Electron cloud effects in Cesr-TF and KEKB

Izawa et.al., Phys. Rev. Lett. 74, 5044 (1995).

BPM spectrum for V motion. Electron 354 mA

Positron 324 mA & 240 mA

Interpretation of instability due to photo-electron cloudPositron beam emits synchrotron radiation. Electrons are produced at the chamber wall by photoemission. Production efficiency ~ 0.1e-/g.Electrons are attracted and interacts with the positron beam, then absorbed at the chamber wall after several 10 ns. Secondary electrons are emitted according the circumferences.Electrons are supplied continuously for multi-bunch operation with a narrow spacing, therefore electron cloud are formed. A wake force is induced by the electron cloud, with the result that coupled bunch instability is caused.K. Ohmi, Phys. Rev. Lett., 75, 1526 (1995).

First figure for electron cloud build-upPRL,75,1526 (1995)Recipes for electron cloud build-up are written in this paper.e-ge+ beamSecondary e-xyModelBeam chamber

Number of produced electrons Bunch populationNp=3.3x1010KEKB-LERdesign2.6A Np=5x109 KEK-PF400mA) Quantum efficiency (h=np.e./ng) 0.1Energy distribution 105 eV

KEKB-LER Yp.e.=0.015 e-/m.e+ KEK-PF Yp.e.=0.17 e-/m.e+ , ionization 10-8 e-/m.e+ , proton loss(PSR) 4x10-6 e-/m.p KEKB-LER g=6850 Yg=0.15/mKEK-PF =4892 Yg=1.7/mNumber of photon emitted by a positron par unit meter.a : fine structure const=1/137

Electron cloud density given by simulation60 bunches pass in every 8ns (KEKB).

Graph1

00

829564000000

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00

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8782050001282050000

8333330001410260000

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00

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889744000769231000

853846000769231000

812821000769231000

779487000897436000

00

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6211260000001038330000000

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6250780000001055130000000

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6270360000001044870000000

416264000000695641000000

260319000000484231000000

159586000000297051000000

104709000000181282000000

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5383720000090897400000

4081030000065769200000

3191790000048205100000

2542560000034615400000

2085380000028846200000

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1251280000015384600000

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81910300009871790000

72000000009615380000

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41961500005256410000

37987200004871790000

34871800003589740000

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29294900002564100000

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18859000002307690000

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15500000002564100000

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10756400002051280000

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9051280001282050000

8641030001153850000

8179490001025640000

7782050001025640000

747436000897436000

Average

Center

Bunch

re(m-3)

