Recent simulation results for the main features of the electron cloud in the storage ring of the Spallation Neutron Source (SNS) at Oak Ridge, and updated results for the Proton Storage Ring (PSR) at Los Alamos are presented in this paper. A refined model for the secondary emission process including the so called true secondary, rediffused and backscattered electrons has recently been included in the electron-cloud code

Furman, M A

Pivi, M

Pivi, M.

Furman, M. A.

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ELECTRON-CLOUD UPDATED SIMULATION RESULTS FOR THE PSR,AND RECENT RESULTS FOR THE SNS ∗M. Pivi and M. A. Furman,† LBNL, Berkeley, CA94720, USAAbstractRecent simulation results for the main features of theelectron cloud in the storage ring of the Spallation NeutronSource (SNS) at Oak Ridge, and updated results for theProton Storage Ring (PSR) at Los Alamos are presentedin this paper. A refined model for the secondary emissionprocess including the so called true secondary, rediffusedand backscattered electrons has recently been included inthe electron-cloud code.1 INTRODUCTIONStudies on the possible electron-cloud effect have beeninitiated at the Spallation Neutron Source (SNS) under con-struction at the Oak Ridge National Laboratory (ORNL).The electron cloud effect may limit the performance of in-tense proton storage rings, causing a fast instability thatmay be responsible for proton losses and collective beammotion above a certain current threshold, accompanied bya large number of electrons. Such a high-intensity instabil-Table 1: Simulation parameters for the PSR and SNS.Parameter Symbol PSR SNSproton beam energy E, GeV 1.735 1.9dipole field B, T 1.2 0.78bunch population Np, ×1013 5 20.5ring circumference C, m 90 248bunch length bl, ns 254 760beam pipe semi-axes a, b, cm 5,5 10,10gauss. tr. bunch size σx, σy , mm 10, 10flat tr. bunch size rx, ry , mm 28, 28proton loss rate ploss, ×10−6 4 0.11proton-electron yield Y 100 100No. steps during gap Ng 100 250No. kicks/bunch Nk 1001 5001max sec. yield δmax 2.0 2.0energy at yield max Emax, eV 300 300yield low energy el. δ(0) 0.5 0.5ity which has been observed in the PSR at the Los AlamosNational Laboratory (LANL) for more than 13 years, isnow recognized to be, although not conclusively proven,an electron-cloud effect. This instability is now believedto be due to the collective coupling between an electron∗Work supported by the SNS project and by the US DOE under con-tract DE-AC03-76SF00098.† mpivi@lbl.gov and mafurman@lbl.govcloud and the proton beam [1, 2]. In this article we presentsimulation results for the SNS and for PSR ring obtainedwith the ECE code that has been developed at LBNL overthe past 6 years. In all results presented here, the protonbeam is assumed to be a static distribution of given chargeand shape moving on its nominal closed orbit, while theelectrons are treated fully dynamically. We defer issueslike the current instability threshold, growth rate and fre-quency spectrum to future studies. We compared in [3] ourresults for the electron current and energy spectrum of theelectrons hitting the walls of the chamber against measure-ments obtained in the PSR by means of dedicated electronprobes. From such comparisons we can assess the effectsof several important parameters such as the secondary elec-tron yield (SEY) at the walls of the chamber, the proton lossrate and electron yield, etc. Furthermore, we can infer de-tails of the electron cloud in the vicinity of the proton beam,such as the neutralization factor, which is important for aself-consistent treatment of the coupled e-p problem [4].2 PHYSICAL MODEL2.1 Sources of electronsThe two main sources of electrons considered for protonstorage rings at the SNS and the PSR, are: lost protonshitting the vacuum chamber walls, and secondary emissionfrom electrons hitting the walls (the electron cloud in thevicinity of the stripper foil is not