This is a summary of the talks presented in Session III ''Simulations of Electron-Cloud Build Up'' of the Mini-Workshop on Electron-Cloud Simulations for Proton and Positron Beams ECLOUD-02, held at CERN, 15-18 April 2002

Furman, M A

CERN Document Server

              Summary of Session III∗M. A. Furman† , LBNL, Berkeley, CA 94720, USAAbstractThis is a summary of the talks presented in Session III(“Simulations of Electron-Cloud Build Up”) of the Mini-Workshop on Electron-Cloud Simulations for Proton andPositron Beams ECLOUD-02, held at CERN, 15–18 April2002.1 CONTRIBUTIONSThe talks presented in Session III, with speakers’ namesunderlined, were:1. Adiabatic Theory of Electron Oscillations and its Ap-plication to SIS-100/200, P. Zenkevich, N. Mustafinand O. Boine-Frankenheim.2. Electron-Cloud Simulations: Build Up and RelatedEffects, G. Rumolo and F. Zimmermann.3. 3D Simulation of Photoelectron Cloud in KEKB LER,L. F. Wang, H. Fukuma, K. Ohmi, S. Kurokawa, K.Oide and F. Zimmermann.4. A Simulation Study of the Electron Cloud in the Ex-perimental Regions of the LHC, A. Rossi, G. Rumoloand F. Zimmermann.5. Qualitative Analysis of Electron Cloud Effects in theNLC Damping Ring, S. Heifets.6. Electron Cloud Updated Simulation Results for thePSR, and Recent Results for the SNS, M. Pivi and M.A. Furman.2 SUMMARIESAdiabatic Theory of Electron Oscillations and its Ap-plication to SIS-100/200. The SIS machines are syn-chrotrons being designed at GSI to store U+28238 ions. SIS-100 will have an energy of 100 MeV/u with four bunches,while SIS-200 will have an energy of 1000 MeV/u. Thesubject of this paper is to study the motion of electronstrapped by the ion beam. The only source of electrons con-sidered is ionization of residual gas. The electron line den-sity, λe, is assumed to be uniform. The ion line densityλi(τ), on the other hand, is a function of the normalizedtime τ = t/T , where t = time and T = revolution period(or bunch period if more than one bunch). The normalizednet line density function isF (τ) =Ziλi(τ)− λeZi〈λi〉 (1)∗Work supported by the US DOE under contract DE-AC03-76SF00098.†mafurman@lbl.govwhere Zi is the ion charge. The scale of F (τ) is set by theneutralization factor η = Ne/NiZi, where Ne and Ni arethe total number of electrons and ions, respectively. The in-vestigation was carried out for 4 assumed shapes of F (τ).In all cases, a gap is assumed between bunches. In the gapthe ion density is assumed to be uniform and is character-ized by a leak parameter χ = (ion density in gap)/(ion den-sity at center of the beam). The transverse density of theions and the electrons is assumed to be round-Gaussian,both of the same σ. For small amplitudes, the transverseequation of motion of an individual electron in the com-bined field of the ions and electron cloud can be linearizedleading to Hill’s equation in which F (τ) plays the role ofthe periodic focusing function. This equation is analyzedby standard transfer-matrix techniques, leading to linear in-stability for certain values of χ. If the electrons are stable,they form a core within the ion beam. Large-amplitudeelectron motion was also investigated. In this case, theheating of the electrons is assumed to be due to ion-electronCoulomb scattering. An electron is assumed to be lost if itsenergy exceeds the net beam potential (it is assumed to beabsorbed at the vacuum-chamber walls with unit probabil-ity). This analysis leads to very small equilibrium values ofη for both SIS-100 and SIS-200 under nominal conditions.Future plans call for code improvements, using the MonteCarlo method, and additional sources of electrons.Electron-Cloud Simulations: Build Up and Re-lated Effects. The CERN electron-cloud simulation codeECLOUD models the build up of an electron cloud in thevacuum chamber under the influence of a charged bunchedbeam. The primary sources of electrons are photoemissionoff the chamber walls, and residual gas ionization. Themodel also takes into account secondary emission by elec-trons striking the chamber walls, including elastic reflec-tion. Direct and image (surface) forces on the electronsare considered, both from the beam and from the spacecharge of the electron cloud. These forces are applied tothe electrons by an appropriate time discretization, bothwithin a bunch and in the gaps between bunches. Longi-tudinal (E × B) forces are also included. Besides field-free regions, the code can describe the electron cloud inseveral magnetic field configurations. Standard cases aredipole, quadrupole and solenoid fields, although any fieldcan be considered