Electron-Cloud Theory & Simulations

Transcription

1 (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

2 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

3 Electron Build Up e production mechanisms: residual gas ionization; typical rate d 2 λ e /(ds dt) e m 1 s 1 synchrotron radiation and photo-emission; typical rate d 2 λ e /(ds dt) e m 1 s 1 secondary emission: (1) true secondaries & (2) elastically reflected or rediffused; exponential growth

4 ENERGY DISTRIBUTION OF SECONDARY ELECTRON EMITTED BY COPPER Ep= 10 ev Ep=30 ev Ep= 100 ev Ep=300 ev Ep=550 ev NORMALISED INTENSITY 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]

5 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.

6 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.

7 γ LOST or REFLECTED γ γ ev 2 kev 10 ev 5 ev 5 ev 10 ev ev 2 kev secondary electron 10 ev secondary electron 5 ev 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

8 accelerator PEP-II KEKB PS SPS LHC PSR SNS species e + e + p p p p p population N b [10 10 ] spacing L sep [m] (108) (248) bunch length σ z [m] h. beam size σ x [mm] v. beam size σ y [mm] ch. 1 2 size h x [mm] ch. 1 2 size h y [mm] circumf. C [km] beta function β parameter n min

9 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

10 Simulation recipe for e build up (code ECLOUD) > A = E = C A A A? JH E = C A I = 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

11 + F F A H? = HE A JA H 9 ) 2 ) = H?? D = > A H 5 2 EF A? D = > A H I JHEF EJ H Transverse aperture in the LHC arcs compared with SPS vacuum chambers. Differences in multipacting behavior.

12 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 ev, where secondary yield is high.

13 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.

14 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.

15 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.

16 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.

17 0.02 delta_max=1.3, emax=450 ev, Y=0.025, R= 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 = Two vertical stripes emerge! F. Zimmermann SPS: Electron-Cloud Theory & Simulations

18 Electron flux on chamber wall in A/m 2 vs. the horizontal position in an SPS dipole.

19 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

20 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 ). 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 )

21 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

22 1.5e e+07 vx (m/s) 1e+07 vy (m/s) 1e+07 5e+06 5e e+06-5e+06-1e+07-1e+07 dn/dx (1/m) -1.5e e+06 3e e+06 x/ σ x dn/dy (1/m) -1.5e e+06 5e+06 4e+06 y/ σ y 2e e+06 3e+06 1e+06 2e e 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)].

23 2e+18 W x(y) (V/C/m) 1.5e+18 1e+18 5e e+17-1e e 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).

24 Single-Bunch Instability y (m) 0 y (m) z (m) 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)

25 estimated TMCI thresholds accelerator PEP-II KEKB PS SPS LHC PSR SNS e osc./bunch n osc ω e σ z /(πc) TMCI threshold (0.6) (0.5) ρ e [10 12 m 3 ] density ratio (92) (27) ρ e,sat /ρ e,thresh Natural e densities in saturation almost always exceed the TMCI threshold!

26 14 Effect of chromaticity on the emittance growth ε y (µm) Q =0 2 Q =5 Q = 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).

27 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!

28 Further informations, publications, and more details: Proceedings of Chamonix X (-SL DI), and Chamonix XI (-SL DI) /publications/chamx2k/contents.html /publications/chamx20/contents.html electron-cloud web page ECLOUD 02 Workshop, April 15-18,