modelled here). Althoughour code accommodates other sources of electrons, suchas residual gas ionization, we have turned them off for thepurposes of this article.2.2 Secondary emission processThe SEY δ(E0) and the corresponding emitted-electronenergy spectrum dδ/dE (E0 =incident electron energy, E= emitted secondary energy) are represented by a detailedmodel described elsewhere [5]. Its parameters were ob-tained from detailed fits to the measured SEY of stain-less steel [6]. The main SEY parameters are the energyEmax at which δ(E0) is maximum, and the peak value it-self, δmax = δ(Emax) (see Table 1). Furthermore, for theresults shown below, we do take into account the elasticbackscattered and rediffused components of the secondaryemitted-electron energy spectrum dδ/dE. The backscat-tered component typically becomes more important at lowincident electron energies. To account for this behavior wehave used a fit extrapolated data for copper measured atCERN [7]. The value of δ(E0) at incident electron ener-gies E0 <10eV is an important parameter since it deter-mines the electron survival rate at the end of the gap. Thisquantity is difficult to measure experimentally, and remainsan uncertainty for the model. However, the decay time ofthe electron cloud at the end of the beam pulse has beenmeasured in the PSR, see Fig. 1. A long exponential tailseen with 170 ns decay time may imply a high reflectivityfor low energy electrons. In Fig. 1, we reproduce the pas-sage of one single PSR beam assuming different values forδ(0).Figure 1: Experimental data from PSR (R. Macek courtesy)and simulated decay time of the electron cloud at end of thebeam pulse. Different SEY values for low energy electrons,δ(0), have been assumed in the simulation.2.3 Simulation ModelThe PSR and the SNS rings store a single proton bunchof length τb followed by a gap of length τg with a typicalcurrent intensity profile shown in Figs. 2 and 3. A Gaus-sian transverse beam with rms sizes σx = σy =10mm,and the actually measured longitudinal intensity profile areassumed for the PSR. The transverse beam distribution forthe SNS is assumed to be constant with rx=ry=28 mm. Thevacuum chamber is assumed to be a cylindrical perfectly-conducting pipe. The number of electrons generated by lostprotons hitting the vacuum chamber wall is Np×Y ×plossper turn for the whole ring, where Y is the effective electronyield per lost proton, and ploss is the proton loss rate perturn for the whole ring per beam proton. The lost-protontime distribution is proportional to the instantaneous bunchintensity. The electrons are then simulated by macropar-ticles. The secondary electron mechanism adds to these avariable number of macroparticles, generated according tothe SEY model mentioned above. The bunch is divided upinto Nk kicks, and the interbunch gap into Ng intermedi-ate steps. The image and space charge forces are computedand applied at each slice in the bunch and each step in thegap. Typical parameter values are shown in Table 1. By thecomparison of the measured and simulated decay time ofthe electron cloud, shown in Fig. 1, we assume δ(0) ' 0.5for the following simulations presented here.Figure 2: Simulated electron density during the first bunchpassages, in a PSR field-free region and a dipole section.Figure 3: Simulated electron neutralization factor in a SNSfield-free region. The fractional charge neutralization com-puted within the beam radius exceeds 10% at the tail of thebunch.3 RESULTS AND DISCUSSIONThe build-up of the electron cloud in a PSR field-free re-gion and a dipole section during the passage of the beam isshown in Fig. 2. The saturation level in the PSR is reachedafter few bunch passages, when assuming δmax =2. Theestimated average number of electrons in a field free re-gion is ∼ 4 × 107 e/cm3 or 50 nC/m. In particular, whenassuming δ(0) '0.5 the simulated electron density in thePSR increases by a factor∼3 relative to