if specified in analytic form. The sec-ondary emission yield (SEY) has been modeled by fits toexperimental data, including the reflected component. Thecode has been applied to describe various electron-cloudeffects (ECEs) such as the electron density build-up and re-lated phenomena such as electron energy spectra, heat loadon the LHC beam screen, spatial patterns of the electron      cloud, electron flux at pick-up buttons, multi-bunch insta-bility growth rates, electron trapping by magnetic fields,and electron-cloud build up for electron beams. Resultsfor the electron-cloud build up and heat load (for LHC) aresensitive to the parametrization of secondary emission andphotoemission. Important are also the beam and electronimage charges, the electron space charge, and magneticfields, even if they are only a few Gauss. The simulatedelectron-cloud build up is in good agreement with obser-vations for the CERN SPS, the CERN PS and the KEKBLER. An interesting disagreement between measurementsand simulations pertains to the exact position of the two“vertical stripes” (locations of peak electron density) in anSPS dipole. The simulated separation between the stripes isabout a factor ∼ 2 larger than observed for a bunch popu-lation of 8 × 1010. In recent developments, the code hasbeen applied to study the electron cloud in KEKB LERquadrupole magnets, predicting the trapping of electronsfor very long times. The code has also been applied to thecase of electron (rather than positron) beams, in which casean electron cloud is seen to develop, although at lesser in-tensity than for positron beams.3D Simulation of Photoelectron Cloud in KEKBLER. A 3-dimensional particle-in-cell (PIC) simulationcode, PICEC3, has been developed to study the photoelec-tron cloud, including all space-charge effects. The codeuses an irregular mesh in order to adequately represent theshape of the vacuum chamber. This irregular mesh requiresa modification of the conventional algorithm to assign thecharge of any given macroparticle to the nodes of the cellthat contains it. Besides field-free regions, the code can beapplied to any magnetic field configuration. The code in-cludes models for photoemission and secondary emission,and has been applied to study the instabilities in the KEKBLER. Results show that a solenoidal field is very effectivein confining the photoelectrons near the vacuum chamberwall, thereby creating a beneficial charge-free region in thevicinity of the beam. The more uniform the solenoid field,the more effective the confinement. A comparison with C-yoke magnets shows that solenoids are more effective atelectron trapping. Multipacting can occur in a field-free re-gion and in a dipole magnet. The code has been appliedto quadrupole and sextupole magnets, for which a seriouselectron trapping phenomenon has been found during thetrain gap. The mechanism is analogous to the magneticbottle confinement of plasmas. In order for the trapping toget started, the adiabatic condition of the electron motionin a magnetic field must be broken. This happens for suffi-ciently short bunches, in which case the electrons get a sub-stantial impulse kick. The condition on the bunch length isσz < 2pimc/eB, where B is the field at the mirror pointof the trapped electron trajectory. In practical units, thiscondition reads σz [mm] < 10.7/B [T]. For KEKB condi-tions, the simulated trapping time in a quadrupole is ∼ 105ns. This long confinement time may cause multibunch in-stabilities. Simulation results on the trapping mechanismsagree well with theoretical analysis. The code has so farbeen applied to cylindrical vacuum chamber geometry andround gaussian beams, but the extension to more compli-cated cases is in progress.A Simulation Study of the Electron Cloud in the Ex-perimental Regions of the LHC. The vacuum chamberin the experimental regions of the LHC will be at room tem-perature and will have complicated geometry in order to ac-commodate the detectors (ATLAS, CMS-TOTEM, LHCband ALICE) and the two coexisting beams. The baselinedesign calls for coating the chamber with TiZrV, a gettermaterial that possesses the virtues of effective pumping af-ter activation at 200 C, low SEY, and good stability vis-a`-vis exposure to air. The primary motivation for these elec-tron cloud studies is to determine the residual gas pressureand composition, of critical importance for the acceptabledetector background level. Also important is the contribu-tion of these warm sections to the electron-cloud effects onthe beams. As opposed to the arcs, where the basic cri-terion on