(1) e cloud build up Electron-Cloud Theory & Simulations Frank Zimmermann,, SL/AP distribution, line & volume density, dose ( scrubbing), energy spectrum, LHC heat load, various fields (dipole, solenoids, electrodes,...) (2) coupled-bunch instability bunch-to-bunch wake, growth rate (3) single-bunch instability (e.g., in SPS) single-bunch wake, threshold, growth rate, coherent tune shift (4) incoherent tune spread (5) synergetic effects: beam-beam, space-charge, impedance
1965 INP PSR transverse instability & beam loss 1971 ISR e-p, 1977 beam-induced multipacting 1988 LANL PSR vertical instability & beam loss 1989 KEK PF multibunch instability since 1996 BEPC IHEP-KEK collaboration 1997 LHC crash program launched at 1997 CESR anomalous anti-damping explained 1997/98 APS e cloud studies start since 1998 SPS e cloud with LHC beam 2000 PS e cloud with LHC beam since 1999 e cloud at KEKB and PEP-II since October 20 evidence for e cloud at RHIC
Electron Build Up e production mechanisms: residual gas ionization; typical rate d 2 λ e /(ds dt) 5 10 11 e m 1 s 1 synchrotron radiation and photo-emission; typical rate d 2 λ e /(ds dt) 5 10 18 e m 1 s 1 secondary emission: (1) true secondaries & (2) elastically reflected or rediffused; exponential growth
ENERGY DISTRIBUTION OF SECONDARY ELECTRON EMITTED BY COPPER 1000.00 900.00 800.00 700.00 Ep= 10 ev Ep=30 ev Ep= 100 ev Ep=300 ev Ep=550 ev NORMALISED INTENSITY 600.00 500.00 400.00 300.00 200.00 100.00 0.00 0.00 0.20 0.40 0.60 0.80 1.00 1.20 ENERGY (norm.) Normalized secondary electron energy distribution for conditioned copper, revealing three components: true secondaries (E E p ), elastically scattered (E E p ) and rediffused (in between). [N. Hilleret, 20]
Secondary emission yield for perpendicular incidence vs. primary electron energy with and w/o elastically scattered electrons. Parametrization based on measurements [Noel Hilleret, 20]. Two parameters: δ max and ɛ max.
Initial energy spectrum of true secondaries as modelled in 1999/2000 compared with new parametrization by Noel Hilleret, October 20. Now ρ 0 for E e 0.
0 0 1 1 γ LOST or REFLECTED γ γ 01 01 200 ev 2 kev 10 ev 5 ev 5 ev 10 ev 0 0 1 1 200 ev 2 kev secondary electron 10 ev secondary electron 5 ev 00 0 1 11 01 01 200 ev photoelectron 20 ns 5 ns 20 ns 5 ns time Schematic of electron-cloud build up in the LHC beam pipe. [Courtesy Francesco Ruggiero] Proper multipacting: n min (O. Gröbner, 1977) h2 y N b r e L sep =1
accelerator PEP-II KEKB PS SPS LHC PSR SNS species e + e + p p p p p population N b [10 10 ] 10 3.3 10 10 10 5000 10000 spacing L sep [m] 2.5 2.4 7.5 7.5 7.5 (108) (248) bunch length σ z [m] 0.3 0.004 0.3 0.3 0.077 25 30 h. beam size σ x [mm] 1.4 0.42 2.4 3 0.3 25 0.6 v. beam size σ y [mm] 0.2 0.06 1.3 2.3 0.3 7.5 0.6 ch. 1 2 size h x [mm] 25 47 70 70 22 50 100 ch. 1 2 size h y [mm] 25 47 35 22.5 18 50 100 circumf. C [km] 2.2 3.0 0.63 6.9 27 0.09 0.22 beta function β 18 15 15 40 80 5 6 parameter n min 1 10 0.58 0.24 0.15 0.0002 0.00
indicators of e build up (1) nonlinear pressure rise ρ e (2) pick ups or dedicated e monitors ρ e (3) tune shift along the train ρ e (4) beam-size blow up along the train (5) luminosity drop
Simulation recipe for e build up (code ECLOUD) > A = E = C A A A? JH E = C A I A? @ = HO A A? JH I represent e by macroparticles (2000/bunch), slice bunches and interbunch gaps > K? D A I F HE = HO F D J A A? JH I I E? A I for each bunch slice, create photo-el. and accelerate existing e in beam and beamimage fields if e hit the wall secondary e ; change macro charge at each gap slice the e are propagated in the magnetic field; kicks from e spacecharge and e image charges
+ F F A H? = HE A JA H 9 ) 2 ) + 0 + = H?? D = > A H 5 2 5 @ EF A? D = > A H I JHEF EJ H Transverse aperture in the LHC arcs compared with SPS vacuum chambers. Differences in multipacting behavior.
