OBSERVATIONS AND PREDICTIONS FOR DAΦNE AND SUPERB

Theo Demma, LAL, CNRS-IN2P3, Orsay, France.

AbstractIn this paper the observations and simulations of the

electron cloud induced instability in the DAΦne positronring are presented. Predictions on electron cloud build-upand induced instability in the SuperB High Energy Ring areobtained through a simulation study.

INTRODUCTIONUnder certain conditions, electrons can accumulate in

the vacuum chamber of a positron storage ring. Primaryelectrons are generated by the interaction of beam syn-chrotron radiation with the chamber walls or by ionizationof residual gas. These primary electrons produce secondaryelectrons after impact with the vacuum chamber walls. Anelectron cloud develops if beam and chamber properties aresuch to generate secondaries at a sufficiently high rate. De-pending on the electron density level, the interaction be-tween the cloud and beam may lead to detrimental effectssuch as single-bunch and coupled-bunch instabilities. Elec-tron cloud effects have been a limitation for the DAΦneΦfactory, requiring installation of solenoids and clearingelectrodes [1] to suppress the build-up of the cloud, and areexpected to be a serious issue in the SuperB positron (HER)ring. In this communication simulation results relative tothe coupled-bunch instability induced by the electron cloudbuildup in the arcs of the DAΦne positron ring are reportedand compared to experimental observation in the next sec-tion. Following we present estimates, based on numericalsimulations, of the cloud density at which single-bunch in-stability is expected to set in, and of the density levels ofthe electron cloud in the SuperB High Energy Ring (HER).Conclusions follow in the last section.

ELECTRON CLOUD IN THE DAΦNEPOSITRON RING

After the 2003 shutdown for the FINUDA detector in-stallation, and some optics and hardware modifications,the appearance of a strong horizontal instability for thepositron beam at a current I ≈ 500mA, triggered the studyof the e-cloud effect in the DAΦne collider. Experimentalobservation that seems to provide an evidence that the elec-tron cloud effects are present in the DAΦne positron ringcan be summarized as follow: a larger positive tune shiftis induced by the positron beam current [2]; the horizontalinstability rise time cannot be explained only by the beaminteraction with parasitic HOM or resistive walls and in-crease with bunch current [3]; the anomalous vacuum pres-sure rise with beam current in positron ring [4], bunch-by-

bunch tune shifts measured along the DAΦne bunch trainpresent the characteristic shape of the electron cloud build-up [5]. There are also indications that wigglers play animportant role in the instability, since the main changes af-ter the 2003 shutdown were the modification of the wigglerpoles, and lattice variation which gave rise to an increaseof the horizontal beta functions in wigglers [6]. Recentlythe horizontal feedback for the DAΦne positron ring hasbeen successfully upgraded [7] by doubling the entire sys-tem and allowing to operate the machine at a positron cur-rent higher than 1A.

To better understand the electron cloud effects and pos-sibly to find a remedy, a detailed simulation study has beenperformed [8], [9].

Electron Cloud Induced Coupled-Bunch Instabil-ity

Once the electron cloud is formed, the beam passingthrough the cloud interacts with it. The motions of bunchesbecome correlated with each other if the memory of aprevious bunch is retained in the electron cloud -i.e., asmall displacement of a bunch creates a perturbation ofthe electron cloud, which affects the motions of the fol-lowing bunches, with the result that a coupled-bunch in-stability is caused. A complete discussion of the electroncloud induced multi-bunch instability formalism is outsidethe aim of this paper . The reader is referred to [10] fora detailed presentation of the subject. Experimental obser-vations [2]-[6] show that the horizontal instability affect-ing the DAΦne positron beam is a multi-bunch instability.The observed oscillation mode of the instability is alwaysa very slow frequency mode and can be identified as the -1mode, i.e., the mode that has a line closest to the frequencyorigin (zero frequency) from the negative part of the spec-trum. The same behaviour has been observed even after thesolenoid installation [7]. For this reasons the attention hasbeen focused on the interaction of the beam with the cloudin wigglers and bending magnets where the solenoids arenot effective.

Simulations for DAΦneTo estimate the multi-bunch instability induced by the

electron cloud in the arcs of the DAΦne positron ring thecode PEI-M [11],[12] has been used. The code computesthe transverse amplitude of each bunch as a function oftime, while evolving the build-up of the electron cloud self-consistently. To save computation time, the Poisson equa-tion for the space charge potential is solved only once for

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120 equi-spaced bunchesBeam current 1.2 AGrowth time ~ 100 turn

a

b

c

Figure 2: Beam signal (a), beam envelope (b), and mode spectrum (c) for a completely filled DAΦne bunch train.

