Beam Dynamics Studies in SuperKEKB. K. Ohmi (KEK) SuperB workshop at INFN-Frascati March 19-24, 2012

Transcription

1 Beam Dynamics Studies in SuperKEKB K. Ohmi (KEK) SuperB workshop at INFN-Frascati March 19-24, 2012

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3 Contents Strong-strong beam-beam simulation, synchro-beta resonances Tolerance of IP parameter Electron cloud & Ion TMCI and beam tilt due to mask impedance Injection, life time, background, dynamic aperture

4 Progress of Strongstrong simulation Gaussian approximation Particle In Cell-Gauss composite Fully Particle In Cell

5 Bunch slicing Integral along collision, bunch slicing nslice=(5~10)xσzθ/σx= (5~10)x25 Should be smooth function for z. σz+>σzσzθ/σx=1 for KEKB x s Neglect parallel translation to x

6 Gaussian and PIC combined method (done 2010) Dx> 5σx Gaussian approximation Dx< 5σx Partcle In Cell Potential solve 5000 PIC sub collision and gaussian collision

7 Strong-strong beam-beam L (cm -2 s -1 ) simulation Coherent instability should be studied by 1.2e+36 1e+36 8e+35 6e+35 4e+35 strong-strong model =(0.525,0.570) =(0.52,0.570) =(0.530,0.570) x e-05 =(0.525,0.570), e+ e- 2e turn 0 1e-06 8e turn =(0.525,0.570), e+ e- y (m) 6e-07 4e-07 2e turn

8 Gaussian and PIC combined method Example: study of synchro-beta effect L (cm -2 s -1 ) 1.2e+36 1e+36 8e+35 6e+35 4e+35 2e+35 =(0.525,0.570) =(0.52,0.570) =(0.530,0.570) <xz> 0 4e-08 3e-08 2e-08 1e e-08-2e-08-3e turn =(0.525,0.570), e+ e- -4e

9 Particle in Cell Potential solve for arbitrary beam distribution in transverse plane KEKB 50(~7x7) subcollision/collision SuperKEKB 40,000(~200x200) subcollision/ collision

10 Shifted Green function "(r) = # 1 ' dr'g(r # r'#r 2$% 0 )&(r'+r 0 ) 0 Potential where apart from a distance J. Qiang f (x i+ " x 0, y i+ " y 0 ) " f (x i+ " x 0, y i" " y 0 ) " f (x i" " x 0, y i+ " y 0 ) + f (x i" " x 0,y i" " y 0 ) f (x i+ " 2#x " x 0,y i+ " y 0 ) " f (x i+ " 2#x " x 0,y i" " y 0 ) " f (x 0 " 2#x + x i", y i+ " y 0 ) + f (x i" " 2#x " x 0, y i" " y 0 ) f (x 0 + x i+,y 0 " 2#y + y i+ ) " f (x 0 + x i+,y 0 " 2#y + y i" ) " f (x 0 + x i", y 0 " 2#y + y i+ ) + f (x 0 + x i",y 0 " 2#y + y i" ) f (x 0 " 2#x + x i+, y 0 " 2#y + y i+ ) " f (x 0 " 2#x + x i+,y 0 " 2#y + y i" ) " f (x 0 " 2#x + x i", y 0 " 2#y + y i+ ) + f (x 0 " 2#x + x i", y 0 " 2#y + y i" ) f (x, y) = " dxdyg(r) = #3xy + x 2 tan #1 (y / x) + y 2 tan #1 (y / x) + xy log(x 2 + y 2 ) Φij is given on the grid space far from colliding beam.

11 Beam distribution and potential x s Neglect parallel translation to x σz+>σz-

12 Beam distribution and potential x s Neglect parallel translation to x σz+>σz- 2nd x 199th 2nd x 2nd

13 Tentative result Equilibrium luminosity is not obtained in fully PIC simulation yet. Degradation of the luminosity is weak for CW.

14 Tolerance of IR parameters beam-beam Weak-strong simulation is used for the parameter scan, because the strong-strong requires very long CPU time. Examples, x-offset and r1*. L (10 35 cm -2 s -1 ) NoCW CW x (µm)

15 Summary tolerance for parameters with 20% luminosity degrada:on Parameter w/ crab waist w/o crab waist r 1 * (mrad) ±5.3 ±3.5 r 2 * (mm) ±0.18 ±0.13 r 3 * (m - 1 ) ±44 ±15 r 4 * (rad) ±1.4 ±0.4 r 1 * / δ (rad) ±2.4 ±2.1 r 2 * / δ (m) ±0.086 ±0.074 r 3 * / δ (m - 1 ) ± ±8400 r 4 * / δ (rad) ±400 ±290 η y * (µm) ±62 ±31 η yʹ * ±0.73 ±0.23 Δx (μm) collision offset Δs (μm) waist error Δy,Δy (μm,μrad) collision offset 0.02 (100) δx (μm) turn by turn noise δy (nm) 4 4 The degrada:on is roughly quadra:c σx=6-10μm σy=60 nm

16 Beam noise Turn by turn noise without correla:on in turns. L (10 35 cm -2 s -1 ) y (nm) x =6-10µm x (µm) x does not change NoCW CW x (µm) NoCW CW L (10 35 cm -2 s -1 ) y (nm) y =60nm y (nm) x does not change NoCW CW NoCW CW δy x (nm) (µm)

17 Ion instability Turn- by- turn noise due to ion instability. Coupled bunch instability with very high growth rate. Feedback system suppresses the instability. Residual dipole mo:on as a turn by turn noise may degrade the beam- beam performance. 17

18 Instability growth with bunchby-bunch feed back Examples of ion instability growth Bunch train length of Nb=2500 with spacing=4ns.