Electron Energy Spectrum Energy distribution of e s incident on SPS dipole chamber for two different bunch lengths, σ z =0.26 m (left) and σ z =0.33 m (right), and various intensities. Energies of many e are in the range 100 250 ev, where secondary yield is high.
Simulated average LHC arc heat load and cooling capacity as a function of bunch population N b, for various δ max. Other parameters are ɛ max = 262 ev, R =5%, Y =5%, and elastic electron reflection is included.
Heat load per unit length in the LHC as a function of bunch population N b, for various magnetic fields. Other parameters: δ max =1.1, ɛ max = 262 ev, R =5%, Y =5%, and elastic electron reflection is included. Dipole field is best.
Simulated electron-cloud build up in the SPS for a field-free region (left) and a strong dipole (right), comparing various bunch populations. In field-free regions threshold is higher, but build up above threshold stronger.
Evolution of electron line density in units of m 1 vs. time during the passage of a two 72-bunch LHC batches through a SPS dipole chamber, separated by gaps of 8, 21, 84, and 105 missing bunches, for δ max =1.8. Gap larger than 2.6 µs needed for reset.
0.02 delta_max=1.3, emax=450 ev, Y=0.025, R=0.1 0.5 0. 0.005 0-0.005-0. -0.5-0.02-0.03-0.02-0. 0 0. 0.02 0.03 Snapshot of transverse e distribution in an LHC dipole chamber (F.Z., 1997). Parameters: δmax = 1.3, max = 450 ev, R = 0.1, and Y = 0.025. Two vertical stripes emerge! F. Zimmermann SPS: Electron-Cloud Theory & Simulations
Electron flux on chamber wall in A/m 2 vs. the horizontal position in an SPS dipole.
Single-Bunch Instability e are accumulated near the beam center during bunch passage if there is a displacement between head and tail, the tail experiences a wake force effective short-range wake field TMCI-like instability such instability is observed in the SPS, at KEKB LER, and PEP-II
Single-Bunch Instability - Approaches adapt FBII theory 1/τ N 3/2 b σz 1/2 /L sep /σy 1/2 2-particle model with length (F.Z., -SL-Note-2000-004). 1/τ BBU N 2 b σ z/l sep /σ y (for σ z ω e >cπ/2); N b,thr Q s L sep rise time or threshold for BBU, HT and TMCI instabilities (K. Ohmi & F.Z., PRL 85, 3821). wake field simulation & either TMCI calculation or threshold for fast blow up (K. Ohmi, et al., HEACC ). N b,thr Q s ωeσ 2 z/(cr 2 S /Q) N b,thr γ 2 Q 2 sl 2 sepσ z /σ y various simulation codes microbunches, soft Gaussian, PIC codes (G. Rumolo, K. Ohmi) 3 and 4-particle models incl. space charge & beam-beam (G. Rumolo & F.Z., 2-STREAM )
Physical model beam orbit Numerical implementation SLICE k time i Electrons Particles in SLICE k Simulation recipe for 1-bunch instability (code HEADTAIL, G. Rumolo) time = i t Flux of the interaction bunch-cloud Electrons (updated) Particles in SLICE k (updated, transported to the next interaction point) t = T rev / N int k = 1,..., N sl N bunch slices sl N el electrons concentrated at the kick section s = s el One of the N interaction int points. N p bunch particles SLICE k time (i+1) Time flux i = 0,..., N turn x N int - 1 s y x represent bunch and e by 10 5 macroparticles each (density from other program) concentrate e cloud at one (or more) location around the ring compute electric fields of either species on a 2-D grid forces ±10σ x,y ) interaction proceeds in steps, via the passage of 50 bunch slices between turns the beam macroparticles can change slices due to synchr. motion optionally include ξ x,y, broadband impedance, space charge, and beam beam
