes a phase shift of the transmitted microwave • Phase shift Df is prop. to aver. ne in the region LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 24

Analysis and simulations § Dispersion relation: =pipe cutoff angular freq. =plasma freq. of ecloud:

Analysis and simulations § Dispersion relation: =pipe cutoff angular freq. =plasma freq. of ecloud: § Phase shift per unit length (relative to ne=0): § Choose as close as possible to c Simulation with VORPAL (Tech. X) fc=2 GHz LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 25

Experiment § PEP-II IR 12 straight section § L=~ 50 m § Several quads

Experiment § PEP-II IR 12 straight section § L=~ 50 m § Several quads plus an ecloudcontrolling solenoid § Solenoid was switched on and off § Beam gap (~30 m) causes ecloud to clear with frequency=frev sidebands when Solenoid is off LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 26

Experiment at =2. 149925 GHz frev=136 k. Hz (from De Santis et. al. ,

Experiment at =2. 149925 GHz frev=136 k. Hz (from De Santis et. al. , PRL 100, 094801 (7 March 2008)) LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 27

Conclusions From Df and analytic LARP CM 10, BNL, Apr. 2008 Electron Cloud -

Conclusions From Df and analytic LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 28

Propagation in a dipole field: PEP-II chicane March-April 2008 § Electrons in a dipole

Propagation in a dipole field: PEP-II chicane March-April 2008 § Electrons in a dipole field: VORPAL simul. (Tech. X) § If there is a magnetron resonance with a large Df § R=4. 45 cm § TE 11 mode: =12. 266 Grad/s § Bres= me /e=697. 4 G experiment Bres multiply by 2296 to get Gauss LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 29

Microwave transmission: conclusions § Inexpensive, relatively easy way of measuring average ecloud density §

Microwave transmission: conclusions § Inexpensive, relatively easy way of measuring average ecloud density § Advantages: • Direct average volumetric density measurement • In a local region of the machine (~a few to ~10’s of meters) • Parasitic • In real time • Relatively simple § What’s next: • Will repeat at SPS LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 30

Ecloud cyclotron resonances: new effect e– flux on chamber surface simul. meas. § Resonances

Ecloud cyclotron resonances: new effect e– flux on chamber surface simul. meas. § Resonances 1 st seen in ILCDR build-up simulations (C. Celata) § Predicted and quickly seen at PEP-II § Collaboration: • SLAC: M. Pivi, J. Ng, L. Wang, C. Spencer • LBNL: C. Celata, M. Furman, J. -L. Vay, M. Venturini, K. Sonnad LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 31

Ecloud cyclotron resonances simulated e– density § We understand the basic physical mechanism §

Ecloud cyclotron resonances simulated e– density § We understand the basic physical mechanism § Resonances need: § But agreement with expt. is imperfect: • Low B fields (fc tb<~20 -40), and • Spacing is perfect • Short bunches ( c t<~a few) • But there is a shift in the location of peaks • 2 D vs. 3 D effects? • Instrumental issues? LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 32

PEP-II ecloud chicane in e+ beam (M. Pivi) § § 4 dipoles, tunable B-field

PEP-II ecloud chicane in e+ beam (M. Pivi) § § 4 dipoles, tunable B-field (1. 5 k. G max), R=4. 45 cm 2 chambers (1 covers 3 dipoles, the 2 nd covers 1) Multiple detectors Surfaces: 1) bare Al and 2) Ti. N-coated • A grooved surface and a NEG-coated surface were eliminated by budget § Parasitic operation (typ. Nb=6 e 10, Eb=3. 1 Ge. V, z=1. 15 cm, tb=4. 2 ns) § PEP-II stopped for good on April 7 th, 2008 • Chicane will be moved to CESR-TA LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 33

Ecloud resonances: possible implications for LHC and injectors § Resonances introduce a correlation between

Ecloud resonances: possible implications for LHC and injectors § Resonances introduce a correlation between B fields and the EC density – But, LHC bunch way too long to directly excite cyclotron resonances § However: there is a possible related effect: “magnetron effect” (F. Caspers) § Electron cyclotron motion may be excited by beam-induced wake fields – “largest microwave oven ever built” § CERN is encouraging us to study the effect (F. Zimmermann and F. Caspers, ongoing email exchanges) § What’s next: – look at basics, eg. : energy stored in wake fields, time constants, … – no plans for simulations at this point LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 34