the SEY is the maximum tolerable heat deposi-tion from the electron cloud, in the experimental regionsthe basic criterion on the SEY is the maximum tolerablegas pressure, particularly from electron-stimulated desorp-tion (ESD). Depending on the exact location, the chamberradius varies in these regions from 22 to 200 mm. Sincethe electron-cloud simulation tool used does not at presentallow for the modeling of two counter-circulating beams,the assumption was made that the ECEs could be brack-eted by studying two extreme cases with the conventional(single-beam) simulation, namely: (a) bunch spacing hasthe nominal value (sb = 7.48 m) but bunch intensity istwice the nominal value (2Nb = 2.1×1011), and (b) bunchspacing is sb/2 but bunch intensity is Nb. In the real ma-chine, these two cases obtain at discrete points along thechamber whenever the distance from the IP is an integeror half-integer multiple of sb, respectively. Besides ESD,photon-stimulated desorption (PSD) was also taken into ac-count (ion-stimulated desorption was considered and foundto be negligible). Assuming peak SEY values of 1.1 or 1.4and a calculated photon flux of 1016 γ/m/s, the simulationcode yields the electron flux and energy spectrum at thechamber walls for a given radius. These results, combinedwith measured values of the PSD and ESD for TiZrV, yieldthe local pressure of H2, CH4, CO and CO2. It was foundthat ESD is the main source of gas. In order to sharpen thequantitative predictive ability of the code, the simulationshave been repeated for the SPS and compared with pickupelectron signals and pressure rise measurements (in thiscase the main source of electrons is residual gas ionization).For a 72-bunch train at 26 GeV and Nb = 8.3 × 108, themeasured pickup signal in a field-free section matches thesimulations for a pressure of 200 nT and a peak SEY=1.6.Similar tests have been carried out for other bunch-trainpatterns. Further benchmarks will be carried out, includingtests in a special section of chamber coated with TiZrV.      Qualitative Analysis of Electron Cloud Effects in theNLC Damping Ring. The motivation of this work is totry to obtain analytic estimates of the electron-cloud den-sity and magnitude of the resultant wake in order to inter-pret numerical results from simulations and allow parame-ter scaling without additional lengthy calculations. In thisapproach the beam is assumed to be non-dynamical henceunperturbable by the cloud. The analysis is developed fora quasi steady state equilibrium, defined by the conditionκ¿ 1, where κ is given byκ =Nbresbb2(2)Here Nb and sb are the bunch population and spacing, re-spectively, re is the classical radius of the electron, andb is the vacuum chamber radius. The condition κ = 1defines the beam-induced multipacting resonance condi-tion [1], corresponding to the equality of the bunch spacing(in time units) and the traversal time of an electron acrossa chamber diameter under the impulse of a single bunchpassage. The limit κ = 0 at fixed Nb and b correspondseffectively to a coasting beam, hence only a static electroncloud can develop in this limit. The condition 0 < κ ¿ 1corresponds to a regime in which the beam and the electroncloud (or, at least, most of the electrons in the cloud) areweakly coupled hence an analytic approach may be fruit-ful. In the high-current limit of a bunched beam, κ À 1,the electrons cross the chamber so quickly under the actionof a single bunch that an electron cloud in the usual senseis not well defined.As a first approximation, the electron cloud distributionis computed in steady state for a coasting beam in a cylin-drical chamber of radius large compared with the trans-verse beam dimensions. The electrons move in the com-bined potential of the beam and the space charge of thecloud. The requirement of zero radial electric field at thewall yields an average electron-cloud densityn0 =Nbpib2sb, (3)corresponding to the average beam neutralization condi-tion. The charge distribution is given by a Boltzmann form,n(r) ∝ exp(−U(r)/T ) where U is the self-consistentbeam-cloud potential and T is a temperature. For abunched beam with κ ¿ 1, an electron takes, on aver-age κ−1 bunch passages to cross the chamber. Since thisis a large number, its motion can be taken to be sensi-bly random. Thermalization of the electrons takes placewithin some distance from the beam. Even if the lin-ear bounce frequency of an electron within a bunch is Àbunch frequency, such electrons can still be described bythe Boltzmann distribution due to randomness of the elec-tron motion. Assuming