Electron-cloud build up, incoherent tune spread and electron-induced beam instability are likely to be responsible for the vertical beam-size increase observed at the KEKB Low Energy Ring (LER). We report on recent simulations and analytical estimated, a ddressing the electron-cloud evolution for various magnet configurations, computing the beam size blow up predicted by three different simulation models (micro-bunches, multiparticle tracking with soft Gaussian approximation, particle-in cell) and finally discussing analytical expressions for the instability threshold

Fukuma, H

Ohmi, K

Rumolo, Giovanni

Zimmermann, Frank

CERN Document Server

Electron Cloud Studies for KEKBG. Rumolo, F. Zimmermann, SL/AP, CERN, Geneva, Switzerland;H. Fukuma, K. Ohmi, KEK, Tsukuba, JapanAbstractElectron-cloud build up, incoherent tune spread andelectron-induced beam instability are likely to be respon-sible for the vertical beam-size increase observed at theKEKB Low Energy Ring (LER). We report on recent sim-ulations and analytical estimates, addressing the electron-cloud evolution for various magnet configurations, com-paring the beam size blow up predicted by three differentsimulation models (micro-bunches, multi-particle trackingwith soft Gaussian approximation, particle-in-cell), and fi-nally discussing analytical expressions for the instabilitythreshold.1 INTRODUCTIONSince 1999, a blow up of the vertical beam size is seen atthe Low-Energy Ring positron (LER) of the KEK B factorywhen the current exceeds a certain threshold value, whichdepends on the filling pattern [1, 2, 3]. At a bunch spacingof 4 rf buckets (8 ns) the threshold bunch current is about0.5 mA, equivalent to a bunch population of N b ≈ 3.3 ×1010. For short bunch trains, the first few bunches after along gap are of nominal size. The blow up starts around the7th bunch in a train, as was observed by a gated camera [4].The evolution of the beam-size blow up coincides with thatof the coherent tune shift which equally increases along thetrain and saturates after about the same number of bunches[5]. During usual luminosity operation, there is a long trainof colliding bunches,with a single gap of about 1 µs. In thiscondition, there is no significiant difference between thefirst bunches after the gap and the others, and all bunchesappear to blow up more or less equally, which is evidencedby a uniform loss in specific luminosity for all bunches.The similarity of the blow up measured for short trainswith the simulated electron-cloud build up suggested thatphotoelectrons, and possibly secondary electrons, were theculprits. In order to constrain the electrons to the vicinityof the chamber wall, first ‘C-yoke’ quadrupole magnets ofabout 0.3 T/m were installed. Motivated by simulations, inthe summer of 2000 these magnets were replaced by 50-G solenoids, and further solenoids have been added at theend of the year. Partly as a result of these installations theluminosity of KEKB has increased, which confirms that theelectron cloud was indeed limiting the performance.2 ELECTRON BUILD UPSimulations of the electron cloud build up are performedusing the programs and procedures described in Refs. [6, 7,8]. A few parameters are listed in Table 1.Table 1: Selected simulation parameters.chamber radius b 47 mmbeam rms-sizes σx,y,z 0.4–0.06–4 mmbunch spacing Tsep 8 nsphoton reflectivity R 10–100%photoel. yield Y 0.002–0.05/e+/mcenter of photoel. energy Epe,0 7 eVphotoel. energy spread σe 5 eVmax. sec. emission yield δmax 1.8energy of max. sec. yield max 300 eVsynchrotron tune Qs 0.015slippage factor η 1.8× 10−4circumference C 3000 maverage beta function βy 15 mThe simulations show that the equilibrium electron linedensity in a field-free region increases roughly in propor-tion to the bunch current [1, 9]. Figures 1–2 display simu-lated electron volume densities near the center of the beampipe for a weak periodic quadrupole field and a weak peri-odic solenoid field. These pictures can be compared withthe simulation results for a field-free region presented inRefs. [1, 9, 10]. In