PS 2 simulated ecloud build-up C=1256 m, tb=25 ns, Nb=4 e 11, z=0. 935

PS 2 simulated ecloud build-up C=1256 m, tb=25 ns, Nb=4 e 11, z=0. 935 m (F. Z. psplusetcparameters option 2) density heat load § Contrasts between PS 2 and MI upgrade: • PS 2 significantly above Gröbner multipacting condition, at least for the 25 ns option • MI upgrade, even at 3 e 11/bunch, significantly below • But ecloud density roughly comparable § MI ecloud measurement efforts have been valuable § What’s next: better characterization of ecloud distribution and intensity in PS 2 LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 35

FNAL Main Injector C=3319. 4 m, tb=19 ns, Nb=(0. 6– 1)e 11, z=0. 19

FNAL Main Injector C=3319. 4 m, tb=19 ns, Nb=(0. 6– 1)e 11, z=0. 19 m • For this exercise, take measured RFA signal only at Eb=60 Ge. V • this is the peak signal for all cases § Field-free region, R=7. 3 cm, St. § To convert RFA voltage signal to e– flux (R. Zwaska): Measured e– flux at RFA vs. Nb for various fill patterns (Eb=60 Ge. V all cases; extracted from I. Kourbanis report, ~26 Aug. 2007) • assume 1 m. A/V • divide by 1. 5 cm 2 - this assumes 30% area efficiency LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 36

MI: e– flux at wall vs. peak SEY at Eb=60 Ge. V • Nicely

MI: e– flux at wall vs. peak SEY at Eb=60 Ge. V • Nicely clustered set of solutions for dmax – Indicates consistency in the model and the measurements – Conclude: dmax~1. 25– 1. 35 (M. Furman, CBP-TN-387, Nov. 07) • Simulation then implies ne~1010 -1011 m– 3 • A mystery remains: simulations show insensitivity to Eb • Measurements are sensitive to Eb • Qualitatively similar to SPS! (G. Electron Arduini, Proc. ECLOUD’ 04) Cloud - M. Furman LARP CM 10, BNL, Apr. 2008 37

MI upgrade goal: Nb x 5 relative to today simulation of ecloud density vs.

MI upgrade goal: Nb x 5 relative to today simulation of ecloud density vs. Ntot for frf=53 and 212 MHz linear § Present: Nb=6 e 10, f. RF=53 MHz, M=548 (no. of bunches) § Upgrade goal: Nb=3 e 11, or Ntot=1. 64 e 14 LARP CM 10, BNL, Apr. 2008 log § Exercise: what happens if – f. RFx 4, Nb Nb/4, M Mx 4 ( preserve Ntot)? § Answer: 212 MHz clearly better than 53 MHz: – Threshold in Ntot roughly doubles Electron Cloud - M. Furman 38

Long-Term Simulation of Space-Charge-Driven Dynamic Emittance Exchange • • • MARYLIE/IMPACT code (3 D

Long-Term Simulation of Space-Charge-Driven Dynamic Emittance Exchange • • • MARYLIE/IMPACT code (3 D parallel) Ramp longit. tune from below to above resonance Protons, sp. ch. tune shift ~0. 1– 0. 3 Propagate beam through a linac – 1 linac period=35 deg phase adv. – Constant focusing lattice approx. Check scaling law by I. Hofmann and G. Franchetti, PAC 07 • • 106 macroparticles, 643 grid ~1. 3 x 106 space-charge kicks, 32 hrs on 64 proc. (IBM/SP 5) • LBNL would like to participate in a joint simulation effort on PSB and PS 2 with other institutions: • Space-charge effects • Ecloud • Traditional impedance/instabilities • Longstanding collaboration with GSI • R. Ryne, J. Qiang, M. Furman LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 39

Status summary and future goals 1. 2. 3. 4. 5. 6. 7. 8. 9.

Status summary and future goals 1. 2. 3. 4. 5. 6. 7. 8. 9. Injector upgrade heat load: (*) continuing Effects from ecloud on beam: (*) Benchmarks: POSINST-WARP and WARP-HEADTAIL: mostly done, need to refine lattice model • 3 D self-consistent simulations: challenging; continuing • Lorentz-boosted frame method: shows good agreement with QSM in benchmarks • Effects of ionized gas on heat load and beam: not started Analyze SPS data, esp. measured heat load and e– spectrum: (*) started; need better benchmarks against expts. Apply Iriso-Peggs maps to LHC: (–) delayed or deleted Simulate e-cloud for RHIC detectors and benchmark against measurements: (**) nothing to report; e– detectors broken Simulate ecloud for LHC IR 4 “pilot diagnostic bench: ” not started ecloud suppression at SPS by feedback: • Simulations: started ccloud suppression at SPS via specialized chambers: new proposed activity Requested additional funding for items 8 and 9 is spelled out on slide 16 (*) endorsed by CERN AP group (**) endorsed by CERN vacuum group LARP CM 10, BNL, Apr. 2008 (–) no longer endorsed by CERN AP group Electron Cloud - M. Furman 40