that an electron that hits the cham-ber wall is absorbed, equating the average energy gainfrom a bunch-electron kick with the average energy lostby an electron hitting the wall defines the cloud temper-ature T in steady state. This calculation also yields theenergy spectrum of the electrons hitting the wall. Photo-electrons and secondary electrons are attracted towards thebeam. These newly-generated electrons produce jets thatmay have higher density than the average n0. The calcu-lation shows that these jets significantly increase the clouddensity near the chamber center. Once saturation level isachieved, which takes a few bunch passages, the newly-generated photoelectrons and secondary electrons are re-pelled by the potential and are sent back to the chamberwall. This implies that the level of the density at saturationis fairly independent of the photoelectron and secondaryyield. Multipacting does not change the temperature muchbut rather affects the distribution of electrons only in thevicinity of the wall. This explains why the average densityof the cloud is close to that given by the beam neutralitycondition. The analysis also yields the long-range wakeand the corresponding linear growth rate of coupled-bunchinstability.This qualitative analysis for κ ¿ 1 was applied to theNLC Main Damping Ring, for which κ = 0.28. Goodgeneral agreement is found with available simulations.Electron Cloud Updated Simulation Results for thePSR, and Recent Results for the SNS. The LBNLelectron-cloud code POSINST, which was initially devel-oped to study the ECE in the PEP-II positron beam start-ing in 1995, has been recently applied to the electron-cloud instability seen at the Proton Storage Ring (PSR)ring at LANL, and to the storage ring of the SpallationNeutron Source (SNS), presently under construction atORNL. The physical model embodied by this code is sim-ilar to that of the code ECLOUD, described above. How-ever, the secondary emission process is somewhat differ-ent. An improved, complete, model for this process, in-cluding detailed descriptions of the three main componentsof the emission spectrum (true secondary, rediffused andbackscattered electrons) has been recently included in thecode. The code has been benchmarked against measure-ments at the PSR obtained by means of dedicated electronprobes which measure the flux, time structure, and energyspectrum of the electrons striking the chamber walls. ThePSR contains a single proton bunch of full length ∼ 60m and energy 1.735 GeV in a stainless steel chamber of 5cm radius and 90 m ring circumference. The simulationsshow very clear trailing-edge beam-induced multipacting(BIM), in good agreement with measurements. This effectwas clearly seen in a digital simulated movie of the elec-tron cloud build up and dissipation during two bunch pas-sages. The electrons that are present in the chamber duringthe beam gap typically have low energy; they are capturedadiabatically by the beam during the passage of its leadingedge, and released with equally low energy towards the endof the trailing edge. These electrons, therefore, do not con-tribute to trailing-edge BIM. However, the electrons thatare generated from stray protons hitting the chamber dur-ing the bunch passage, especially those produced near thepeak of the bunch current, are captured non-adiabatically     and are released at high energy soon after the passage ofthe peak of the bunch, and contribute strongly to trailing-edge BIM. This phenomenon leads to a strong sensitivityof the electron-wall current (and hence the electron distri-bution) to the longitudinal profile of the bunch. The time-energy joint electron spectrum is in good qualitative agree-ment with measurements, although the quantitative agree-ment is within a factor ∼ 2, assuming a peak SEY value of2. Preliminary simulations for the SNS show that an aver-age electron line density of ∼ 150 nC/m may be reachedin a field-free region, leading to a significant tune shift dueto beam neutralization. Due to an unexpectedly large elec-tron multiplication during the passage of the SNS beam,simulations have have so far used a low number of seedmacroparticles per bunch passage, leading to poor statis-tics for peak SEY values above 1.3. The code will soon beimproved to deal with this problem.3 ACKNOWLEDGMENTSI am grateful to G. Rumolo for his effective job as theScientific Secretary of Session III, and to F. Zimmermannfor organizing such an informative workshop.4 REFERENCES[1] O. Gro¨bner, “Bunch-Induced Multipactoring,” Proc. 10thIntl. Accel. Conf., Serpukhov, 1977, p. 277.