all cases, the electron density is stronglyfluctuating; the bunches pass near the minima. The equi-librium density for a field-free region is 5–10×1011 m−3[1, 10], or roughly ten or fifty times higher than for thequadrupole and solenoid field, respectively. In the 64-nsgap between trains, the central density remains almost con-stant in case of the quadrupole field. By contrast, it decayswith a time constant of about 30 ns in the field-free region[1, 10], where, however, it is rapidly re-established after thefirst bunch of the second train. Good agreement of the latterbehavior with observations was interpreted to mean that theblow up was predominantly due to electrons in many smallresidual field-free regions [1]. This motivated the (further)installation of tightly packed solenoids.However, we must note that the simulations do not showany long-term accumulation of electrons, even when real-istic solenoid fields are modeled. Therefore, the apparentsurvival of a large number of electrons over a 1 µs gap andan additional hysteresis effect with a time constant of 100 s[2] could not be explained by simulations so far.Attempts were made to clear the center of the chamberfrom electrons by special filling patterns. None of theseimproved the performance, neither in the simulation nor inthe experiment. The optimum filling pattern depends onthe decay time of the cloud behind a train. In a field-freeregion the total number of electrons decays over about 500-7803-7191-7/01/$10.00 ©2001 IEEE. 1889Proceedings of the 2001 Particle Accelerator Conference, Chicagons, and in a weak solenoid field over 100 ns [9]. If a largecomponent of elastically reflected low-energy electrons isincluded in the simulation, the decay time for both field-free region and solenoid increases to 150–200 ns [9].05e+101e+111.5e+112e+112.5e+110 2e-08 4e-08 6e-08 8e-08 1e-07 1.2e-07 1.4e-07 1.6e-07 1.8e-07 2e-074 bucket spacing, symmetric configurationat moment of bunch passageFigure 1: Electron density near beam in units of m−3 as afunction of time in seconds, for a perodic quadrupole con-figuration, with a peak gradient of 0.5 T/m, minimum 0.1T/m and period 10 cm, during the passage of two bunchtrains (4 bucket spacing) with a train-to-train gap of 32buckets [9].05e+091e+101.5e+102e+102.5e+103e+103.5e+100 2e-08 4e-08 6e-08 8e-08 1e-07 1.2e-07 1.4e-07 1.6e-07 1.8e-07 2e-074 bucket spacing, solenoid, with z dependenceat bunch positionFigure 2: Electron density near beam in units of m−3 fora sinusoidal solenoid field with a peak field of ±50G and1-m longitudinal period as a function of time in seconds,during the passage of 20-two bunch trains with 4 bucketbunch-to-bunch spacing and 32-bucket separation betweentrains [9].3 BEAM BLOW UPThe interaction of the previously established electroncloud with a single bunch is studied in separate simulations[11, 12, 13]. Figures 3 and 4 show a very satisfactoryagreement between the soft-Gaussian and the PIC ap-proaches. In particular, the beam vertical size growthis represented for two different values of the electroncloud density. In Fig. 3 the density was assumed to beρe = 2.5× 1011 m−3, and the emittance growth is actuallyincoherent because this value is below the threshold for theinset of the TMCI. The plots show that in this case theremight be a strong dependence of the predicted growth onthe number of interaction points between bunch and cloudper turn. It is evident that the emittance, which is predictedto become 15% higher after 500 ms if we localize theelectron cloud action in one single point along the ring,stays quite constant at its initial value if we split the cloudaction over 5 or more different sections.5.6e-055.8e-056e-056.2e-056.4e-056.6e-056.8e-057e-050 200 400 600 800 1000sigy (m)TurnDependence of number of cloud section1 cloud section5 cloud sections10 cloud sections5.4e-055.5e-055.6e-055.7e-055.8e-055.9e-056e-056.1e-056.2e-056.3e-056.4e-050 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 0.002sigy (m)5 cloud sections1 cloud sectionρe= 2.5 x 10 m11 -3ρe= 2.5 x 10 m11 -3PIC simulations [13]Soft-Gaussian approach [12]t (s)Figure 3: Emittance growth for ρe = 2.5 × 1011 m−3,with 1 or 5 electron cloud sections along the ring. Thesimulation with the soft-Gaussian code stops at 200 turnsdue to the large CPU time required for 5 cloud sections.In Fig. 4 the emittance growth is shown for the caseρe = 1012 m−3. Again, the profiles look very similar forthe PIC and soft-Gaussian approaches. This electron clouddensity value is actually above the TMCI threshold, anda coherent vertical motion can be observed. This can beseen in Fig. 5, which depicts the evolution of the centroidvertical position and of the yz correlation normalized to thebunch rms-length over 5 ms for both cloud densities (seefollowing discussion).1890Proceedings of the 2001 Particle Accelerator Conference, Chicago4 DISCUSSIONWithout solenoids, a coherent tune shift ∆Qy of about0.01 builds up along the bunch train. Estimating, the elec-tron density as ρe = 2γ∆Qy/(βyCre) ≈ 1012 m−3, themeasured value of ∆Qy is consistent with the electron den-sity simulated for a field-free region [3, 10]. Note that theincoherent tune shift can be much larger due to electronaccumulation inside the bunch. The measured incoherenttune spread (full width) is of the order 0.03 when solenoidsare switched off.The single-bunch wake field generated by the electroncloud can be approximated by a broad-band resonator [14].At ρe = 5 × 1011 m−3, typical resonator parameters forKEKB in the vertical plane are [14] ωR = 2.2× 1011 s−1,and cRS/Q ≈ 4 × 106 m−2. If ωRσz/c  1 theTMCI threshold for a broadband resonator can be estimatedas [15] Nb,thr ≈ 5.3QRγQs(ωRσz/c)2/(cRs/Q)/βy/re,which evaluates to Nb,thr ≈ 3 × 1010, assuming QR ≈ 1.Note that the threshold scales as Nb,thr ∝ Qsω2Rσ2z/ρe. Analternative calculation using the formalism of fast blow up[16] predicts a slightly higher threshold bunch populationNb,thr ≈ 6×1010; a similar number is obtained by a directTMCI calculation considering 9 betatron sidebands and ig-noring the radial modes (like the estimate above) [14].05e-050.00010.000150.00020.000250.00030.000350.00040.000450 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.00505e-050.00010.000150.00020.000250.00030.000350.00040.000450.00050.000550 50 100 150 200 250 300 350 400 450 500sigy (m)Turnsigy (m)PIC simulations [13]Soft-Gaussian approach [12]ρe= 10 m12 -3ρe= 10 m12 -3t  (s)Figure 4: Emittance growth for ρe = 1012 m−3. The dif-ferent curves in the upper graph represent the evolutions fordifferent betatron tune values.-0.2-0.100.10.20 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5time (ms)y centroid (mm)-0.06-0.04-0.0200.020.040.060 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5time (ms)r(yz)/σz (mm)ρe= 10 m ρe= 2.5 x10 m-3 -31112Figure 5: Beam centroid vertical motion and yz correlationversus time for the two cases ρe = 2.5 × 1011 m−3 andρe = 1012 m−3. Below threshold, no coherent motion inthe y-direction is observed.5 REFERENCES[1] H. Fukuma, et al., EPAC2000 Vienna (2000).[2] K. Oide, Chamonix XI, CERN-SL-2000-007 DI (2001).[3] H. Fukuma, et al., HEACC’01 Tsukuba (2001).[4] J. Flanagan et al., EPAC 2000 Vienna (2000).[5] T. Ieiri, et al., HEACC01 Tsukuba (2001).[6] K. Ohmi, Phys. Rev. Lett. 75, 1526 (1995).[7] G. Rumolo et al., PRST-AB 012801, (2001).[8] F. Zimmermann, Proc. Chamonix X & XI, CERN-SL-2000-007-DI and CERN-SL-2001-003-DI.[9] F. Zimmermann, CERN-SL-Note-2000-004 AP; CERN-SL-2000-017 (AP); CERN SL-Note-2001-022 AP; F. Zimmer-mann, H. Fukuma, K. Ohmi, CERN-SL-Note-2000-061 AP.[10] F. Zimmermann, these proceedings.[11] K. Ohmi, F. Zimmermann, Phys. Rev. Lett. 85, 3821 (2000).[12] G. Rumolo, et al., Chamonix XI, CERN-SL-2001-003-DI.[13] K. Ohmi, these proceedings.[14] K. Ohmi, et al., HEACC’01 Tsukuba (2001).[15] B. Zotter, CERN/ISR-TH/82-10 (1982).[16] R.D. Ruth, J. Wang, IEEE Tr. NS-28, no. 3 (1981); P. Ker-nel, et al., EPAC 2000, Vienna (2000).1891Proceedings of the 2001 Particle Accelerator Conference, Chicago

Electron cloud studies for KEKB

Abstract

Similar works

Full text

Available Versions

CERN Document Server