Electron cloud density for bunch passage

kekbs4

100

28.30E+100

31.66E+114.86E+11

42.32E+116.71E+11

52.82E+117.37E+11

63.23E+117.90E+11

73.56E+118.96E+11

83.82E+119.37E+11

94.04E+119.42E+11

104.24E+119.76E+11

114394500000001.02E+12

124.53E+111.02E+12

134.66E+111.03E+12

144.77E+111.05E+12

154.87E+111.06E+12

164.95E+111.06E+12

175.04E+111.07E+12

185.11E+111.07E+12

195.18E+111.08E+12

205.24E+111.07E+12

215.30E+111.06E+12

225.35E+111.06E+12

235.40E+111.09E+12

245.44E+111.08E+12

255.48E+111.06E+12

265.52E+111.06E+12

275.56E+111.08E+12

285.59E+111.07E+12

295.62E+111.07E+12

305.65E+111.06E+12

315.67E+111.05E+12

325.70E+111.06E+12

335.73E+111.07E+12

345.76E+111.08E+12

355.78E+111.05E+12

365.81E+111.09E+12

375.84E+111.08E+12

385.87E+111.05E+12

395.88E+111.07E+12

405.91E+111.06E+12

415.93E+111.05E+12

425.96E+111.05E+12

435.98E+111.04E+12

445998500000001.05E+12

456.02E+111.06E+12

466.04E+111.06E+12

476.06E+111.04E+12

486080500000001.06E+12

496.10E+111.05E+12

506.12E+111.05E+12

516.14E+111.05E+12

526.15E+111.07E+12

536.17E+111.05E+12

546.18E+111.06E+12

556.20E+111.07E+12

566.21E+111.05E+12

576.23E+111.06E+12

586.24E+111.05E+12

596.25E+111.06E+12

606.26E+111.06E+12

616.27E+111.05E+12

624.16E+116.84E+11

632.60E+114.88E+11

641.59E+112.88E+11

651.05E+111.73E+11

667.40E+101.18E+11

675.40E+108.41E+10

684.09E+105.92E+10

693.17E+104.54E+10

702.52E+103.69E+10

712.06E+103.03E+10

721.71E+102.76E+10

731.45E+102.21E+10

741.24E+101.74E+10

751.07E+101.49E+10

7693000000001.14E+10

778.17E+091.05E+10

787.27E+099.49E+09

796.40E+098.97E+09

805.78E+097.69E+09

815.16E+097.05E+09

824.65E+096.79E+09

8342500000006.92E+09

843.89E+095.77E+09

853.56E+094.49E+09

863.27E+093.46E+09

873.03E+093.21E+09

882.79E+093.21E+09

892.61E+092.95E+09

902.41E+092.31E+09

912.22E+092.18E+09

922.08E+091.92E+09

931.93E+091.79E+09

941.81E+091.79E+09

951.68E+091.92E+09

961.56E+091.67E+09

9714500000001.54E+09

981.37E+091.28E+09

991.32E+091.41E+09

1001.24E+091.54E+09

1011.16E+091.41E+09

1021.09E+091.67E+09

1031.03E+091.67E+09

1049.92E+081.41E+09

1059.32E+081.15E+09

1068.86E+081.15E+09

1078.41E+081.15E+09

1087.95E+081.15E+09

1097.58E+081.15E+09

1107.27E+081.03E+09

32100

3228.29E+100

3231.66E+114.83E+11

3242.32E+116.79E+11

3252.82E+117.30E+11

3263.23E+118.03E+11

3273.56E+118.84E+11

3283.82E+119.27E+11

3294.04E+119.41E+11

3304.24E+111.00E+12

3314.40E+119.95E+11

3324.54E+111.03E+12

3334.66E+111.04E+12

3344.77E+111.05E+12

3354.87E+111.05E+12

3364.96E+111.03E+12

3375.04E+111.06E+12

3385.11E+111.05E+12

3395.17E+111.07E+12

3405.24E+111.08E+12

3415.29E+111.07E+12

3425.34E+111.07E+12

3435.39E+111.06E+12

3445.45E+111.08E+12

3455.48E+111.06E+12

3465.52E+111.07E+12

3475.56E+111.07E+12

3485.59E+111.08E+12

3495.62E+111.07E+12

3505.65E+111.06E+12

3515.68E+111.06E+12

3525.71E+111.09E+12

3535.73E+111.07E+12

3545767000000001.07E+12

3555.80E+111.09E+12

3565.82E+111.04E+12

3575.85E+111.06E+12

3585.87E+111.07E+12

3595.89E+111.08E+12

3605.91E+111.06E+12

3615.94E+111.05E+12

3625.96E+111.05E+12

3635.98E+111.08E+12

3646.00E+111.06E+12

3656.02E+111.04E+12

3666.04E+111.05E+12

3676.06E+111.05E+12

3686.07E+111.07E+12

3696.09E+111.07E+12

3706.11E+111.07E+12

3716.14E+111.07E+12

3726.15E+111.05E+12

3736.17E+111.04E+12

3746.19E+111.06E+12

3756.20E+111.06E+12

3766.21E+111.05E+12

3776.23E+111.06E+12

3786.24E+111.07E+12

3796.25E+111.05E+12

3806.26E+111.05E+12

3816.28E+111.06E+12

3824.17E+116.78E+11

3832.61E+114.77E+11

3841.60E+112.91E+11

3851.05E+111.79E+11

3867.38E+101.17E+11

3875.41E+108.82E+10

3884.10E+1065000000000

3893.20E+104.74E+10

3902.55E+103.71E+10

3912.09E+102.90E+10

3921.74E+102.37E+10

3931.46E+101.85E+10

3941.25E+1015000000000

3951.07E+101.21E+10

3969.39E+091.08E+10

3978.24E+099.23E+09

3987.27E+098.59E+09

3996.48E+098.08E+09

4005.80E+097.44E+09

4015.18E+096.54E+09

4024.67E+095.64E+09

4034.22E+095.38E+09

4043.85E+095000000000

4053.57E+095000000000

4063.24E+094.74E+09

4073.00E+094.23E+09

4082.78E+093.85E+09

4092.58E+093.33E+09

4102.40E+093.08E+09

4112.21E+092.69E+09

4122.05E+092.18E+09

4131.89E+092.18E+09

4141.77E+091.67E+09

4151.66E+091.54E+09

4161.57E+091.67E+09

4171.49E+091.92E+09

4181.39E+091.79E+09

4191.32E+091.67E+09

4201.26E+091.67E+09

4211.20E+091.54E+09

4221.15E+091.28E+09

4231.10E+091.15E+09

4241.06E+091.28E+09

4251.01E+091.03E+09

4269.72E+081.03E+09

4279.21E+081.15E+09

4288.78E+081.28E+09

4298.33E+081.41E+09

4307.94E+081.15E+09

64100

6428.30E+100

6431.66E+114.83E+11

6442.32E+116.73E+11

6452.82E+117.28E+11

6463.23E+118.06E+11

6473.55E+118.75E+11

6483.82E+119.18E+11

6494.04E+119.54E+11

6504.23E+119.79E+11

6514.39E+111.01E+12

6524.53E+1199000000000

6534.66E+111.02E+12

6544.77E+111.05E+12

6554.86E+111.05E+12

6564.95E+111.05E+12

6575.04E+111.07E+12

6585.11E+111.08E+12

6595.17E+111.08E+12

6605.23E+111.08E+12

6615.29E+111.06E+12

6625.34E+111.07E+12

6635.39E+111.06E+12

6645.43E+111.06E+12

6655.48E+111.07E+12

6665.51E+111.06E+12

6675.55E+111.05E+12

6685.59E+111.07E+12

6695.62E+111.07E+12

6705.65E+111.05E+12

6715.68E+111.08E+12

6725.69E+111.06E+12

6735.72E+111.05E+12

6745.76E+1110950000000

6755.78E+111.08E+12

6765.81E+111.06E+12

6775.84E+111.07E+12

6785.87E+111.06E+12

6795.90E+111.07E+12

6805.92E+111.07E+12

6815.94E+111.08E+12

6825.96E+111.06E+12

6835.98E+111.05E+12

6846.01E+111.06E+12

6856.03E+111.08E+12

6866.04E+111.06E+12

6876.07E+111.07E+12

6886.08E+111.04E+12

6896.10E+111.06E+12

6906.11E+111.06E+12

6916.13E+111.07E+12

6926.15E+111.07E+12

6936.16E+111.06E+12

6946.18E+111.07E+12

6956.19E+111.05E+12

6966.21E+111.05E+12

6976.23E+111.04E+12

6986.24E+111.02E+12

6996.26E+111.06E+12

7006.27E+111.07E+12

7016.28E+111.05E+12

7024.17E+116.87E+11

7032.61E+114.88E+11

7041.59E+112.99E+11

7051.05E+111.71E+11

7067.37E+101.23E+11

7075.41E+108.77E+10

7084.10E+106.24E+10

7093.19E+104.74E+10

7102.55E+103.71E+10

7112.08E+102.83E+10

7121.74E+102.55E+10

7131.46E+101.90E+10

7141.25E+101.69E+10

7151.08E+101.41E+10

7169.32E+091.17E+10

7178.17E+091.06E+10

7187.20E+098.21E+09

7196.45E+096.28E+09

7205.73E+094.87E+09

7215.14E+093.85E+09

7224.66E+093.46E+09

7234.19E+092.82E+09

7243.84E+093.21E+09

7253.51E+093.59E+09

7263.26E+093.21E+09

72730000000003.72E+09

7282.77E+093.46E+09

7292.58E+093.08E+09

7302.40E+092.82E+09

7312.23E+092.82E+09

7322.09E+092.82E+09

7331.96E+092.31E+09

7341.82E+092.05E+09

7351.71E+091.92E+09

7361.59E+091.79E+09

7371.50E+091.92E+09

7381.42E+091.54E+09

73913500000001.28E+09

7401.28E+098.97E+08

7411.20E+098.97E+08

7421.13E+098.97E+08

7431.07E+098.97E+08

7441.01E+097.69E+08

7459.47E+087.69E+08

7469.08E+087.69E+08

7478.90E+087.69E+08

7488.54E+087.69E+08

7498.13E+087.69E+08