Summary of Session III

Furman, M. A.

UNT Digital Library

                LBNL–50762Summary of Session III∗M. A. Furman† , LBNL, Berkeley, CA 94720, USAAbstractThis is a summary of the talks presented in Session III(“Simulations of Electron-Cloud Build Up”) of the Mini-Workshop on Electron-Cloud Simulations for Proton andPositron Beams ECLOUD-02, held at CERN, 15–18 April2002.1 CONTRIBUTIONSThe talks presented in Session III, with speakers’ namesunderlined, were:1. Adiabatic Theory of Electron Oscillations and its Ap-plication to SIS-100/200, P. Zenkevich, N. Mustafinand O. Boine-Frankenheim.2. Electron-Cloud Simulations: Build Up and RelatedEffects, G. Rumolo and F. Zimmermann.3. 3D Simulation of Photoelectron Cloud in KEKB LER,L. F. Wang, H. Fukuma, K. Ohmi, S. Kurokawa, K.Oideand F. Zimmermann.4. A Simulation Study of the Electron Cloud in the Ex-perimental Regions of the LHC, A. Rossi, G. Rumoloand F. Zimmermann.5. Qualitative Analysis of Electron Cloud Effects in theNLC Damping Ring, S. Heifets.6. Electron Cloud Updated Simulation Results for thePSR, and Recent Results for the SNS, M. Pivi and M.A. Furman.2 SUMMARIESAdiabatic Theory of Electron Oscillations and its Ap-plication to SIS-100/200. The SIS machines are syn-chrotrons being designed at GSI to store U+28238 ions. SIS-100 will have an energy of 100 MeV/u with four bunches,while SIS-200 will have an energy of 1000 MeV/u. Thesubject of this paper is to study the motion of electronstrapped by the ion beam. Theonly sourceof electronscon-sidered is ionization of residual gas. Theelectron lineden-sity, λe, is assumed to be uniform. The ion line densityλi(τ), on the other hand, is a function of the normalizedtime τ = t/T , where t = time and T = revolution period(or bunch period if more than one bunch). The normalizednet linedensity function isF (τ) =Ziλi(τ)− λeZi〈λi〉(1)∗Work supported by the US DOE under contract DE-AC03-76SF00098. Proc. ECLOUD02 Workshop, CERN, 15–18 April 2002.†mafurman@lbl.govwhereZi is the ion charge. The scale of F (τ) is set by theneutralization factor η = Ne/NiZi, whereNe and Ni arethetotal number of electronsand ions, respectively. Thein-vestigation was carried out for 4 assumed shapes of F (τ).In all cases, a gap is assumed between bunches. In the gapthe ion density is assumed to be uniform and is character-ized by a leak parameter χ = (ion density in gap)/(ion den-sity at center of the beam). The transverse density of theions and the electrons is assumed to be round-Gaussian,both of the same σ. For small amplitudes, the transverseequation of motion of an individual electron in the com-bined field of the ions and electron cloud can be linearizedleading to Hill’s equation in which F (τ) plays the role ofthe periodic focusing function. This equation is analyzedby standard transfer-matrix techniques, leading to linear in-stability for certain values of χ. If the electrons are stable,they form a core within the ion beam. Large-amplitudeelectron motion was also investigated. In this case, theheating of theelectronsisassumed to bedueto ion-electronCoulomb scattering. An electron isassumed to belost if itsenergy exceeds the net beam potential (it is assumed to beabsorbed at the vacuum-chamber walls with unit probabil-ity). Thisanalysis leadsto very small equilibrium valuesofη for both SIS-100 and SIS-200 under nominal conditions.Future plans call for code improvements, using the MonteCarlo method, and additional sources of electrons.Electron-Cloud Simulations: Build Up and Re-lated Effects. TheCERN electron-cloud simulation codeECLOUD models the build up of an electron cloud in thevacuum chamber under the influenceof acharged bunchedbeam. The primary sources of electrons are photoemissionoff the chamber walls, and residual gas ionization. Themodel also takes into account secondary emission by elec-trons striking the chamber walls, including elastic reflec-tion. Direct and image (surface) forces on the electronsare considered, both