Figure 1: Typical electron cloud distribution in the trans-verse x-y plane. The number of electrons in an arbitraryunit is plotted in the vertical axis, as obtained by PEI-Mafter the first bunch train passage in a DAΦne arc bend.

zero beam amplitude, and is used as a constant field intracking simulation. The beam and chamber parametersused in the simulation are collected in Table 1. A uniformvertical magnetic field Bz = 1.7 T was used to model themotion of the electrons both in wigglers and dipoles, anda circular chamber of radius R = 45mm is used insteadof the real chamber geometry in order to solve analyticallythe Poisson equation for the space charge potential Φ . Inthese tracking simulations, the motion of bunches fillingthe DAΦne positron ring while interacting with the cloudis followed for 500 turns. The instability mode spectrum is

Table 1: DAΦNE beam and pipe parameters used as inputfor ECLOUD simulations.

parameter unit valuebunch population Nb 1010 2.1number of bunches N – 100missing bunches Ngap – 20bunch spacing Lsep m 0.8bunch length σz mm 18bunch horiz. size σx mm 1.4bunch vert. size σy mm 0.05wiggler chamber horiz. aperture 2hx mm 120wiggler chamber vert. aperture 2hy mm 20straight sections radius mm 44primary photo-emission yield dλ/ds – 0.0088photon reflectivity – 50%maximum SEY δmax – 1.9energy for max. SEY Emax eV 250

obtained by taking the Fourier transform of the transverseamplitude of each single bunch as computed by the code,and the grow-rate is obtained by an exponential fit to thebeam signal envelope. In Figure 1 is shown a snapshot ofthe electron cloud distribution in the transverse x-y plane,as obtained bu the simulation code at the end of the firstbunch train turn, assuming a uniform illumination of thebeam chamber walls. The two stripes structure, typical of

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electron cloud central densities (i.e., within a region of10σx × 10σy around the beam center) as obtained fromECLOUD for different values of the peak secondary emis-sion yield (SEY) and of the antechamber protection fac-tor η. Simulation were performed for a typical SuperBbending magnet, assuming a uniform vertical bending fieldBy = 0.5T and an elliptical chamber geometry with hor-izontal and a vertical aperture 95mm, and 55mm respec-tively.

Table 4: Electron cloud densities from ECLOUD simula-tions.

SEY η rhoe[1012e−/m3]1.1 95% 0.41.1 99% 0.091.2 95% 0.91.2 99% 0.21.3 95% 8.01.3 99% 4.0

The density values given in Table 4 have to be scaled bythe ”filling” factor of dipoles (i.e., the fractions they coverthe ring), which amount to about 0.5. The results showthat a that a peak secondary electron yield of 1.1 and 99%antechamber protection result in a cloud density below theinstability threshold. In this scenario the adoption of mit-igation techniques to keep the e-cloud density level belowthe instability threshold are essential. Following the exam-ple of the ILC [15] and SuperKEKB [16] collaborations adatailed study of a range of mitigation options includingcoatings, clearing electrodes, grooves and novel conceptsshould be performed taking into account the efficacy, cost,and possible impact on the machine of the proposed miti-gation scheme.

CONCLUSIONSCoupled-bunch instability simulations are in good agree-

ment with the experimental observations, and indicate thatthe observed horizontal instability is compatible with acoupled bunch instability induced by the presence of anelectron cloud in the arcs of the DAΦne positron ring.Work is in progress to include more realistic models forthe space charge potential and the chamber boundaries inthe simulation code.

REFERENCES[1] M. Zobov et al, ”OPERATING EXPERIENCE WITH

ELECTRON CLOUD CLEARING ELECTRODES ATDAΦNE”, these Proceedings.

[2] C. Vaccarezza, et al, ECLOUD04, Napa Valley proc.

[3] A.Drago et al., Proceedings of PAC05, p.1841.

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[5] A.Drago, proc. of the 40th ICFA Workshop on High Lumi-nosity e+e- Factories.

[6] A.Drago et al., DAΦne Tech. Notes, G-67.

[7] A.Drago et al., TH5RFP057 in Proceedings.of IPAC2011

[8] T.Demma et al., Proceedings of EPAC08, p.1607.

[9] T.Demma, ICFA Beam Dynamics Newsletter n.48 (2009),pp.64-71.

[10] S.S.Win et al., Phys. Rev. ST Accel. Beams 8, 094401(2005).

[11] K. Ohmi, Phys. Rev. Lett. 75, 1526 (1995).

[12] Y.Cai et al., Phys. Rev. ST-AB 7, 024402 (2004).

[13] M. Pivi, CMAD: A Self-consistent Parallel Code to Simu-late the Electron Cloud Build-up and Instabilities, proceed-ings of PAC ’09.

[14] F. Zimmermann, CERN, LHC-Project-Report-95, 1997.

[15] M. Pivi et al, ”Recomendation for Mitigation of the ElectronCloud Instability in the ILC”, proceedings of IPAC2011.

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