7507.79E+088.97E+08

96100

9628.30E+100

9631.66E+114.78E+11

9642.32E+116.85E+11

9652.82E+117.37E+11

9663.23E+118.13E+11

9673.55E+118.82E+11

9683.82E+119.33E+11

9694.04E+119.47E+11

9704.23E+119.73E+11

9714.40E+119.97E+11

9724.54E+111.02E+12

9734.66E+111.02E+12

9744.77E+111.03E+12

9754.86E+111.04E+12

9764.95E+1110450000000

9775.02E+111.06E+12

9785.10E+111.07E+12

9795.16E+111.07E+12

9805.23E+111.07E+12

9815.28E+111.07E+12

9825.33E+111.06E+12

9835.39E+111.07E+12

9845.43E+111.06E+12

9855.48E+111.07E+12

9865.52E+111.05E+12

9875.55E+111.08E+12

9885.59E+111.06E+12

9895.62E+111.08E+12

9905.65E+111.08E+12

9915.67E+111.07E+12

9925.70E+111.07E+12

9935.73E+111.07E+12

9945.76E+111.06E+12

9955.79E+1110850000000

9965.82E+111.07E+12

9975.84E+111.07E+12

9985.87E+111.06E+12

9995.90E+111.08E+12

10005.92E+111.07E+12

10015.94E+111.06E+12

10025.96E+111.06E+12

10035.98E+111.05E+12

10046.00E+111.05E+12

10056.02E+111.07E+12

10066.04E+111.07E+12

10076.06E+111.06E+12

10086.08E+111.06E+12

10096.10E+111.05E+12

10106.12E+111.05E+12

10116.13E+111.04E+12

10126.15E+111.06E+12

10136.16E+111.06E+12

10146.18E+111.05E+12

10156.19E+111.05E+12

10166.21E+111.04E+12

10176.22E+111.05E+12

10186.24E+111.08E+12

10196.25E+111.06E+12

10206.26E+111.07E+12

10216.27E+111.04E+12

10224.16E+116.96E+11

10232.60E+114.84E+11

10241.60E+112.97E+11

10251.05E+111.81E+11

10267.37E+101.22E+11

10275.38E+109.09E+10

10284.08E+106.58E+10

10293.19E+104.82E+10

10302.54E+103.46E+10

10312.09E+102.88E+10

10321.72E+102.44E+10

10331.46E+101.83E+10

10341.25E+101.54E+10

1035107500000001.37E+10

10369.33E+091.13E+10

10378.19E+099.87E+09

103872000000009.62E+09

10396.46E+098.33E+09

10405.75E+097.18E+09

10415.10E+096.41E+09

10424.62E+096.03E+09

10434.20E+095.26E+09

10443.80E+094.87E+09

10453.49E+093.59E+09

10463.21E+093.33E+09

10472.93E+092.56E+09

10482.71E+092.31E+09

10492.51E+092.44E+09

10502.34E+092.56E+09

10512.18E+092.44E+09

10522.05E+092.56E+09

10531.89E+092.31E+09

10541.75E+092.56E+09

10551.64E+092.56E+09

105615500000002.56E+09

10571.46E+092.44E+09

10581.38E+092.56E+09

10591.30E+092.18E+09

10601.22E+092.05E+09

10611.14E+092.18E+09

10621.08E+092.05E+09

10631.04E+092.18E+09

10649.88E+081.79E+09

10659.51E+081.41E+09

10669.05E+081.28E+09

10678.64E+081.15E+09

10688.18E+081.03E+09

10697.78E+081.03E+09

10707.47E+088.97E+08

kekbs4

Average

Center

Bunch

re(m-3)

Electron cloud density for bunch passage

Measurement of electron cloud(Y. Suetsugu, K. Kanazawa et.al.)e-ge+ beamSecondary e-xyBeam chamberMonitore-Schematic viewBeam field is shielded in actual monitors.This measurement gives electron cloud absorption rate(=production rate in equilibrium).To estimate the density, storing time should be multiplied.

Experiment and simulation resultsIpe=10 mA at I+=600 mA at 1.5 m down stream of Bend.

Graph1

4.90.9

5.61.1

6.8466

4451.5

7.71.8

Ipe (1.5m)

Ipe (6.5m)

I+(mA)

Ipe (uA)

Photo-current at button electrode

Sheet1

I (mA)Ipe (1.5m)Ipe (6.5m)

3534.90.9

3935.61.1

4666.8

4451.5

4997.71.8

Sheet1

Ipe (1.5m)

Ipe (6.5m)

I+(mA)

Ipe (uA)

Photo-current at button electrode

Sheet2

Sheet3

Recent measurement of electron cloud(not recent but 200*)Electron production rate increase as a function of the beam current. Ie=k Ib1.8 .Photoemission, . Ie=k Ib.Index, 0.8 , is due to multipactoring. Y.Suetsugu, K. Kanazawa

ILC-DR 5GeV 400 mA

Coupled-bunch instability (CBI) caused by the electron cloudWake field is induced by the electron cloudCoupled bunch instability due to the wake field causes beam loss.

Wake force and unstable mode for KEK-PFVery fast growth of the coupled bunch instability was explained.K.Ohmi, PRL,75,1526 (1995)

Measurement of the coupled bunch instability in KEKBFast amplitude growth which causes beam loss has been observed.The mode spectrum of the instability depends on excitation of solenoid magnets.

Solenoid off on (measurement)

M. Tobiyama et al., PRST-AB (2005)

Tracking simulationSolve both equations of beam and electrons simultaneouslyyxze+bunchesElectron cloud~mK.Ohmi, PRE55,7550 (1997)K.Ohmi, PAC97, pp1667.Take FFT for the bunch motion

Solenoid-OffSu Su Win et al,(EC2002)CBI mode spectra in KEKBBunches are filled every 4 bucket.

Effect of Solenoid magnetSolenoid magnets suppress the electron cloud effect partially. We can observe electron cloud effect characterized by solenoid magnet.

Cloud distribution (K. Ohmi, APAC98)

10 G 20 G 30 G

Solenoid-ONSu Su Win et al., EC2002KEKB

Single bunch instabilityVertical Beam size blow up of positron beam at commissioning of KEKBA beam-size blow-up has been observed above a threshold current. The threshold is given for total current.The blow-up was observed in multi-bunch operation, but was perhaps single bunch effect. Beam size was measured by putting a bunch with an arbitrary current in a bunch train.Luminosity is limited by the beam size blow-up.

Synchro-beta sideband induced by electron cloud head-tail instability was observed.

Measurements of the single bunch instabilityBeam size blow-upSynchro-beta sidebandny~ny+ nsFukuma et al.J. Flanagan et al.

Head-tail instability modelSimulation using Gaussian model, the same method as the study for CBI.Wake field approach, the same as CBI.PIC simulation (like beam-beam strong-strong)

Electron cloud Positron bunchEzy,xyxSimulation using Gaussian micro-bunch model

Bunch head-tail motion w/wo synchrotron motion.Vertical amplitude of the macro-particles in the longitudinal phase space are plotted. Multi-airbag model (z-d) is used to visualize in these figures.K. Ohmi, F. Zimmermann, PRL85, 3821 (2000).

Head-tail and strong head-tail instabilityUnstable for Positive chromaticity --- head-tailUnstable for re= 10x1011 m-3 irrelevant to chromaticity --- strong head-tailns=0 ns=0.015 x=8 ns=0.015 x=0re=2x1011 , 4x1011, 10x1011 m-3

Wake field approachLinearized model.Numerical calculation including nonlinearity. (Similar way to the calculation of the multi-bunch wake field)

K=1 for Linearized model. K~2-3 for the numerical calculation.

Vertical wake field given by the numerical method(1,1) is consistent with the analytical calculation.(10,10) is twice larger than (1,1).Instability threshold is calculated by the wake force.K. Ohmi, F. Zimmermann, E. Perevedentsev, PRE65,016502 (2001)Q=5~10

Threshold of strong head-tail instabilityMode coupling theory Threshold : re=1-2x1012m-3

Coasting beam model

Threshold : re=5x1011m-3

Coasting beam model is better coincident with simulation.Q=min(Qnl, wesz/c)

Simulation with Particle In Cell methodElectron clouds are put at several positions in a ring.Beam-could interaction is calculated by solving 2 dimensional Poisson equation on the transverse plane. A bunch is sliced into 20-30 pieces along the length.