from the beam and from the spacecharge of the electron cloud. These forces are applied tothe electrons by an appropriate time discretization, bothwithin a bunch and in the gaps between bunches. Longi-tudinal (E × B) forces are also included. Besides field-free regions, the code can describe the electron cloud inseveral magnetic field configurations. Standard cases aredipole, quadrupole and solenoid fields, although any fieldcan be considered if specified in analytic form. The sec-ondary emission yield (SEY) has been modeled by fits toexperimental data, including the reflected component. Thecode has been applied to describe various electron-cloudeffects(ECEs) such astheelectron density build-up and re-lated phenomenasuch aselectron energy spectra, heat loadon the LHC beam screen, spatial patterns of the electron        cloud, electron flux at pick-up buttons, multi-bunch insta-bility growth rates, electron trapping by magnetic fields,and electron-cloud build up for electron beams. Resultsfor theelectron-cloud build up and heat load (for LHC) aresensitive to the parametrization of secondary emission andphotoemission. Important are also the beam and electronimage charges, the electron space charge, and magneticfields, even if they are only a few Gauss. The simulatedelectron-cloud build up is in good agreement with obser-vations for the CERN SPS, the CERN PS and the KEKBLER. An interesting disagreement between measurementsand simulations pertains to the exact position of the two“vertical stripes” (locations of peak electron density) in anSPSdipole. Thesimulated separation between thestripesisabout a factor ∼ 2 larger than observed for a bunch popu-lation of 8 × 1010. In recent developments, the code hasbeen applied to study the electron cloud in KEKB LERquadrupole magnets, predicting the trapping of electronsfor very long times. The code has also been applied to thecaseof electron (rather than positron) beams, in which casean electron cloud is seen to develop, although at lesser in-tensity than for positron beams.3D Simulation of Photoelectron Cloud in KEKBLER. A 3-dimensional particle-in-cell (PIC) simulationcode, PICEC3, has been developed to study the photoelec-tron cloud, including all space-charge effects. The codeuses an irregular mesh in order to adequately represent theshapeof thevacuum chamber. This irregular mesh requiresa modification of the conventional algorithm to assign thecharge of any given macroparticle to the nodes of the cellthat contains it. Besides field-free regions, the code can beapplied to any magnetic field configuration. The code in-cludes models for photoemission and secondary emission,and hasbeen applied to study the instabilities in theKEKBLER. Results show that a solenoidal field is very effectivein confining the photoelectrons near the vacuum chamberwall, thereby creating abeneficial charge-freeregion in thevicinity of the beam. The more uniform the solenoid field,the more effective the confinement. A comparison with C-yoke magnets shows that solenoids are more effective atelectron trapping. Multipacting can occur in afield-freere-gion and in a dipole magnet. The code has been appliedto quadrupole and sextupole magnets, for which a seriouselectron trapping phenomenon has been found during thetrain gap. The mechanism is analogous to the magneticbottle confinement of plasmas. In order for the trapping toget started, the adiabatic condition of the electron motionin a magnetic field must be broken. This happens for suffi-ciently short bunches, in which casetheelectronsget asub-stantial impulsekick. Thecondition on thebunch length isσz < 2πmc/eB, whereB is the field at the mirror pointof the trapped electron trajectory. In practical units, thiscondition readsσz [mm] < 10.7/B [T]. For KEKB condi-tions, thesimulated trapping time in aquadrupole is∼ 105ns. This long confinement time may cause multibunch in-stabilities. Simulation results on the trapping mechanismsagree well with theoretical