LBNL-40256 UC-414 Q ~ F9-705 0 3 RNEST ORLANDO LAWRENCE B ERKELEY NATIONAL LABORATORY The Electron-Cloud Instability in PEP4I: An Update
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LBNL-40256 UC-4 14 The Electron-Cloud Instability in PEP-11: An Update M.A. Furrnan and G.R. Lambertson Accelerator and Fusion Research Division Ernest Orlando Lawrence Berkeley National Laboratory University of California Berkeley, California 94720 May 1997 This work was supported by Director, Office of Energy Research, Office of High Energy and Nuclear Physics, of U.S. Department of Energy under Contract No. DE-ACO3-76SFOOO98.
LBNL-40256KBP Note-224 / THE ELECTRON-CLOUD INSTABILITY IN PEP-11: AN UPDATE M. A. F m a n and G. R. Lambertson, LBNL? MS 71-259, Berkeley, CA 94720, USA Abstract section of semi-axes (a,b)=(4.5,2.7) cm, with an antechamber slot of full height 1.5 cm on outer-radius side. The electric field of bunches is calculated taking into account this elliptical geometry boundary condition (however, for simplicity, we use approximation that chamber is closed). Furr details are described in our previous report [4]. The main new improvement is inclusion of space-charge forces from electron cloud. We present an update on estimate of growth time of multi-bunch transverse instability in PEP-I1 collider arising from interaction of positron beam with accumulated electron cloud. We estimate contributions to growth rate arising from dipole magnets and from pumping straight sections. We emphasize those quantities upon which instability is most sensitive. The simulation includes measured data on secondary emission yield for TiN-coated samples of actual vacuum chamber. Although our analysis is still in progress, we conclude that instability risetime is of order 1 ms, which is well within range controllable by feedback system. 2.1 Geomety of arcs. The LER, which contains 3.1-GeV positron beam, has six arcs. For purposes of studying ECI, we make simplifying assumption that each arc is composed only of 32 dipole bending magnets and 32 pumping straight sections. The dipole magnets are 0.45 m in length and are evenly spaced by a distance of 7.6 m center-to-center, and pumping straight sections span distance between each pair of magnets. The model also assumes that six utility straight sections, each 121.6 m long, are empty. INTRODUCTION 1 A novel type of fast coupled-bunch instability was identified some two years ago at Photon Factory at KEK when operating with a positron beam [l], and has been subsequently reproduced at BEPC machine [2]. The initial suggestion that its origin is an electron cloud [l] in vacuum chamber that couples transverse motion of successive bunches has been endorsed by simulations for se and or machines [3,4,5] and analytic work [6]. A related multi-bunch instability induced by electrons is observed in CESR collider [7]. Here we report an update on our previous estimate [4] of electron-cloud instability (ECI) growth time that is expected for PEP-II[8] low-energy ring (LER), obtained from our simulation code POSINST. While certain input data needs to be sharpened, and numerical issues in simulation need to be refined, we currently conclude that growth time for multibunch coherent dipole instability is in range 1-2 ms. 2.2 Photoemission. SIMULATION Our simulation has been developed in same spirit as in Ref. 3. We study separately electron cloud in pumping straight sections and in dipole bending magnets since se two elements comprise most of ring. It is legitimate to separate problem in this fashion because longitudinal drift of electron cloud is slow and because, as it turns out, range of wake function is short compared to betatron wavelength. As a result, it is a good approximation to simply add up contributions to wake function from such individual elements in ring. The PEP-I1 vacuum chamber has an elliptical cross2 Work supported by US Department of Energy under Contract No. DE-AC03-76SF00098. Submitted to PAC97, Vancouver, May 1997. 1 We have refined computation of energy spectrum and geometrical distribution of synchrotron radiation photons generated by positrons. The PEP-11 vacuum chamber has an antechamber on outer-radius side through which -99% of se photons escape and thus are inconsequential for our purposes. The remaining -1% of photons, which are emitted with relatively large opening angle, strike vacuum chamber wall just above and just below slot with an average energy of -15 ev and a mean grazing angle of -15 m a d ( critical energy is 4.8 kev). On average, each positron in any given bunch generates -0.02 such low-energy photons when it traverses any given dipole bending magnet. Some 20% of se photons land on bending magnet immediately downstream of emitting dipole, and remaining -80% land in two pumping sections downstream of emitting dipole. If photon reflectivity R of chamber walls is close to 0, photons yield photoelectrons upon first striking wall. If, on or hand, R is close to 1, photons bounce inside chamber many times before yielding photoelectrons. In first case, photoelectrons are generated along narrow strips just above and just below chamber slot; in second case, photons get redistributed more or less uniformly both azimuthally and transversely in chamber, so that photoelectrons are generated almost uniformly throughout. Since we have not yet measured reflectivity of vacuum chamber, in our simulations