the δ(0) '0.1 case(refer to previous results for PSR, see [3]). These are ex-amples of strong parameter sensitivity that calls for furtherexperimental investigations.The SNS beam pipe chamber will be coated with TiN.Recent measurements of an as-received sample of the TiNcoated SNS vacuum chamber, has shown δmax =2 [8].The build-up of the electron cloud and previous results forFigure 4: Build-up of the electron cloud in the SNS field-free region assuming a δmax =1.3 and 1.1. The electronsgradually increase in number during successive bunch pas-sages until, owing to the space-charge forces, a balance isreached between emitted and absorbed electrons.the SNS field-free region and dipole section for δmax =2are shown in [1]. Due to the large electron multiplication,we have used a very low initial number of macroparticlesper bunch passage, leading to a significant fluctuations inthe turn-by-turn electron density. Simulation results for theSNS obtained with a different code [10] show a qualitativeagreement with our results, although they show a lower es-timated electron density at this SEY value. The neutraliza-tion factor, ratio e−/p+, computed within the beam radiusregion, is shown in Fig. 3. For δmax=1.3 and 1.1, we wereable to increase significantly the number of macroparticles,leading to better statistics. The build-up of the electroncloud during the first few bunch passages is shown in Fig.4.The simulated electron density (averaged over the wholerun) in a SNS field free region is shown in Fig. 5, whenassuming δmax=2. Proton losses corresponding to 10−7protons loss per proton per turn are expected in the SNSring.4 CONCLUSIONWe present updated electron cloud simulations for PSRand preliminary simulations for the SNS. When consider-ing proton losses of 10−7, an average density 10 nC/m withpeaks of ≥ 150 nC/m may be reached in an SNS field-free region. The related neutralization factor exceeds 10%at the tail of the beam pulse. High electron density maylead to a significant tune shift and consequent high protonlosses, see [3]. Due to a large unexpected electron multipli-cation in the case of the SNS, we have used a low numberof macroparticles per bunch passage.5 ACKNOWLEDGEMENTSWe are particularly grateful to our colleagues of the PSRInstability Studies Program for many stimulating discus-Figure 5: Average electron density (over whole run) in aSNS field free region. Proton losses of 10−7 protons lossper proton per turn are expected in the SNS ring. Secondaryelectron yield δmax=2.sions, especially to R. Macek for discussions and for pro-viding us the experimental data. We are grateful to NERSCfor supercomputer support.6 REFERENCES[1] For an updated summary and links on electron cloud studies,see: Mini-Workshop on Electron-Cloud Simulations for Pro-ton and Positron Beams ECLOUD02, CERN, 15-18 April2002, http://slap.cern.ch/collective/ecloud02/, or also Phys-ical Review Special Topic (PRST) - Accelerator and Beams(AB) ECLOUD02 Special Collection Edition, future publi-cation.[2] R. Macek ECLOUD02 proceedings, see ref. [1].[3] M. Furman and M. Pivi, Proc. PAC01, Chicago, IL, p. 708,and also ECLOUD02 proceedings, see ref. [1].[4] For an updated on the self consistent treatment of the in-stability see, for example ECLOUD02 proceedings, seeref. [1].[5] M. A. Furman and M. Pivi Microscopic Probabilistic Modelfor the Simulation of the Secondary Electron Emission,LBNL-49711, CBP Note-415, to be submitted to PhysicalReview Special Topics, May 2002.[6] R. Kirby, private communication.[7] V. Baglin, I. Collins, B. Henrist, N. Hilleret, G. Vor-laufer, A Summary of Main Experimental Results Concern-ing the Secondary Electron Emission of Copper, LHC-Project-Report-472.[8] M. Blaskiewicz, private communication, May 2002.[9] T. Toyama, K. Ohmi, Study for ep Instability in High Inten-sity Proton Ring, these proceedings.[10] M. Blaskiewicz Electron Cloud in the PSR and SNS theseproceedings.

