Lattices and Multi-Particle Effects in ILC Damping Rings

Transcription

1 Lattices and Multi-Particle Effects in ILC Damping Rings Yunhai Cai Stanford Linear Accelerator Center November 12, 25 Electron cloud- K. Ohmi and M. Pivi Fast Ion- L. Wang Super B-Factories 25 workshop, November 11-12, 25, Frascati, Ital

2 Motivations and Challenges PEP-II: Emittance: 5 nm Beam current: 3 A Damping time: 5 ms ILC damping rings: Emittance:.5 nm Beam current: < 1 A Damping time: 2 ms Super-B rings: Emittance:.5 nm Beam current: 4 A Damping time: 1.5 ms

3 How to Obtain Ultr-Low Emitance Horizontal equilibrium emittance due to dipole magnet with bending angle: φ d in arc can be written as ε C γ J F F arc q c = FODO c C q F = 55hc c γ 2 φ / 32 - Lorentz factor = 3 d / J cos µ L sin µ 1 cos µ l 3mc - Partition number ~ 1 - Cell factor: how dipole and quadrupole magnets are arranged its theoretical minimum value 1/ d c Reduce energ Increase number of cell Choose a better cell Make dipole longer

4 Dnamic Aperture v.s. Strength of Setupoles in 5-Gev Ring Dnamic aperture scales inversel proportional to the strength of the setupoles! It is not so bad and it can be worse.

5 Scaling of Dnamic Aperture scaling of phase space solid lines are inverse curves Dnamic aperture is determined b the location of fi points In phase space when a single resonance dominates the sstem. Perturbation theor can be used to eplain this scaling propert of the dnamic aperture.

6 Reduce Emittance b Enlarging the Ring While Keeping the Cell Structure Simulation of actual lattices: 4 cells -> 8 cells -> 16 cells, ε =47 nm -> 7 nm -> 1 nm C=96 m -> 156 m -> 276 m Scaling properties: ε ε /1 θ N ρ dip c 2.15N dip SF, SD DA θ / 2.15ρ dip 3 c dip 1 η η / ( SF, SD) DA/ 2.15 = θ dip / 2.15

7 Cells Used in ILC Damping Rings TME(TESLA) TME(OCS) PI(PPA) FODO(MCH)

8 Dnamic Aperture of PPA with Permanent-Magnet Wigglers 3σ of injected beam Linear wiggler Full nonlinear wiggler Dnamic aperture is entirel dominated b 24 wigglers in the lattice. The act like phsical scrappers.

9 Tunes vs. Amplitudes (PPA) Calculated with nonlinear map and normal form using LEGO & LIELIB: ν ε ν ε ν ε ν, ε Linear Wiggler Single-Mode Wiggler For single-mode wiggler: dν ds 2 sin kws 2 2 = [ β ( ) + ( ) 2 s kwβ s J 4π (1 + δ ) ρ +...]

10 Main Parameters of ILC Damping Rings Parameters PPA OCS TESLA MCH Energ E(Gev) Circumference (m) , 15,815 Horizontal emittance (nm) Damping time (ms) Tunes, n,n,n s 47.81, 47.68, , 4.8, , 41.18, , 76.41,.19 Momentum compaction a c Bunch length s z (mm) Energ spread s e /E Chromaticit, -63,-6-65, , , Energ loss per turn (Mev) RF Frequenc (MHz) RF Voltage (MVolt)

11 Tune vs. Amplitude and Energ Deviation NAME ν ε ν ε ν ε, ν ε 2 ν δ ν δ ν 2 δ 2 3 ν δ 3 PPA OCS TESLA MCH Clearl, the OCS lattice has the best chromatic properties.

12 Dnamic Aperture with Mutilpole Errors and Single-Mode Wigglers (Injected Positron Beam γε =.1m-rad) PPA OCS 3 km 6 km TESLA/S-Shape MCH 17 km 16 km

13 Conclusion of Acceptance Stud Well optimized wigglers do not cause much degradation of dnamic aperture It is challenge but achievable to design a lattice with adequate dnamic aperture for a ver large injected positron beam. More attention has to be paid to the energ acceptance Lattice with man super periods has advantage in terms of acceptance Tpe of cell is a determinant factor for large acceptance

14 Issues Due to Electron Clouds How electron clouds are generated? Photoelectron build-up Snchrotron radiation Geometr of bending Antechamber Reflectivit Secondar eletrcon ield (SEY) Multipacting of electrons Solenoid wining in straight sections What are the effects on the positron beam? Coupled bunch instabilit Transverse bunch-b-bunch feedback sstem Single bunch instabilit Growth of beam size especiall in the vertical plane