PIC simulationSnap shot of beam and cloud shape for ns=0 and ns>0 Pink: size along bunch lengthyellow: of cloudDark blue: of bunch BBUHead-tail motion

Graph1

0.000012880.059770.00009529

-0.000015880.060130.00002605

-0.00075780.05979-0.00005334

0.0008520.06007-0.0001516

0.00083320.05972-0.0002195

0.00014880.06008-0.0002638

0.00046240.05943-0.0003024

-0.00038770.06055-0.0003292

0.0010080.05976-0.0003627

0.00032330.05974-0.0003345

-0.00028240.06049-0.0002806

0.0009240.06044-0.000224

0.001040.05987-0.000146

0.0010190.05996-0.00002798

-0.00015820.06050.000104

0.00010080.061910.000192

0.001010.062790.0002307

0.0025120.062840.0002717

0.0063670.063360.0003079

0.0091510.064110.0004154

0.011130.066620.0006869

0.016570.068340.001166

0.023180.072930.00211

0.031690.078330.00389

0.036180.092180.00712

0.014980.10310.01242

-0.057160.091150.01937

-0.15010.073650.02496

-0.20020.08280.02456

-0.012650.070050.01014

y (beam)

sy (beam)

y (cloud)

z/sz

y (mm)

b0

199122.09E+001.89E-06-7.95E-071.29E-081.09E-084.22E-044.26E-055.98E-056.05E-06-8.94E-089.53E-084.62E-042.31E-042.09E+001.29E-055.98E-029.53E-05

2100021.65E+002.88E-068.73E-07-1.59E-085.45E-084.22E-044.21E-056.01E-056.02E-06-5.86E-082.61E-084.52E-042.18E-041.65E+00-1.59E-056.01E-022.61E-05

398611.39E+005.57E-06-5.97E-07-7.58E-07-3.57E-084.28E-044.23E-055.98E-055.98E-06-2.67E-09-5.33E-084.39E-042.03E-041.39E+00-7.58E-045.98E-02-5.33E-05

4100661.19E+008.82E-061.48E-078.52E-071.37E-084.27E-044.33E-056.01E-056.04E-068.75E-08-1.52E-074.25E-041.87E-041.19E+008.52E-046.01E-02-1.52E-04

5101121.04E+003.35E-06-4.60E-078.33E-071.91E-084.27E-044.24E-055.97E-056.05E-062.22E-07-2.20E-074.11E-041.70E-041.04E+008.33E-045.97E-02-2.20E-04

6100539.04E-01-5.25E-07-4.41E-091.49E-072.46E-084.29E-044.21E-056.01E-056.04E-063.69E-07-2.64E-073.95E-041.53E-049.04E-011.49E-046.01E-02-2.64E-04

799197.84E-01-5.82E-072.01E-084.62E-075.69E-084.24E-044.25E-055.94E-055.98E-064.82E-07-3.02E-073.77E-041.36E-047.84E-014.62E-045.94E-02-3.02E-04

8100346.74E-012.89E-065.31E-07-3.88E-072.20E-084.23E-044.28E-056.06E-056.10E-065.80E-07-3.29E-073.59E-041.20E-046.74E-01-3.88E-046.06E-02-3.29E-04

9100995.73E-013.55E-066.20E-071.01E-06-9.05E-094.27E-044.25E-055.98E-056.05E-066.76E-07-3.63E-073.40E-041.04E-045.73E-011.01E-035.98E-02-3.63E-04


11100233.86E-011.81E-064.26E-07-2.82E-07-2.91E-084.24E-044.29E-056.05E-055.96E-069.10E-07-2.81E-072.98E-047.98E-053.86E-01-2.82E-046.05E-02-2.81E-04

12100932.97E-012.19E-06-7.73E-089.24E-07-1.27E-074.17E-044.26E-056.04E-056.01E-061.01E-06-2.24E-072.75E-047.33E-052.97E-019.24E-046.04E-02-2.24E-04



1599814.18E-026.03E-06-4.29E-08-1.58E-07-5.90E-094.28E-044.20E-056.05E-056.10E-061.31E-061.04E-072.00E-048.11E-054.18E-02-1.58E-046.05E-021.04E-04

1610070-4.18E-026.60E-061.11E-061.01E-072.96E-084.28E-044.25E-056.19E-056.26E-061.41E-061.92E-071.74E-048.89E-05-4.18E-021.01E-046.19E-021.92E-04

179909-1.26E-013.48E-063.43E-071.01E-06-2.12E-074.31E-044.22E-056.28E-056.30E-061.55E-062.31E-071.48E-049.73E-05-1.26E-011.01E-036.28E-022.31E-04

189947-2.11E-01-1.01E-053.94E-072.51E-06-1.87E-074.24E-044.21E-056.28E-056.37E-061.73E-062.72E-071.22E-041.05E-04-2.11E-012.51E-036.28E-022.72E-04




229812-5.73E-01-2.48E-061.27E-071.66E-054.05E-074.27E-044.18E-056.83E-057.02E-061.77E-061.17E-069.25E-051.28E-04-5.73E-011.66E-026.83E-021.17E-03


2410013-7.84E-01-2.64E-065.98E-073.17E-052.23E-064.23E-044.21E-057.83E-058.28E-061.93E-063.89E-061.50E-041.31E-04-7.84E-013.17E-027.83E-023.89E-03


2610148-1.04E+00-5.75E-06-1.25E-071.50E-051.01E-054.24E-044.28E-051.03E-048.51E-062.08E-061.24E-052.31E-041.31E-04-1.04E+001.50E-021.03E-011.24E-02

279998-1.19E+00-1.94E-063.25E-07-5.72E-051.28E-054.24E-044.22E-059.12E-059.24E-062.19E-061.94E-052.80E-041.30E-04-1.19E+00-5.72E-029.12E-021.94E-02

2810054-1.39E+00-8.74E-063.44E-07-1.50E-049.08E-064.26E-044.23E-057.37E-051.05E-052.29E-062.50E-053.37E-041.32E-04-1.39E+00-1.50E-017.37E-022.50E-02

2910040-1.65E+00-8.40E-06-2.56E-07-2.00E-04-5.65E-064.24E-044.22E-058.28E-059.18E-062.30E-062.46E-054.12E-041.42E-04-1.65E+00-2.00E-018.28E-022.46E-02

3010007-2.09E+00-3.14E-067.33E-08-1.27E-05-1.88E-054.29E-044.26E-057.01E-056.89E-062.12E-061.01E-055.29E-041.83E-04-2.09E+00-1.27E-027.01E-021.01E-02

b0

y (beam)

sy (beam)

y (cloud)

z/sz

y (mm)