Electron-cloud updated simulation results for the PSR, and recent results for the SNS

CERN Document Server

ELECTRON-CLOUD UPDATED SIMULATION RESULTS FOR THE PSR,AND RECENT RESULTS FOR THE SNS. ∗M. Pivi and M. A. Furman,† LBNL, Berkeley, CA94720, USAAbstractWe present recent simulation results for the main fea-tures of the electron cloud in the storage ring of the Spal-lation Neutron Source (SNS) at Oak Ridge, and updatedresults for the Proton Storage Ring (PSR) at Los Alamos.In particular, a complete refined model for the secondaryemission process including the so called true secondary,rediffused and backscattered electrons has been includedin the simulation code.1 INTRODUCTIONThe Spallation Neutron Source (SNS) under construc-tion at the Oak Ridge National Laboratory (ORNL), hasinitiated studies on the possible electron-cloud effect,which may limit the performances of the proton storagering. A similar high-intensity instability which has beenobserved in the PSR at the Los Alamos National Labora-tory (LANL) for more than 13 years, is now recognized tobe, although not conclusively proven, an electron-cloud ef-fect. Since 1987 the PSR has reported a fast instability thatis responsible for proton losses and collective beam mo-tion above a certain current threshold, and is accompaniedby a large number of electrons. This instability is now be-lieved to be due to the collective coupling between an elec-tron cloud and the proton beam [1, 2]. Such instability is aparticular manifestation of the electron-cloud effect (ECE)that has been observed or is expected at various other ma-chines. In this article we present simulation results for theSNS and for PSR ring obtained with the ECE code thathas been developed at LBNL over the past 6 years, suit-ably augmented to deal with very long and intense bunchessuch as in the case of long proton beams. At the presentstage, we have restricted our studies to look in detail at thedynamics of the electron cloud rather than the instabilityper se. Thus in all results presented here, the proton beamis assumed to be a static distribution of given charge andshape moving on its nominal closed orbit, while the elec-trons are treated fully dynamically. This approximation isvalid for stable beam operation, and it is probably reason-able for mild instability. We defer issues like the current in-stability threshold, growth rate and frequency spectrum tofuture studies. We compared in [3] our results for the elec-tron current and energy spectrum of the electrons hittingthe walls of the chamber against measurements obtained inthe PSR by means of dedicated electron probes. From suchcomparisons we can assess the effects of several importantparameters such as the secondary electron yield (SEY) at∗Work supported by the SNS project and by the US DOE under con-tract DE-AC03-76SF00098.† mpivi@lbl.gov and mafurman@lbl.govthe walls of the chamber, the proton loss rate and electronyield, etc. Furthermore, we can infer details of the electroncloud in the vicinity of the proton beam, such as the neu-tralization factor, which is important for a self-consistenttreatment of the coupled e-p problem [4].Table 1: Simulation parameters for the PSR and SNS.Parameter Symbol PSR SNSproton beam energy E, GeV 1.735 1.9dipole field B, T 1.2 0.78bunch population Np, ×1013 5 20.5ring circumference C, m 90 248revolution period T , ns 350 945bunch length bl, ns 254 760gauss. tr. bunch size σx, σy , mm 10, 10flat tr. bunch size rx, ry , mm 28, 28beam pipe semi-axes a, b, cm 5,5 10,10proton loss rate ploss, ×10−6 4 0.11proton-electron yield Y , 100 100No. kicks/bunch Nk 1001 5001No. steps during gap Ng 100 250SEY params:max sec. yield δmax 2.0 2.0energy at yield max Emax, eV 300 300yield low energy el. δ(0) 0.5 0.52 PHYSICAL MODEL2.1 Sources of electronsIn this article we consider what we expect to be the maintwo sources of electrons for proton storage rings as theSNS and the PSR, namely: lost protons hitting the vacuumchamber walls, and secondary emission from electrons hit-ting the walls (we are not interested here in simulating theelectron cloud in the vicinity of the stripper foil). Althoughour code accommodates other sources of electrons, suchas residual gas ionization, we have turned them off for thepurposes of this article.2.2 Secondary emission processWe represent the SEY δ(E0) and the correspondingemitted-electron energy spectrum dδ/dE (E0 =incidentelectron energy, E = emitted secondary energy) by a de-tailed model described elsewhere [5]. Its parameters wereobtained from detailed