Additional material LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 41

Additional material LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 41

SPS simulations-2 arc dipole case LARP CM 10, BNL, Apr. 2008 Electron Cloud -

SPS simulations-2 arc dipole case LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 42

MI: e– flux at wall vs. peak SEY at Eb=60 Ge. V • Nicely

MI: e– flux at wall vs. peak SEY at Eb=60 Ge. V • Nicely clustered set of solutions for dmax • Indicates consistency in the model and the measurements • Conclude: dmax~1. 25– 1. 35 (St. ) (M. Furman, CBP-TN-387, Nov. 07) LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 43

Preliminary simul. study of SPS EC feedback -1 § SPS at injection • =27.

Preliminary simul. study of SPS EC feedback -1 § SPS at injection • =27. 729 • Np=1. 1 1011 • continuous focusing - x, y= 33. 85, 71. 87 - x, y= 26. 12, 26. 185 - z= 0. 0059 • Nb ecloud station/turn=10 • Initial EC dist. From Posinst LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 44

Effects of ecloud: e growth in LHC beam code WARP (J. -L. Vay) §

Effects of ecloud: e growth in LHC beam code WARP (J. -L. Vay) § one-turn e growth simulation § E=450 Ge. V, Nb=1. 1 x 1011, single bunch, 1 -turn fractional emittance growth vs. Nstn for 3 values of the ecloud density • Code WARP, parallel, 3 D calc. - Quasi-static approx. mode (QSM) - AMR, parallel 8 processors • Beam transfer maps from EC station to next - Up to 3000 stations • Actual LHC chamber shape • Constant focusing approx. • Electrons allowed to move vertically only • No synchr. oscillations • Beam launched offset by 0. 1 y § Conclusion: need to resolve l to reach convergence, as expected (ie. , # of EC stations > tune) LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 45

Effects of ecloud: e growth in LHC beam 1 -turn e growth vs. ne

Effects of ecloud: e growth in LHC beam 1 -turn e growth vs. ne § Emittance growth simul. § Same conditions as previous slide • except Nstn=3000=fixed § Conclusion: • De/e ne as ne-->0 LARP CM 10, BNL, Apr. 2008 1 -turn fractional emittance growth vs. ecloud density (Nstn=3000) Electron Cloud - M. Furman 46

Ecloud build-up in PS 2 at 50 Ge. V vs. chamber radius § Looked

Ecloud build-up in PS 2 at 50 Ge. V vs. chamber radius § Looked only at a bending dipole § Vary pipe radius keeping all else fixed heat load § Nb=4 x 1011 for tb=25 ns, Nb=5. 4 x 1011 for tb=50 ns; other parameters as specified in LUMI 06 by FZ § Averages taken over 2 trains § PS+ also looked at § Conclusions: • Low heat load wants small radius • Low e– density wants large radius • Beam-induced multipacting condition broadens and gets shifted to lower radius relative to the impulse approximation (Gröbner, ) LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman density 47

Ecloud build-up in PS 2 at 50 Ge. V (contd. ) vs. chamber radius

Ecloud build-up in PS 2 at 50 Ge. V (contd. ) vs. chamber radius § e– flux at the walls (Je) § Conclusions: • Ratio Je/ne in good agreement with analytic expectation as r-->0: (R. Zwaska) LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 48

Furthermore… § Flux/density consistent with simple theory, as expected • Je/re≈a/(2 tb) (R. Zwaska)

Furthermore… § Flux/density consistent with simple theory, as expected • Je/re≈a/(2 tb) (R. Zwaska) - This becomes exact in the limit a 0 § From Je results (previous slide), conclude ne~1010 -1011 m– 3 LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 49

Quasi-static mode (“QSM”) 2 -D slab of electrons 3 -D beam lattice quad drift

Quasi-static mode (“QSM”) 2 -D slab of electrons 3 -D beam lattice quad drift s s 0 bend drift 1. 2 -D slab of electrons (macroparticles) is stepped backward (with small time steps) through the frozen beam field • 2 -D electron fields are stacked in a 3 -D array, 2. push 3 -D proton beam (with large time steps) using • maps - “WARP-QSM” - as in HEADTAIL (CERN) or • Leap-Frog - “WARP-QSL” - as in QUICKPIC (UCLA/USC). LARP CM 10, BNL, Apr. 2008 Electron Cloud - M. Furman 50