19 Residual vertical amplitude The dipole oscillation has correlation time of 1/G turns. The tolerance is relaxed with G 1/2. (J/ε) 1/2 = 4/60/ G 1/2 ~0.38. Not very serious

20 Electron cloud instability ωeσz/c is very high in low emittance rings. Single bunch instability Coupled bunch instability

21 U Threshold of the strong head- tail instability (Balance of growth and Landau damping) Stability condi:on for ω e σ z /c>1 3λ pr0 β Z ( ) 3λ e pr0 β ω KQ λe L = = = 1 ν γ ω σ c Z ν γ ω σ c 4 π λ σ ( σ + σ ) s e z 0 s e z p y x y ω e = λ r c p e 2 σ ( σ + σ ) y x y Since ρ e =λ e /2πσ x σ y, 2γν s ωeσ z c ρe, th = 3KQr β L 0 Origin of Landau damping is momentum compac:on ν s σ z = ασ δ L Q=min(Q nl, ω e σ z /c) Q nl =10 in this presenta:on, depending on the nonlinear interac:on. K characterizes cloud size effect and pinching.

22 Parameters SuperKEKB

23 SuperKEKB {/Symbol s}_y e e11 1.4e11 1.6e11 1.8e11 2.e11 2.2e11 2.4e11 2.6e11 Y. Susaki, K. Ohmi, IPAC turn Simulation ρth=2.1x10 11 m -3.(νs=0.012) Analytic ρth=2.7x10 11 m -3. Target ρe~1x10 11 m -3 Take care of high β section. Effects are enhanced. ρ e β y ds/l = m 2 23

24 Es:ma:on of cloud density and coupled bunch instability Ante- chamber, δ 2,max =1.2 without special structure like groove ρe=2.2x10 11 m -3 Wake field and growth rate of the couplied bunch instability. Growth time is 40 turns. It should be suppressed at ρe=1x10 11 m -3. Suetsugu- san es:mates the density based on measurements and is designing the chamber to achieve density.

25 Impedance designed in 2011 d=2.4mm mask for LER d=5mm mask for HER 2 types numbered 56 & 57

26 TMCI (σz=6mm) LER : d=2.42 mm gap collimator at βy=94m. Ith=1.44mAx5~6=7.2~8.6mA HER : two d=5 mm gap collimators at βy=508m. Ith=1.04mAx2~3=2~3mA 1.04x1~1.5=1~1.5mA Consistent design for QCS aperture and TMCI is on going.

27 Beam tilt due to the impedance = β i β y (i)y 0 (i) 1 ee 0 ρ(z + z)w y1 (z )dz D. Zhou & A. Chao One mask Round model Round model impedance: 1/10 of instability threshold. For the case of the impedance corresponding the instability threshold, tolerance of the orbit shift is 0.5 mm for 10% beam size increase.

28 Space charge tune shift in LER ν x = ν y = Mikhail pointed out λ p r e β x L 2πγpσ 3 x (σ x + σ y ) λ p r e β y L 2πγ 3 pσ y (σ x + σ y ) 0.11 This tune shift is not very large compare than recent proton machines. Manageable perhaps?

29 Injection and life time beam-beam & simple revolution matrix beam-beam interaction, Nslice=300 σx=6μm x0=180μm σzφ=250μm dz=x0/φ=4mm βy/βy0=180 Crab waist βy/βy0=1 SAD simulation including lattice is also done.

30 x/ x,0, y/ y, turn x/ x y/ y No CW40 x / x,0, y / y, turn x / x,0 y / y,0 y /J x, turn y /1e-6 εy 4?

31 CW x/ x,0, y/ y, x/ x y/ y x / x,0, y / y, x / x,0 y / y, turn turn y /1e-6 y /J x, εy =0.04%Jx turn

32 Motion of three sampled particles NoCW CW Large vertical amplitude is induced for NoCW. Samll for Crab waist εy=1.3x10-10, σy=0.2μm

33 Synchrotron injection dδ=7σδ z oscillation does not induce vertical motion. Synchrotron injection is proposed especially in HER (smaller dynamic aperture than LER)

34 Touschek life time Horizontal amplitude is induced by dispersion at Touschek events. Vertical emittance increases for large horizontal amplitude without CW. Beam-beam make worse Touschek life time. This effect is being studied.

35 Crab waist and IR nonlinearity CW sext Quad s Solenoid Quad s CW sext M IR = e axy2 e H Q s e H Sol e H BB e H Sol e H Q s e axy 2 e H Q s e H Sol e xp2 y /2φ e H BB e xp2 y /2φ e H Sol e H Q s Strong dynamic aperture degradation is seen by crab sextupole installation (H. Koiso). We do not know how to handle the nonlinear terms of Q s and Solenoid located at very high β.

36 Study with a simple model K.Ohmi & H.Koiso, IPAC10 Dynamic aperture is degraded by installation of crab waist sextupoles.

37 Crab waist or not Crab waist scheme well matches the large Piwinski angle collision for injection and Touschek event if dynamic aperture is sufficient. It seems to be hard to use the crab waist scheme in very low beta interaction point for the dynamic aperture issue. Do we have a local chromaticity and nonlinearity compensation technique? This is very interesting subject.

38 Summary Beam dynamics studies have been continued as is listed in SuperKEKB. Dynamic aperture study is most important. Especially, crab waist or not is interesting subject for beam-beam interaction, aperture, injection, life time... This can be one of collaboration subjects between SuperB and SuperKEKB.

39 Others Background studies are being performed by H. Nakayama, Y. Ohnishi et al. Damping ring micro-bunch instability is studied by H. Ikeda and D. Zhou.