we study two extreme cases, R=O and R-1. into account such a coating. We assume a quantum efficiency Y=l, meaning that one photoelectron is ejected per photon that penetrates 3.1 Pumping straight sections wall (not per photon that hits wall). By using this If we assume that R-1, electron cloud saturates at an definition of quantum efficiency, we substantially average density - 4. 7 ~ 1 0electrons/cm3, ~ which is -1/27 decouple knowledge of R from photoemission of beam neutralization level (one should keep in process. Thus, for nominal charge of 5. 6 ~ 1 0 ~ mind, however, that distribution itself is time positrons per bunch, an average of -1xO.02x5.6~10~~= dependent and not perfectly uniform, as seen in Fig. 1). 1.lxl0lo photoelectrons are generated per bunch passage The contribution to ECI growth rate from all in region downstream from any given dipole magnet. pumping straight sections in ring is cl-1100 s-l. If It can be shown that this quantity is independent of we assume R=O, n r1-1400 s-l, and average value of R provided R is not extremely close to 1. density at saturation is -1/21 of beam neutralization The photoelectronsare generated with a mean energy level. of 5 ev and an rms width also of 5 ev. The simulation At se relatively low densities space-charge represents each burst of se photoelectrons with a fixed force is expected to have a minor effect on dynamics; number of macroparticles, typically 1000 per bunch we have verified that this is case. Since passage, and follows se (and ensuing secondary computation of space-charge effect is by far most electrons) for up to 1000bunch passages. computationally-expensive part of simulation, neglecting it amounts to a considerable savings of CPU 3 RESULTS and wall-clock time (our simulations are carried out on a When an electron strikes surface it can emit secondary Cray C90 computer at NERSC). electrons. The basic quantity that describes process is 3.2 Dipole bending magnets secondary emission yield (SEY) 6, which is a function of incident electron energy and angle, and In this case magnetic field confines electrons in surface material. The secondary emission process is taken cloud to move in tight vertical helices whose radius is into account in detail [4] in our simulation because, for typically a few microns, and whose cyclotron frequency is particular case of PEP-11 LER parameter regime, v=eb/2ncmc=21 GHz. Since nns bunch length (in 3 electrons typically perform -1 ECI depends in a non-smooth fashion on 6. In time units) is ( ~ 3ps, practice, it is eflective secondary emission 8 that cyclotron revcllution during a bunch passage. This means plays crucial role in determining intensity of that bunch length effects are expected to be important, as electron cloud. By definition, 8 is SEY folded with we have verified. The main consequence of cyclotron energy-angle spectrum of electrons that hit phase averaging of beam-electron interaction is severe suppression (relative to impulse wall. If s > l, a chain reaction ensues, so that number of electrons grows rapidly until space-charge approximation) of horizontal component of forces are strong enough that a saturation is reached, momentum transferred to electrons in cloud. An roughly correspondingto beam neutralization level. If analytic estimate of this suppressionfactor yields < 1, on or hand, chamber walls act as a net (1) e ~ p ( - ( 2 ~ ~ 0 ) 2 /=2 )5.9~10-5 absorber of electrons, and an equilibrium is reached when which implies that kick experienced by an electron is number of electrons absorbed per bunch passage equals number of photoelectrons generated in such a essentially purely vertical. A correct simulation, refore, requires representing bunch-electron time interval. interaction by many kicks, which is accomplished by The PEP-I1 vacuum chamber is made of aluminum, dividing bunch longitudinally into several slices. We which is normally covered with a layer of oxide. Recent have carried out spot-checks, however, that show that measurements 191 for actual vacuum chamber samples results can be accurately obtained, for PEP-I1 (duly cleaned) show that 6 peaks at a value -2 at an parameter regime, by resorting to short-cut of using incident energy -250 ev at normal incidence. Our impulse approximation and n suppressing simulation results show that such a value is high enough horizontal component of kick for each electron by that 5 > 1 both in pumping sections and in dipole in Eq. (1). factor given magnets. The electron cloud saturates at average beam If we assume R-1, electron cloud saturates at an neutralization density of 1.26~10 electrons/cm3, and average density - 3. 