1.5e+07 1.5e+07 vx (m/s) 1e+07 vy (m/s) 1e+07 5e+06 5e+06 0 0-5e+06-5e+06-1e+07-1e+07 dn/dx (1/m) -1.5e+07-10 -8-6 -4-2 0 2 4 6 8 10 3.5e+06 3e+06 2.5e+06 x/ σ x dn/dy (1/m) -1.5e+07-10 -8-6 -4-2 0 2 4 6 8 10 6e+06 5e+06 4e+06 y/ σ y 2e+06 1.5e+06 3e+06 1e+06 2e+06 500000 1e+06 0-10 -5 0 5 10 0-10 -5 0 5 10 x/ σ y/ σ x y Snapshots of the horizontal and vertical electron phase space (top) and their projections onto the position axes (bottom). [G. Rumolo, Chamonix XI)].
2e+18 W x(y) (V/C/m) 1.5e+18 1e+18 5e+17 0-5e+17-1e+18-1.5e+18-1.2-1 -0.8-0.6-0.4-0.2 z (m) 0 Simulated vertical wake field in V/m/C, excited by displacing various slices inside the Gaussian bunch, vs. position in m, for an SPS field-free region. The bunch center is at 0.6 m, the bunch head (2σ z ) on the right. (G. Rumolo, 20).
Single-Bunch Instability 0.008 0.08 0.006 0.06 0.004 0.04 0.002 0.02 y (m) 0 y (m) 0-0.002-0.02-0.004-0.04-0.006-0.06-0.008-0.6-0.4-0.2 0 0.2 0.4 0.6 z (m) -0.08-0.6-0.4-0.2 0 0.2 0.4 0.6 Simulated bunch shape after 0, 250 and 500 turns (centroid and rms beam size shown) in the SPS with an e cloud density of ρ e =10 12 m 3, without (left) and with (right) proton space charge (Courtesy G. Rumolo). z (m)
estimated TMCI thresholds accelerator PEP-II KEKB PS SPS LHC PSR SNS e osc./bunch 0.8 1.0 1 0.75 3 34 970 n osc ω e σ z /(πc) TMCI threshold 1 0.5 5 0.25 3 (0.6) (0.5) ρ e [10 12 m 3 ] density ratio 19 4 0.35 11 4 (92) (27) ρ e,sat /ρ e,thresh Natural e densities in saturation almost always exceed the TMCI threshold!
14 Effect of chromaticity on the emittance growth 12 10 ε y (µm) 8 6 4 Q =0 2 Q =5 Q =10 0 0 1 2 3 4 5 t (ms) Simulated vertical emittance vs. time in the SPS, for three different chromaticities. Broadband impedance and transverse proton space charge are included in addition to e cloud (G. Rumolo, 20).
Conclusions most worriesome effects: heat load in LHC, single-bunch instability in the SPS simulations reproduce most of the observations (build-up time, decay time, tune shift, effect of chromaticity, etc.), but results are sensitive to model parameters (δ max,refl.e,...) calibration against experiments is important!
Further informations, publications, and more details: Proceedings of Chamonix X (-SL-2000-07 DI), and Chamonix XI (-SL-20-003 DI) http://cern.web.cern.ch//divisions/sl /publications/chamx2k/contents.html http://cern.web.cern.ch//divisions/sl /publications/chamx20/contents.html electron-cloud web page http://wwwslap.cern.ch/collective/electroncloud/electron-cloud.html ECLOUD 02 Workshop, April 15-18, 2002 http://wwwslap.cern.ch/collective/ecloud02