Graph1

-0.093980.15540.001514

-0.17390.1493-0.002172

-0.17590.1353-0.008596

-0.15810.1266-0.01639

-0.14320.1197-0.02493

-0.12520.1147-0.03393

-0.11560.1086-0.04307

-0.10510.1058-0.05216

-0.10070.1029-0.06094

-0.098830.1015-0.06941

-0.092640.1002-0.07766

-0.09060.0993-0.08568

-0.089390.09938-0.09347

-0.081910.09986-0.101

-0.074740.09994-0.1081

-0.06650.098-0.1146

-0.059960.0977-0.1201

-0.048230.09537-0.1243

-0.036970.09565-0.1269

-0.025310.09551-0.1277

-0.014040.0943-0.1264

-0.0010830.09441-0.1229

0.011790.09686-0.1169

0.026390.09593-0.1079

0.041620.1003-0.0955

0.060040.1027-0.07867

0.077490.1045-0.05594

0.098970.1057-0.02461

0.11610.10540.02192

0.12940.1040.1012

y (beam)

sy (beam)

y (cloud)

z/sz

y (mm)

b5

199972.09E+00-5.31E-066.01E-07-9.40E-05-2.76E-054.29E-044.26E-051.55E-049.41E-065.08E-071.51E-064.60E-042.31E-042.09E+00-9.40E-021.55E-011.51E-03

2100311.65E+004.93E-06-7.32E-08-1.74E-04-1.92E-054.22E-044.24E-051.49E-041.42E-053.91E-07-2.17E-064.51E-042.21E-041.65E+00-1.74E-011.49E-01-2.17E-03

3100571.39E+006.76E-076.46E-07-1.76E-04-1.30E-054.25E-044.24E-051.35E-041.60E-053.79E-07-8.60E-064.39E-042.11E-041.39E+00-1.76E-011.35E-01-8.60E-03



699509.04E-01-2.69E-061.64E-07-1.25E-04-8.04E-064.27E-044.20E-051.15E-041.41E-054.01E-07-3.39E-053.99E-041.78E-049.04E-01-1.25E-011.15E-01-3.39E-02

7100197.84E-01-7.39E-07-3.27E-07-1.16E-04-7.94E-064.19E-044.24E-051.09E-041.34E-054.15E-07-4.31E-053.83E-041.65E-047.84E-01-1.16E-011.09E-01-4.31E-02


998145.73E-01-6.02E-063.21E-07-1.01E-04-9.12E-064.25E-044.21E-051.03E-041.24E-054.26E-07-6.09E-053.49E-041.37E-045.73E-01-1.01E-011.03E-01-6.09E-02

1097664.77E-012.57E-06-1.92E-07-9.88E-05-9.73E-064.23E-044.20E-051.02E-041.23E-053.88E-07-6.94E-053.30E-041.23E-044.77E-01-9.88E-021.02E-01-6.94E-02






169966-4.18E-02-2.88E-06-6.52E-08-6.65E-05-1.35E-054.18E-044.29E-059.80E-051.09E-055.37E-07-1.15E-041.94E-047.57E-05-4.18E-02-6.65E-029.80E-02-1.15E-01

1710088-1.26E-012.24E-063.82E-07-6.00E-05-1.41E-054.22E-044.24E-059.77E-051.07E-056.12E-07-1.20E-041.69E-048.09E-05-1.26E-01-6.00E-029.77E-02-1.20E-01





2210100-5.73E-012.16E-07-2.67E-07-1.08E-06-1.49E-054.26E-044.27E-059.44E-059.96E-067.41E-07-1.23E-048.48E-051.29E-04-5.73E-01-1.08E-039.44E-02-1.23E-01

2310015-6.74E-012.28E-06-5.36E-071.18E-05-1.47E-054.25E-044.27E-059.69E-051.01E-056.90E-07-1.17E-041.01E-041.39E-04-6.74E-011.18E-029.69E-02-1.17E-01

249925-7.84E-01-1.47E-068.64E-082.64E-05-1.45E-054.25E-044.23E-059.59E-051.00E-056.74E-07-1.08E-041.29E-041.49E-04-7.84E-012.64E-029.59E-02-1.08E-01

2510065-9.04E-01-2.88E-06-1.49E-074.16E-05-1.42E-054.28E-044.21E-051.00E-049.93E-066.05E-07-9.55E-051.65E-041.61E-04-9.04E-014.16E-021.00E-01-9.55E-02

2610113-1.04E+006.11E-062.16E-076.00E-05-1.38E-054.26E-044.25E-051.03E-049.95E-065.34E-07-7.87E-052.07E-041.74E-04-1.04E+006.00E-021.03E-01-7.87E-02

2710059-1.19E+00-6.59E-06-4.28E-077.75E-05-1.25E-054.31E-044.29E-051.05E-049.81E-065.41E-07-5.59E-052.56E-041.89E-04-1.19E+007.75E-021.05E-01-5.59E-02

289860-1.39E+00-3.50E-06-8.89E-089.90E-05-1.12E-054.29E-044.21E-051.06E-049.50E-065.11E-07-2.46E-053.15E-042.08E-04-1.39E+009.90E-021.06E-01-2.46E-02

2910000-1.65E+00-7.41E-062.74E-081.16E-04-9.16E-064.23E-044.21E-051.05E-049.68E-063.83E-072.19E-053.92E-042.33E-04-1.65E+001.16E-011.05E-012.19E-02

309917-2.09E+002.81E-068.48E-071.29E-04-4.64E-064.21E-044.27E-051.04E-049.55E-06-1.82E-091.01E-045.12E-042.74E-04-2.09E+001.29E-011.04E-011.01E-01

b5

y (beam)

sy (beam)

y (cloud)

z/sz

y (mm)

Threshold behaviorns=0 no threshold, ns>0 clear threshold. re,th=5x1011m-3 The cloud density is consistent with that predicted by the measurement of electron current. This beam size blow-up can be understood as strong head-tail instability caused by electron cloud.

Solenoid winding in KEKB ring(0) C-yoke permanent magnets are attached in the arc section of ~800m(1) Solenoids are wound in the arc section of 800m (Sep. 2000).(2) Solenoids are wound additionally in the arc section of 500m (Jan. 2001).(3) Solenoids are wound in the straight section of *100m (Apr. 2001).(4) Add solenoids even in short free space (August 2001).(5) 95 % of drift space is covered (~2005).(6) Solenoid in of quadrupole magnets (2005)

Solenoid magnets

Luminosity for Solenoids ON/OFFWhen solenoids turn off, stored current is limited to a lower value than usual operation due to beam loss (coupled bunch instability).Luminosity is quite low (~half).

Specific Luminosity for Solenoid ON/OFF (measurement at May.2001)Solenoid ONOFFI+I-L/I+I-

Effect of additional solenoidTypical luminosity behavior at Dec. 2000 and March. 2001Adding solenoid, positron current with peak luminosity increases.Now peak luminosity is given at around 1600-1800 mA. 750mAL (x1030)Beam-beam tuning also improves the luminosity.Solenoid covers 800 m1300 mLonger and longer

Luminosity history of KEKB

Measurement of synchro-beta sideband - evidence for head-tail instability If the beam size blow-up is due to head-tail instability, a synchro-betatron sideband should be observed above the instability threshold.The sideband spectra was observed with a bunch oscillation recorder.The threshold was consistent with simulations.