15 Poisson solver with the Finite Element Method Mesh.3 Triangulation ρ e N cm Y cm X Antechamber suppress the cloud line densit to a few percent level (5-1m downstream), if multipacting can be avoided. φ cloud N cm cm 2

16 Densit of Electron Cloud in Arcs r =1 mm as a function of z.

17 Coupled Bunch Instabilit Wake force induced b electron cloud λ e =7 1 7 m -1 (OTW) 51 7 m -1 (OCS) This line densit corresponds to that at 1 m down stream. The wake is 5 times stronger at 5 m downstream. At Injection, the wake is 1-2 times stronger. 5 5 W (m^-1) -5 W (m^-1) bunch bunch

18 Growth rate of the coupled bunch instabilit Slow growth rate (τ~1 turn), if the conditions (average densit =1m down stream) are kept. At injection, growth rate increases 1-2 times, (τ~5-1 turn).15.1 OTW OCS.3.2 Growth rate/turn Growth rate/turn Mode Mode

19 Single Bunch Instabilit Based on Linear Theor Electrons oscillate in a bunch with a frequenc, ω e. ω e = σ ( σ + σ ) ω e σ z /c>1 for vertical. Vertical wake force with ω e was induced b the electron cloud causes strong head-tail instabilit, with the result that emittance growth occurs. Threshold of the instabilit based of linear theor ρ eth, Q=min(Q nl, ω e σ z /c) Q nl =5-1? Depending on the nonlinear interaction K~3 Cloud size effect. ω e σ z /c~12-15 for damping rings. λ p rc e 2 2γνsωσ e z c = 3KQr β L

20 Simulation for OCS Lattice Clear head-tail signal was observed ρ e =21 11 m -3 and more. Threshold ρ e,th =21 11 m -3 (m) 8e-5 6e-5 4e-5 2e-5-2e-5-4e-5 ρ e =51 11 m -3 sig (um) rho=1e12 m^-3 5e11 2e11 1e turn (m) -6e z/sigz ρ e =21 11 m e-5 3e-5 2.5e-5 2e-5 1.5e-5 1e-5 5e-6-5e-6-1e z/sigz

21 Simulation for TESLA Lattice sig (m) e-5 5e turn 2e11 1e11 5e1 1e1, 2e1 IP=1 (m) 7e-5 6e-5 5e-5 4e-5 3e-5 2e-5 1e-5-1e-5-2e-5-3e-5-4e z/sigz sig (m).1 8e-5 6e-5 4e-5 2e-5 rhoe=1e11 m^-3 IP=1 rhoe=5e1 m^-3 IP= turn IP=4 (m) 4e-5 3.5e-5 3e-5 2.5e-5 2e-5 1.5e-5 1e-5 5e-6-5e-6-1e z/sigz Threshold ρ e,th =11 11 m -3

22 Simulation vs. Linear Theor? The threshold densit simulation linear theor OTW ρ e,th =51 11 m -3 ( ) OCS =21 11 m -3 ( ) TESLA =11 11 m -3 ( ) The sstematic difference (3-4) between simulation and linear theor ma be due to the cloud pinching. Simulations are accurate because the pinching is taken into account. To make lower densit, multipacting should be avoided. Cloud densit has been estimated with considering photoelectron production and antechamber geometr.

23 Production of Electron Cloud in Bending Magnets OCS has a factor of 1 more electron densit than the TESLA dogbone ring. We epect a factor of 3 simpl based on the argument of neutralization densit.

24 Threshold of Single Bunch Instabilit for ILC Damping Ring 1.E+13 Single-bunch instabilit thresholds Instabilit threshold SEY=1.2 SEY=1.2 + solenoid SEY=1.4 SEY=1.4 + solenoid cloud densit [m^-3] 1.E+12 1.E+11 1.E+1 TESLA MCH DAS 2 OCS OCS BRU OTW PPA PEP-II LER KEKB LER

25 Conclusion of Electron Cloud Stud The growth time for coupled bunch instabilit could be 5 turns at the injection due to the large positron beam size. However, the instabilit could be easil control b a bunch-b-bunch feedback sstem. For single bunch instabilit, linear theor predicts a higher threshold than b the strong-strong simulation. Using the tighter threshold, OCS lattice is ver likel to have this instabilit given a reasonabl achievable secondar electron ield between 1.2~1.4.