fits to the measured SEY of stain-less steel (St. St.) [6]. The main SEY parameters arethe energy Emax at which δ(E0) is maximum, and thepeak value itself, δmax = δ(Emax) (see Table 1). Further-more, for the results shown below, we do take into accountthe elastic backscattered and rediffused components of thesecondary emitted-electron energy spectrum dδ/dE. Thebackscattered component typically becomes more impor-tant at low incident electron energies. To account for thisbehavior we have used a fit extrapolated data for coppermeasured at CERN [7].The value of δ(E0) at incident electron energies E0 <10eV is an important parameter since it determines theelectron accumulation rate, and also the electron survivalrate at the end of the gap. This quantity is difficult tomeasure experimentally, and remains an uncertainty for themodel. In our simulations we have made the assumptionthat δ(0) ' 0.5. In this case, the simulated electron den-sity increases by a factor ∼ 3 and the peak detector cur-rent by almost a factor ∼ 2.5, relative to the δ(0) ' 0.1case (refer to previous results for PSR with no rediffusednor backscattered electrons, see [3]). These are examplesof strong parameter sensitivity that calls for further experi-mental investigations.2.3 Simulation ModelThe SNS and the PSR rings store a single proton bunchof length τb followed by a gap of length τg with a typicalcurrent intensity profile shown in Figs. 2 and 4. In our sim-ulation we assume a Gaussian transverse PSR beam withrms sizes σx = σy = 10mm, , and we use the actuallymeasured longitudinal intensity profile. A flat transversebeam with rx = ry = 28mm is assumed for the SNS.We simulate the passage of the proton bunch in a field-free region with a vacuum chamber which we take to be acylindrical perfectly-conducting pipe. The number of elec-trons generated by lost protons hitting the vacuum cham-ber wall is Np × Y × ploss per turn for the whole ring,where Y is the effective electron yield per lost proton, andploss is the proton loss rate per turn for the whole ring perbeam proton. We assume the lost- proton time distribu-tion to be proportional to the instantaneous bunch inten-sity. The electrons are then simulated by macroparticles.The secondary electron mechanism adds to these a vari-able number of macroparticles, generated according to theSEY model mentioned above. The bunch is divided up intoslices, so that the macroparticles experience Nk kicks dur-ing the bunch passage. We divide the interbunch gap intoNg intermediate steps. The space charge force is computedand applied at each slice in the bunch and each step in thegap. The image forces from both protons and electrons aretaken into account, assuming a perfectly conducting wall.Typical parameter values are shown in Table 1.3 RESULTS AND DISCUSSIONThe possible amplification mechanism which may takeplace in long-beam machines is explained in Fig. 1. Anelectron present in the vacuum chamber before the bunchpassage oscillates in the beam well potential, and it is re-leased at the end of the beam passage. Instead, electronsgenerated at the wall by proton losses at the maximum ofthe beam pulse are accelerated and decelerated by the beampotential and hit the opposite wall with a net energy gain,producing secondary electrons.Figure 1: Electron multiplication mechanism in long pro-ton bunches.Electrons which survive the gap between two bunch pas-sages will increase in number. The electrons graduallyincrease in number during successive bunch passages un-til, owing to the space-charge forces, a balance is reachedbetween emitted and absorbed electrons. The build-upof the electron cloud in a PSR field-free region and adipole section during the passage of the beam is shown inFig. 2. The saturation level in the PSR is reached afterfew bunch passages, when assuming δmax = 2. The esti-mated average number of electrons in a field free region is∼ 4 × 107e−/cm3 or 50nC/m. The neutralization factoror fractional charge neutralization, ratio e−/p+, during abunch passage is shown in Fig. 3.The SNS beam pipe chamber will be coated with TiN,and recent measurements of an as-received SNS sample ofthe TiN coated vacuum chamber, has shown δmax = 2 [8].Consistent results where obtained at KEK [9]. The build-up of the electron cloud in the SNS field-free region and adipole section during the passage of the beam is shown inFig. 