The sideband appear near ~ny+ns, while simulation gives ~ny-ns, like ordinary strong head-tail instability.

Fourier power spectrum of BPM dataLER single beam, 4 trains, 100 bunches per train, 4 rf bucket spacingSolenoids off: beam size increased from 60 mm ->283 mm at 400 mAVertical feedback gain loweredThis brings out the vertical tune without external excitationBunch Spacing vs Spec. Lum.Luminosity-bunch current-sideband experiment Measure as a function of bunch current.Sideband is measured for noncolliding bunch.Tune0.51.0Bunch1100V. TuneSideband PeakSynchrotron TuneJ. Flanagan et al., PRL94, 054801 (2005)

Electron cloud induced head-tail instabilityE. Benedetto, K. Ohmi, J. FlanaganMeasurement at KEKBTail of trainHead of trainBetatron sideband Head-tail regime Incoherent regimeSimulation (PEHTS) HEADTAIL gives similar results

Feedback does not suppress the sidebandBunch by bunch feedback suppress only betatron amplitude.Sideband signal is Integrated over the trainBetatron sideband Simulation (PEHTS)

Electron cloud effect in CESR, CesrTF and KEKB-loweTune shift measurement and electron build-up.Coupled bunch instabilitySingle bunch instability Incoherent emittance growth

Number of produced electrons Bunch populationNp=2x1010electrons created by a bunch passage in a meter NpxYpe=1.7x109 (5GeV) 6.8x108 (2GeV)If electrons are accumulated 5 times, electron line density (m-1) 8.5x109 (5GeV), 3.4x109 (2GeV) volume density(m-3) 1.7x1012 , 6.8x1011 Corresponding Tune shift 0.0037, 0.0037 (7.4e-4/bunch) Beam line density Np/4.2=4.8x109CESR 5GeV g=10000 Ype=0.086/m, Ec=3 keVCesr-TF 2GeV (arc) =4000 Ype=0.034/m, Ec=100 eVNumber of photon emitted by a positron par unit bending angle.Quantum eff.=0.1

Tune shift2nd order moment (c, c) of electron cloud distribution gives tune shift., where c=2.if x~y

Tune shift at KEKB (T. Ieiri, Proceedings of Ecloud07)Both showed similar density because of x+y=0.015 and 0.012Without solenoidWith solenoid

Tune shift at CESR=30mN=1.2x1010Dny=0.1 kHz/bunch

Tune shift for 5.3 GeV in CESR5.3 GeV 5 bunch (D. Rice, Sep 06)Tune shift is similar as that for 1.9 GeV.Cloud density is linear for . Sign of photoelectron dominantDny=0.1 kHz/bunch

Measured tune shift is 1/3 of the simple estimationMaybe reasonable considering magnetic fieldElectron distribution depends on magnetic filedStraight section Magnetic field section ny>nx ny~ -nx>0beamcloud

Wiggler section1.3m (1m effective)x12, 2.1T, qtot=3.78 rad.Npe,tot=15.9x2x1010=3.2x1011 (5.2x1011 in arc).If the electrons localized in 20 m (for example), electrons are accumulated by Npe=2.6x1010 m-1bunch-1. Beam line density Np/4.2=4.8x109 m-1.Electron production and buildup are suppressed by the space charge (neutralization) limit.Arc is dominant for the electron cloud tune shift and instabilities in CESR.

Coupled bunch instabilityNp=1x1010, 4 ns spacing.Growth time ~25 turn, 64 msec.

Since tune shift is 1/3 of the estimation, the growth may be also 1/3.

Threshold of the strong head-tail instability (Balance of growth and Landau damping)Stability condition for wesz/c>1

Since re=le/2psxsy,

Q=min(Qnl, wesz/c) Qnl=7 is used. K characterizes cloud size effect and pinching. wesz/c~12-15 for damping rings.We use K=wesz/c and Qnl=7 for analytical estimation.Origin of Landau damping is momentum compaction

Threshold for various rings

ILC-DR study

KEKBKEKBKEKB-DRCesrTFILC-OCSPEPIICESRKEKB-DRKEKB

L301630163016768.4466952200768.4430163016

gamma684968494501391497856067489297856849

Np3.30E+107.60E+102.00E+102.00E+102.00E+108.00E+102.00E+102.00E+106.60E+10

ex1.80E-081.80E-081.50E-092.30E-095.60E-104.80E-082.30E-091.50E-091.80E-08

bx101010103010101010

ey2.16E-102.16E-106.00E-125.00E-122.00E-121.50E-091.50E-126.00E-122.16E-10

by101010103010301010

sigx4.24E-044.24E-041.22E-041.52E-041.30E-046.93E-041.52E-041.22E-044.24E-04

sigy4.65E-054.65E-057.75E-067.07E-067.75E-061.22E-046.71E-067.75E-064.65E-05

sigz0.0060.0070.0090.0090.0060.0120.0060.0090.007

nus0.0240.0240.0110.0980.0670.0250.0980.0110.024

Q3.65.97773.7775.5

omegae1.79E+112.51E+115.29E+115.01E+116.31E+119.20E+106.31E+115.29E+112.34E+11

phasee3.65.915.915.012.63.712.615.95.5

K3.65.915.915.012.63.712.612.55.5

rhoeth6.25E+113.81E+119.60E+102.92E+121.91E+117.67E+111.22E+122.65E+114.09E+11

[email protected]

DampT-xy40407556.4264056.4

DampR-xy2.51E-042.51E-041.34E-044.54E-058.58E-041.83E-044.54E-05

Ib (mA)0.5251.2100.3181.2490.1431.7451.2490.3181.050

lamdap2.75E+125.43E+121.11E+121.11E+121.67E+123.33E+121.67E+121.11E+124.71E+12

0.0

ngam0.15033305720.15033305720.09879029480.21476151030.42145171720.33716137380.1825394743

Ygam0.10.10.10.10.10.100.02

ne0.01503330570.01503330570.00987902950.0214761510.04214517170.033716137400.0036507895

Ne4.96E+081.14E+091.98E+084.30E+088.43E+086.74E+080.0002.92E+08

rhoe4.96E+111.14E+121.98E+114.30E+118.43E+116.74E+110.00E+002.92E+11

0.000

lamdaex0.00E+000.00E+000.00E+000.00E+000.00E+0030.00E+00

omegaex5.91E+108.31E+101.33E+111.33E+111.08E+1103.87E+10

phaseex1.21.94.04.03.20.0001.5

rhoethx0.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00

KEKBKEKBKEKB-DRCesrTFILC-OCSPEPII

L301630163016768.4466952200

gamma684968494501391497856067

Np3.30E+107.60E+102.00E+102.00E+102.00E+108.00E+10

rhoeth6.25E+113.81E+111.22E+114.76E+121.91E+117.67E+11

[email protected]