26 Linear Theor T. Ranbenheimer, F. Zimmerman, G. Stupakov 1 τ eff 1 = w τ i i i coherent tune-shift due to ions: re λ β ion υ = ion 4πγ σ + σ trapped region ( ) ds ion ion σ σ ion = σ electron / 2

27 ATF Measurement, Simulation, and Calculation Radiation damping time is about 3ms Calculated Growth time and Tune-shift (2% is CO+) Bunch intensit.16e1.37e1.63e1 Growth time (ms) Tune shift e e e-5 Emittance Versus Bunch Number 6.E-8 5.E-8 Number of Bunch along the train Normalized Y Emittance 4.E-8 3.E-8 2.E-8 1.E-8 6.E+9 3.7E+9 1.6E+9 Beam size blow-up at ATF (eperiment) Nbunch=2, P=1nTorr.E Bunch

28 Comparison of measured and simulation growth rates at Pohang Light Source Eun-San Kim, PAC25 µs µs µs Good agreement with eperiment and simulation

29 Electron Ring in B-factories KEKB(P=1nTorr) Ø Energ 8.GeV Ø Lsep=2.4m Ø ε=24nm Ø ε=.4nm Ø N= Ø Nbunch=1389 Ø τ feedback =.5ms PEPII(P=1nTorr) Ø Energ 9.GeV Ø Lsep=1.26m Ø ε=5nm Ø ε=1nm Ø N= Ø Nbunch=1732 Assuming 2% is CO+ τcalculated=1.15ms, Qcal=.8; τcalculated=1.8ms, Qcal=.1;

30 Fast Ion Instabilit Ø Assuming there are different pressure at different section: Pwiggler=2nTorr; P_long_straight =.1nTorr & P_arc=.5nTorr Ø Assuiming a tune spread of.3[g.v. Stupakov, Proc. Int. Workshop on Collective Effects and Impedance for B-Factories KEK Proc (1996) p243.] Ø The growth rate has been estimated at each element and the effective growth rate at each section and the whole ring are calculated Ø The trapping condition is considered when the growth time is calculated at each element. Ø Coupling bump is applied in the long straight section Ø The growth rate has been estimated during the whole damping time

31 Growth Time and Tune Shift for 6-km Damping Ring (OCS) 1.8 Growth time (µ s) τ ave τ wig τ arc τ str Time (damping time) Trapping fraction Tune shift trapping in wiggler trapping in arc trapping in whole ring Time (damping time) PPA OTW OCS BRU MCH DAS TESLA Time (damping time)

32 Comparison of Damping Rings Ring PPA OTW OCS 2OC S BRU MCH DAS TESLA τ wiggler (µs) τ arc (µs) τ straight (µs) (52) 929(54) 844(53) τ ring (µs) (2.5) 4.5(4.2) 44.3(43) τ ring in turns Tune shift (.69).12(.72).17(.9) Dependenc on the circumference is not consistent Ring that has longer arcs is worse Ring that has larger beta function is worse

33 How Long for an Effective Ion Gap? The diffusion time of ion-cloud is about 1 times of the ion oscillation period: Wiggler section need a short gap Light ion need a short gap. Gap in PEPII HER: 4m(13ns) /2 (T co+ =11ns; T H+ =3ns) ION-CLOUD f= 7.51MHz, T=133ns, τ=115ns f= 1MHz, T=1ns, τ=82ns f= 12.47MHz, T=8ns, τ=72ns t (ns)

34 A factor of 7.2 improvement with 2 mini-train; More train will get more improvement IRF 1 Ntrain Just a sample! Ever ring can has its different fill pattern! Build of Ions with Mini Bunch Train (2) (for fied gap length) ION-CLOUD Reduction Factor Analtical saturation Level NB=278 Ntrain=2 τ gap =4ns τ=89 ns Bunch Number Accumulation of Ion-cloud with mini-gaps

35 Conclusion of Fast Ion Instabilit Ø Application of the linear theor to the eisting rings (ATF, PLS, KEKB, PEP-II) shows a reasonable agreement between the theor and observation. Ø The effects depend on the bunch spacing and detail of the optics. In general longer arcs or higher beta function is worse. Ø Mini-gaps is ver helpful to reduce the growth time and tune shift. Number of bunches reduced due to the gaps is at a few percent level. Ø Transverse feedback is necessar even with mini-gaps to control the instabilit.