4 for δmax = 2. Due to a large electron multiplica-tion, we have used a very low initial number of macropar-ticles per bunch passage. The simulations present a significant fluctuation in the turn-by-turn electron density, andwe are going to refine the code to accomplish for the SNScase. Simulation results for the SNS [10] show a qualita-tive agreement, but a lower estimated electron density. Theneutralization factor during a bunch passage is shown inFig. 5. The tune shift due to electron neutralization of afactor ∼ 1 may be estimated, for example, at 25% beamintensity, bydQec = − 0.25 f γ2 dQsc ∼ −2 dQsc = − 0.4 (1)where dQsc=0.2 is the space charge tune shift, γ = 2.066is the usual relativistic factor of the beam, and f is the neu-tralization factor. Once the secondary electron yield hasdecreased to 1.3 and 1.1, we were able to increase significantly the number of macroparticles to account for betterstatistics. The build-up of the electron cloud during the firstfew bunch passages is shown in Fig.6.Figure 2: Simulated electron density during the first bunchpassages, in a PSR field-free region and a dipole section.The saturation level is reached after few bunch passages.Figure 3: Simulated electron neutralization factor in aPSR field-free region, the fractional charge neutralizationreaches 50% at the tail of the bunch.4 CONCLUSIONA complete refined model for the secondary emis-sion including the so-called true secondary, rediffused andbackscattered electrons has been recently included in thecode. We present an update of computer simulation resultsfor the main features of the electron cloud at the ProtonStorage Ring (PSR) and recent simulation results for theSpallation Neutron Source (SNS). Preliminary simulationsfor the SNS, show that a density of ≥ 150nC/m may bereached in a field-free region, leading to a significant tuneshift given by electron neutralization. Due to a large unex-pected electron multiplication in the case of the SNS, wehave used a low number of macroparticles per bunch pas-Figure 4: Simulated electron density during the first bunchpassages, in a SNS field-free region.Figure 5: Simulated electron neutralization factor in a SNSfield-free region, the fractional charge neutralization ex-ceeds 1 at the tail of the bunch.sage. The code is going to be implemented to accomplishfor the SNS case.5 ACKNOWLEDGEMENTSWe are particularly grateful to our colleagues of the PSRInstability Studies Program for many stimulating discus-sions, M. Blaskiewicz, K. Harkay, R. Davidson, H. Qin,P. Channell, T. S. Wang. We are especially grateful to R.Macek for discussions and for providing us the experimen-tal data. Thanks to Y.H. Cai, F. Zimmermann, N. Hilleret,J.Wei, A. Wolski, S. Heifets, T. Raubenheimer, R. Kirby,A. Alexandrov, V. Danilov. We are grateful to NERSC forsupercomputer support.6 REFERENCES[1] For a summary, see: Proc. ICFA Workshop on Two-Stream Instabilities, Santa Fe, NM, US, Feb. 16-18,2000, http://www.aps.anl.gov/conferences/icfa/two-Figure 6: Build-up of the electron cloud in the SNS field-free region assuming a δmax = 1.3 and 1.1. The electronsgradually increase in number during successive bunch pas-sages until, owing to the space-charge forces, a balance isreached between emitted and absorbed electrons.stream.html, or also International Workshop on Two-Stream Instabilities in Particle Accelerators and StorageRings, at KEK Tsukuba, Japan, September 11-14, 2001,http://conference.kek.jp/two-stream/.[2] R. Macek, these proceedings.[3] M. Furman and M. Pivi, Proc. PAC01, Chicago, IL, p. 708.[4] For an updated on the self consistent treatment of the insta-bility see, for example, Physical Review Special Topic, Spe-cial Collection Edition on Electron Cloud and Two-StreamInteractions in Long-Bunch Proton Beams, future publica-tion.[5] M. A. Furman and M. Pivi Microscopic Probabilistic Modelfor the Simulation of the Secondary Electron Emission,LBNL-49711, CBP Note-415, to be submitted to PhysicsReview ST, May 2002.[6] R. Kirby, private communication.[7] V. Baglin, I. Collins, B. Henrist, N. Hilleret, G. Vor-laufer, A Summary of Main Experimental Results Concern-ing the Secondary Electron Emission of Copper, LHC-Project-Report-472.[8] M. Blaskiewicz, private communication, May 2002.[9] T. Toyama, K. Ohmi, Study for ep Instability in High Inten-sity Proton Ring, these proceedings.[10] M. Blaskiewicz Electron Cloud in the PSR and SNS theseproceedings.

Electron Cloud Updated Simulation Results for the PSR, and Recent Results for the SNS

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Electron Cloud Updated Simulation Results for the PSR, and Recent Results for the SNS

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