DampT-xy40407556.42640

DampR-xy2.51E-042.51E-041.34E-044.54E-058.58E-041.83E-04

positron

c3.00E+08

KEKBKEKBKEKB-DRKEKB-DRCESRCesrTFSKEKBDAFNEPEPIIJLCGLC IITESLATESLA (05)ILC-3200ILC-OTWILC-OCSre2.82E-15

sigx4.20E-044.20E-041.22E-041.22E-041.50E-041.50E-044.20E-042.00E-036.93E-048.37E-054.90E-052.70E-041.30E-041.00E-041.10E-041.10E-04alpha0.0072992701

sigy6.00E-056.00E-051.22E-051.22E-057.00E-061.00E-056.00E-056.32E-051.22E-047.07E-066.00E-062.70E-047.30E-061.00E-057.30E-067.30E-06

sigz0.0060.0070.0090.0090.0060.0090.0030.0240.0120.0050.00550.00550.00550.00550.0060.006KEKBDAFNEPEPIIJLC DRJLC DR

nus0.0240.0240.0110.0110.0980.0980.0180.0120.0250.010.01180.0650.0650.0650.04180.0337E (GeV)3.50.5531.981.98

L3016301630163016768.44768.44301697.72200395299.791700017000320032236114L (m)301697.72200395395

gamma6849684945019785489239141565699860673875387597859785978597859785Np3.30E+104.00E+106.00E+107.50E+097.50E+09

beta101010101010101010101030303030302.53.23.29.19.1

Np3.30E+107.60E+102.00E+102.00E+102.00E+102.00E+103.30E+104.00E+106.00E+107.50E+097.50E+092.00E+102.00E+101.40E+102.20E+102.00E+100.0180.0120.0250.010.01

rhoe1.00E+121.00E+121.00E+121.00E+121.00E+121.00E+121.00E+121.00E+121.00E+121.00E+121.00E+121.00E+101.00E+111.00E+111.00E+101.00E+1042020007008484

Q35777733.003.005.005.005.005.005.005.005.0060631207.17.1

Ib (mA)0.5251.2100.3180.3181.2491.2490.52519.6521.3090.9111.2010.0560.0560.2100.3280.1570.0040.0240.0120.0050.005

10881931236826826

lamdap2.75E+125.43E+121.11E+121.11E+121.67E+121.11E+125.50E+128.33E+112.50E+127.50E+116.82E+111.82E+121.82E+121.27E+121.83E+121.67E+125.40E+111.85E+121.18E+124.40E+124.40E+12

lamdae1.58E+051.58E+059.35E+039.35E+036.59E+039.42E+031.58E+057.94E+055.33E+053.72E+031.85E+034.58E+035.96E+026.28E+025.04E+015.04E+01

omegae1.56E+112.19E+114.15E+114.15E+116.20E+114.20E+112.20E+114.03E+107.97E+105.45E+117.24E+115.63E+106.79E+115.42E+117.37E+117.03E+11

phasee3.15.112.512.512.412.62.23.23.29.113.31.012.49.914.714.1

K3512.512.512.612.63333333333

Z/Z0431660741079041079041941728579215851133633640293635066361713124258

U1.1331.9209.5004.3700.2660.3210.9340.5390.8490.3790.1610.1420.2230.0510.0060.014

rhoeth8.83E+115.21E+111.05E+112.29E+113.76E+123.11E+121.07E+121.85E+121.18E+122.64E+126.21E+127.03E+104.47E+111.98E+121.82E+127.36E+11Yield

Yield0.0150.004

omegaex5.88E+108.27E+101.31E+111.31E+111.34E+111.08E+118.32E+107.16E+093.35E+101.58E+112.53E+115.63E+101.61E+111.71E+111.90E+111.81E+11Np3.30E+107.50E+090.60759493670.003427192

phaseex1.21.93.93.92.73.30.80.61.32.64.61.02.93.13.83.6e1.60E-191.60E-19

Lsp8.00E-091.40E-09

Zx/Z02061748638637215110351981031201171245736R5.00E+001.00E+00

Ux0.1680.2800.9460.4350.0120.0210.0980.0180.1600.0970.0870.0490.0520.0170.0020.004I (A/cm2)0.00000315290.0000054595

rhoethx5.95E+123.57E+121.06E+122.30E+128.19E+134.67E+131.02E+135.46E+136.27E+121.03E+131.15E+132.04E+111.92E+125.97E+125.57E+122.37E+12Ibeam6.60E-018.57E-01

lamdaex1.11E+061.11E+069.35E+049.35E+041.41E+051.41E+051.11E+062.51E+073.02E+064.40E+041.51E+044.58E+031.06E+046.28E+037.60E+027.60E+02

Zxx/Z0565469485848585901054200335016419102413053593162

Uxx0.3920.3921.3520.6220.0370.0460.2290.1930.3010.2300.1430.0100.1850.0340.0050.013

rhoethx2.55E+122.55E+127.39E+111.61E+122.67E+132.18E+134.37E+125.18E+123.32E+124.36E+127.01E+121.02E+125.39E+112.98E+121.85E+127.85E+11

ngam0.15033305720.15033305720.09879029480.21476151030.42145171720.33716137380.34361841650.67622838220.18253947430.64936051440.85559025720.03810121850.03810121850.20241272350.20096826410.1059405815

Ygam0.10.10.10.10.10.10.020.020.020.020.020.020.020.020.020.02

ne0.01503330570.01503330570.00987902950.0214761510.04214517170.03371613740.00687236830.01352456760.00365078950.01298721030.01711180510.00076202440.00076202440.00404825450.00401936530.0021188116

Ne4.96E+081.14E+091.98E+084.30E+088.43E+086.74E+082.27E+085.41E+082.19E+089.74E+071.28E+081.52E+071.52E+075.67E+078.84E+074.24E+07

rhoe4.96E+111.14E+121.98E+114.30E+118.43E+116.74E+112.27E+115.41E+112.19E+119.74E+101.28E+111.52E+101.52E+105.67E+108.84E+104.24E+10

rhoe1.00E+101.00E+111.00E+11

dny1.47E-032.79E-035.29E-03

proton

c29979

c3.00E+08e1.60E-19

re2.82E-15Zv377

alpha0.0072992701rp1.53E-18

Coasting beam

JHF 3GeVJHF 50GeVPSRISISSNSAGSFNAL MIMR50PSRISISAGSAGSbstFNAL MIKEKPSVLHC

injextinjextext

sigx1.90E-021.20E-021.10E-023.50E-031.00E-023.80E-022.80E-027.00E-031.70E-03sigx3.50E-031.00E-023.80E-021.00E-021.00E-021.70E-030.0052915026

sigy1.90E-021.20E-021.10E-023.50E-031.00E-023.80E-022.80E-027.00E-031.70E-03sigy3.50E-031.00E-023.80E-023.00E-031.00E-021.70E-030.0047328638

lz1108282166560200681.6lz1567.590163800.00202.003319.4339.120.11

nus0.00580.00050.00260.00010.00030.00360.000400.00170.0013nus0.00010.00030.00360.0082