1 ~1Os electrons/cm3, which resultant ECI growth rate is very fast. As a consequence corresponds to -1/41 of beam neutralization level, and of this, we are coating [ 101 chambers with a 1000-A contribution to growth rate of ECI from all thick layer of TN,which has a measured [9] peak value 6 dipole magnets in ring is r l - 3 8 s-l. -1.1. It n turns out that < 1 both for bending If we assume R=O, photoelectrons are generated magnets and pumping straight sections, so that only along narrow strips just above and just below chain reaction is avoided. All results discussed below take antechamber slot. Due to trapping effect of s 2
magnetic field, electrons remain confined to a narrow vertical region at outer edge of chamber, which is -4.5 cm away from beam. In this case, ionization of residual gas by beam produces most of electrons near beam orbit. However, our simulations show that, even assuming a vacuum pressure 150 times larger than nominal specification of 1 ntorr, contribution to r1 from dipoles is only -1.5 s-l. density at equilibrium, we estimate growth rate o he ECI in absence of a TiN coating to be -20-40 times larger than for a coated chamber. In this case ECI growth rate is fairly insensitive to detailed values of R, Y and SEY. We have thus far assumed a certain specific form for incident-angle dependence of SEY, based on standard phenomenology [ 121. In near future we will incorporate actual measured dependence; we do not expect that our results will change appreciably from those presented here. We have yet to evaluate contribution to ECI growth rate from or magnets and regions of ring, and to assess effects of a temporary increase of SEY from potential air exposure of chamber. Furrmore, our analysis thus far applies to coherent dipole multibunch mode in linear (i.e., small amplitude) approximation, and growth rates have been obtained by computing dipole wake function assuming that bunches are rigid charges. Thereforeour approach does not shed any light on ECI at saturation amplitudes, nor about higher-order coherent modes. Such effects remain to be investigated by more complete simulation techniques. 0.M 0.W 0.01 0.01 0.00 0.01. 0.02 0.03 0.04 0.03 0.M 0.m 0.08 0.09.._ v.": 0. P< ACKNOWLEDGMENTS We are grateful to S. Heifets, K. Kennedy, R. Kirby, F. King, A. Zholents, F. Zimmermann and M. Zisman for valuable discussions, to NERSC for supercomputer support, and to J. Peters for his help in making such computer resources available to us. 0.02 0.0; 0.01 O.W REFERENCES Fig. 1. Image plots of electron cloud for R-1. Top: pumping straight section. Bottom: dipole bending magnet. The beam orbit is at center of ellipse. The antechamber slot is at right side of chamber. Brighter colors represent higher local density, and ratio between peak density and average is -2. The units of both scales are meters. [ l ] M. Izawa, Y. Sat0 and T. Toyomasu, Phys. Rev. Lett. 74, 5044 (1995). [2] 2.Y. Guo et al, Proc. EPAC96, Barcelona, Spain, June 10-14, 1996, p. 1042. [3] K. Ohmi, Phys. Rev. Lett. 75, 1526 (1995). [4] M. A. Furman and G. R. Lambertson, Proc. EPAC96, Barcelona, Spain, June 10-14, 1996, p. 1087. [SI F. Zimmermann, LHC Project Report 95, 27 February 1997. [6] S. Heifets, Proc. Intl. Workshop on Collective Effects and Impedance for B Factories (CEIBAM), Tsukuba, Japan, 12-17 June 1995, Y. H. Chin, ed., p. 295, and references rein. [7] T. Holmquist and J. T. Rogers, Proc. EPAC96, Barcelona, Spain, June 10-14, 1996, p. 319 and references rein. [8] PEP-11: An Asymmetric B Factory-Conceptual Design Report, June 1993, LBL-PUB-5379/SLAC-418/CALT68-1869/UCRL-ID-114055/UC-IIRPA-93-01. [9] R. Kirby and F. King, private communications. [lo] K. Kennedy, H. Hartneck, H. Hsieh, G. MiIIos, M. Benapfl and R. Kirby, se proceedings. 1111 W. Barry, J. Corlett, M. Fahmie, J. Greer, G. Lambertson and C. Pike, se proceedings. [12] See, e.g., H. Seiler, J. Appl. Phys. 54, R1 (Nov. 1983). CONCLUSIONS We conclude from our simulationsresults that growth time of ECI for PEP-II positron beam is 7-1 ms, and is dominated by pumping straight sections. Such a growth time is within range controllable by feedback system [113. For R-1, pumping straight sections dominate ECI growth rate by a factor -3O:l over bending magnets, mainly due to ir length. By removing this length factor we obtain r1/l-o.80 s-'/m for pumping sections and ~-~/L-0.44s-'/m for bending magnets. These numbers are in a ratio -2:1, which is in qualitative agreement with ratio of corresponding average equilibrium densities of cloud, and is due to difference in beam-cloud dynamics in se two regions with and without magnetic field. By scaling above results by average electron 4 3