electron cloud effects in cesr-tf and kekb
DESCRIPTION
Electron cloud effects in Cesr-TF and KEKB. K. Ohmi KEK 29 Feb 2008 LEPP, Cornell univ. Contents. History, electron cloud effect in KEK-PF Electron cloud build-up at KEKB Coupled bunch instability caused by electron cloud Single bunch instability caused by electron cloud - PowerPoint PPT PresentationTRANSCRIPT
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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
165585000000486154000000
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00
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6094990000001073210000000
6112350000001073210000000
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6150990000001050640000000
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6199050000001057820000000
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00
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00
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5279910000001074360000000
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5519670000001048460000000
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6211260000001038330000000
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6240810000001080510000000
6250780000001055130000000
6264420000001069360000000
6270360000001044870000000
416264000000695641000000
260319000000484231000000
159586000000297051000000
104709000000181282000000
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5383720000090897400000
4081030000065769200000
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2085380000028846200000
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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
10100874.77E-01-1.24E-062.03E-073.23E-076.05E-084.20E-044.26E-055.97E-056.06E-068.03E-07-3.35E-073.19E-049.05E-054.77E-013.23E-045.97E-02-3.35E-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
13101172.11E-01-8.13E-076.39E-071.04E-063.56E-084.24E-044.23E-055.99E-056.03E-061.14E-06-1.46E-072.51E-047.18E-052.11E-011.04E-035.99E-02-1.46E-04
14100641.26E-01-1.65E-061.19E-071.02E-065.28E-084.22E-044.23E-056.00E-056.03E-061.23E-06-2.80E-082.26E-047.49E-051.26E-011.02E-036.00E-02-2.80E-05
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
1910009-2.97E-012.79E-064.95E-076.37E-06-2.75E-074.23E-044.22E-056.34E-056.39E-061.69E-063.08E-079.95E-051.13E-04-2.97E-016.37E-036.34E-023.08E-04
209901-3.86E-011.63E-072.46E-079.15E-06-1.45E-074.28E-044.25E-056.41E-056.58E-061.67E-064.15E-078.35E-051.19E-04-3.86E-019.15E-036.41E-024.15E-04
219771-4.77E-017.68E-064.48E-071.11E-052.71E-074.23E-044.21E-056.66E-056.66E-061.66E-066.87E-078.02E-051.24E-04-4.77E-011.11E-026.66E-026.87E-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
239943-6.74E-016.01E-078.57E-072.32E-051.10E-064.24E-044.23E-057.29E-057.61E-061.84E-062.11E-061.17E-041.30E-04-6.74E-012.32E-027.29E-022.11E-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
259955-9.04E-016.46E-064.91E-073.62E-055.08E-064.26E-044.21E-059.22E-058.80E-061.97E-067.12E-061.88E-041.31E-04-9.04E-013.62E-029.22E-027.12E-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
499981.19E+005.84E-072.66E-08-1.58E-04-9.54E-064.23E-044.22E-051.27E-041.58E-053.66E-07-1.64E-054.27E-042.01E-041.19E+00-1.58E-011.27E-01-1.64E-02
5101571.04E+003.45E-069.05E-07-1.43E-04-8.36E-064.26E-044.26E-051.20E-041.49E-053.76E-07-2.49E-054.13E-041.90E-041.04E+00-1.43E-011.20E-01-2.49E-02
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
899446.74E-01-1.22E-06-4.49E-07-1.05E-04-8.32E-064.24E-044.24E-051.06E-041.30E-054.23E-07-5.22E-053.66E-041.52E-046.74E-01-1.05E-011.06E-01-5.22E-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
1199233.86E-01-3.60E-07-5.40E-08-9.26E-05-1.02E-054.28E-044.27E-051.00E-041.18E-053.77E-07-7.77E-053.10E-041.09E-043.86E-01-9.26E-021.00E-01-7.77E-02
12100072.97E-012.37E-06-7.70E-07-9.06E-05-1.08E-054.22E-044.24E-059.93E-051.16E-053.77E-07-8.57E-052.89E-049.59E-052.97E-01-9.06E-029.93E-02-8.57E-02
1399372.11E-013.49E-06-2.24E-07-8.94E-05-1.15E-054.22E-044.22E-059.94E-051.15E-054.08E-07-9.35E-052.66E-048.50E-052.11E-01-8.94E-029.94E-02-9.35E-02
1499211.26E-012.67E-06-6.30E-07-8.19E-05-1.21E-054.27E-044.27E-059.99E-051.11E-054.45E-07-1.01E-042.43E-047.75E-051.26E-01-8.19E-029.99E-02-1.01E-01
15100674.18E-02-1.41E-06-6.74E-07-7.47E-05-1.27E-054.28E-044.27E-059.99E-051.12E-054.93E-07-1.08E-042.19E-047.43E-054.18E-02-7.47E-029.99E-02-1.08E-01
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
1810113-2.11E-01-3.70E-06-2.98E-07-4.82E-05-1.44E-054.22E-044.24E-059.54E-051.07E-057.15E-07-1.24E-041.43E-048.89E-05-2.11E-01-4.82E-029.54E-02-1.24E-01
1910083-2.97E-012.77E-062.17E-07-3.70E-05-1.48E-054.23E-044.20E-059.57E-051.05E-057.41E-07-1.27E-041.19E-049.83E-05-2.97E-01-3.70E-029.57E-02-1.27E-01
2010034-3.86E-01-8.43E-06-7.05E-07-2.53E-05-1.49E-054.27E-044.26E-059.55E-051.03E-058.11E-07-1.28E-049.75E-051.08E-04-3.86E-01-2.53E-029.55E-02-1.28E-01
2110074-4.77E-012.45E-064.09E-07-1.40E-05-1.49E-054.27E-044.17E-059.43E-051.03E-057.71E-07-1.26E-048.42E-051.18E-04-4.77E-01-1.40E-029.43E-02-1.26E-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
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
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
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
0.0200000.0067000.0035000.0000100.0340000.0030000.0190000.0001000.0000100.0021000.0250000.4500000.0260.1500000.0005500.0400000.000550
7.55E+093.39E+091.77E+092.59E+071.57E+106.25E+081.95E+101.76E+073.75E+054.45E+088.33E+098.28E+102.28E+091.34E+104.97E+062.97E+081.25E+08
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).