L348.3348.31567.51567.5901632488003319.4L1567.5901638.00E+022023319.4339.122.33E+05

gamma1.404.204.2054.281.851.072.022.50127.90gamma54.281.851.072.50E+011.20E+00127.9012.793176972320000.00

beta101010101010101030beta1010101.00E+011.00E+013010230

Np4.15E+134.15E+134.15E+134.15E+133.00E+131.25E+132.05E+141.20E+136.00E+10Np3.32E+143.00E+133.00E+137.00E+131.80E+133.00E+1325200000000002.50E+10

3.77E+115.06E+115.06E+112.59E+124.62E+112.08E+111.03E+121.76E+113.75E+102.12E+113.33E+111.84E+118.75E+108.91E+109.04E+097.43E+092.27E+11

8.27E+11

Q555555555Q5555.005.00551

Ib (A)5.7275.7271.2731.27316.0223.68639.7310.7210.001Ib (A)10.18016.0228.8464.2064.2830.4340.3570.000

eta*dp/p5.75E-033.70E-044.27E-043.21E-066.81E-044.16E-031.02E-036.13E-07eta*dp/p3.21E-066.81E-044.16E-036.12E-053.26E-036.13E-074.73E-051.32E-08


0.0200000.0067000.0035000.0000100.0340000.0030000.0190000.0001000.0000100.0021000.0250000.4500000.0260.1500000.0005500.0400000.000550


0.0420000.0230000.0500000.0005000.0670000.0050000.0390000.001500

1.58E+101.16E+102.53E+101.30E+093.09E+101.04E+094.00E+102.65E+08

omegae3.64E+086.68E+087.29E+085.18E+097.65E+081.35E+084.07E+086.76E+081.28E+09omegae1.48E+096.50E+081.27E+087.55E+083.36E+086.30E+081.99E+083.30E+10

133.5182.5199.1276.5165.827.1271.5153.26.87739.5195.169.12012.3226.46970.3225.412.1

w01.20E+062.09E+071.16E+072.36E+069.33E+065.68E+055.56E+06

n1231.831.111.0320.336.01109.435.9

K111111111K11111111

Z/Z0 L38393224902025560886711963252.29E+03Z/Z0 L53459447610106212207602801.26E+051.14E+051.46E+06

Z L144726412154513400648959722295054253994507761224528.61E+05Z L201540461687540380982080001885227255354.74E+074.29E+075.50E+08

ZL/Q28945324309068013019194459011508090155244901.72E+05ZL/Q40308093375087619641600037745451079.48E+068.58E+065.50E+08

U L0.0710.2260.1120.0231.6230.0070.2950.00580.027U L1.4041.0141.0091.0071.0121.0421.0352.043E-01

Z/Z0 H806211067128861127281199611224544872Z/Z0 H

Z H303925441724424858069047985824522607423319252771836778Z H

ZH/Q60785183448897161389597169045218466185055367356ZH/Q

U H0.1490.7771.5941.1703.1990.0120.6050.070U H

1.170

fthr0.28163519430.02960803510.03135958410.00042748620.02094718510.41910218940.06447935010.0213715253

Yi (/m.p)8.00E-098.00E-098.00E-09

build-up time8.75E-041.04E-021.88E-01

gammat31.6 I3.085.074.9521.8gammat31.6 I8.54.8821.86.76

1/gammt^2-0.00100144210.10541406650.03890308850.0408121620.0021042-0.00100144210.01384083040.04199140020.00210420.0218829873

eta-0.0013408487-0.1867700095-0.8345356398-0.20426185030.0020430693eta-0.00134084870.0122408304-0.65245304430.00204306930.01577295952.20E-05

dp/p2.50E-034.00E-035.00E-035.00E-033.00E-04dp/p2.50E-035.00E-035.00E-033.00E-043.00E-036.00E-04

eta*dp/p-3.35E-06-7.47E-04-4.17E-03-1.02E-036.13E-07eta*dp/p-3.35E-066.12E-05-3.26E-036.13E-074.73E-051.32E-08

nus-0.00010-0.00033-0.00361-0.000400.00040nus-0.000000.00002-0.001040.000000.000020.00890

114.8325358852

Keil-Shnell

JHF 3GeV

inj

sigx1.90E-02

sigy1.90E-02

lz110

nus0.0058

L348.3

gamma1.40

beta10

Np4.15E+13

3.77E+11

Q5

Ib (A)5.727

eta*dp/p5.75E-03

3.77E+11

0.020000

7.55E+09

0.042000

1.58E+10

omegae3.64E+08

133.5

K1

Z/Z0 L3839

Z L1447264

ZL/Q289453

U L0.071

Z/Z0 H8062

Z H3039254

ZH/Q607851

U H0.149

fthr0.2816351943

gammat

1/gammt^2

eta

dp/p

eta*dp/p

nus

Tune shift at the threshold

KEKBKEKBKEKB-DRCesrTFILC-OCSPEPIIL301630163016768.4466952200gamma6849 6849 4501 3914 9785 6067 Np3.30E+107.60E+102.00E+102.00E+102.00E+108.00E+10rhoeth6.25E+113.81E+111.22E+114.76E+121.91E+117.67E+11

[email protected] 0.0047 0.0023 0.0263 0.0111 0.0078 DampT-xy40407556.42640DampR-xy2.51E-042.51E-041.34E-044.54E-058.58E-041.83E-04

Incoherent emittance growthMechanism: Nonlinear diffusion related to resonances and chaosThe diffusion rate and the radiation damping time

For an incoherent effect, beam size measurement without current dependence is necessary. It seems to be difficult in present KEKB tool.

Incoherent emittance growth below the threshold of the fast head-tail at KEKB-lowe and OCSOCS arc lattice is used for KEKB.e =3x1010 m-3 (e,th =1x1011 m-3 )

y/y=5.7x10-6

Need to check tune dependence and lattice slice dependenceBunch and e-cloud profiles at 500 turnBy H. JinCoherent motionNo coherent motion

Summary for CESR and comment on experimentsThe cloud density is e=1.5-4.5x1011 m-3 for N=1.2x1010, 14 ns spacing at CESR.The density is reasonable for the photo-electron model, and arc section is dominant. The coherent instability is observed at 10 times higher cloud density. More bunches with short spacing or lower a may realize the unstable condition.The operation with N=2x1010, 6 ns spacing, may achieve the threshold e~1-2x1012 m-3.Incoherent emittance growth may be seen in CESR, though may not seen in damping ring nor KEKB lowe.The coupled bunch instability should be seen, if bunches are stored uniformly, for example, 4-8 ns spacing, 100 mA depending on chromaticity (head-tail damping).

Documents

Electron cloud effects in Cesr-TF and KEKB