analysis. The code has so farbeen applied to cylindrical vacuum chamber geometry andround gaussian beams, but the extension to more compli-cated cases is in progress.A Simulation Study of the Electron Cloud in the Ex-perimental Regions of the LHC. The vacuum chamberin theexperimental regionsof theLHCwill beat roomtem-peratureand will havecomplicated geometry in order to ac-commodate the detectors (ATLAS, CMS-TOTEM, LHCband ALICE) and the two coexisting beams. The baselinedesign calls for coating the chamber with TiZrV, a gettermaterial that possesses thevirtuesof effectivepumping af-ter activation at 200 C, low SEY, and good stability vis-à-vis exposure to air. The primary motivation for these elec-tron cloud studies is to determine the residual gas pressureand composition, of critical importance for the acceptabledetector background level. Also important is the contribu-tion of thesewarm sections to theelectron-cloud effectsonthe beams. As opposed to the arcs, where the basic cri-terion on the SEY is the maximum tolerable heat deposi-tion from the electron cloud, in the experimental regionsthe basic criterion on the SEY is the maximum tolerablegas pressure, particularly from electron-stimulated desorp-tion (ESD). Depending on the exact location, the chamberradius varies in these regions from 22 to 200 mm. Sincethe electron-cloud simulation tool used does not at presentallow for the modeling of two counter-circulating beams,the assumption was made that the ECEs could be brack-eted by studying two extreme cases with the conventional(single-beam) simulation, namely: (a) bunch spacing hasthe nominal value (sb = 7.48 m) but bunch intensity istwicethenominal value(2Nb = 2.1×1011), and (b) bunchspacing is sb/2 but bunch intensity isNb. In the real ma-chine, these two cases obtain at discrete points along thechamber whenever the distance from the IP is an integeror half-integer multiple of sb, respectively. Besides ESD,photon-stimulated desorption (PSD) wasalso taken into ac-count (ion-stimulated desorption wasconsidered and foundto be negligible). Assuming peak SEY values of 1.1 or 1.4and a calculated photon flux of 1016 γ/m/s, the simulationcode yields the electron flux and energy spectrum at thechamber walls for a given radius. These results, combinedwith measured valuesof thePSD and ESD for TiZrV, yieldthe local pressure of H2, CH4, CO and CO2. It was foundthat ESD is the main source of gas. In order to sharpen thequantitative predictive ability of the code, the simulationshave been repeated for the SPS and compared with pickupelectron signals and pressure rise measurements (in thiscasethemainsourceof electronsisresidual gasionization).For a 72-bunch train at 26 GeV and Nb = 8.3 × 108, themeasured pickup signal in a field-free section matches thesimulations for a pressure of 200 nT and a peak SEY=1.6.Similar tests have been carried out for other bunch-trainpatterns. Further benchmarkswill becarried out, includingtests in aspecial section of chamber coated with TiZrV.         Qualitative Analysis of Electron Cloud Effects in theNLC Damping Ring. The motivation of this work is totry to obtain analytic estimates of the electron-cloud den-sity and magnitude of the resultant wake in order to inter-pret numerical results from simulations and allow parame-ter scaling without additional lengthy calculations. In thisapproach the beam is assumed to be non-dynamical henceunperturbable by the cloud. The analysis is developed fora quasi steady state equilibrium, defined by the conditionκ¿ 1, whereκ is given byκ =Nbresbb2(2)HereNb and sb are the bunch population and spacing, re-spectively, re is the classical radius of the electron, andb is the vacuum chamber radius. The condition κ = 1defines the beam-induced multipacting resonance condi-tion [1], corresponding to theequality of thebunch spacing(in time units) and the traversal time of an electron acrossa chamber diameter under the impulse of a single bunchpassage. The limit κ = 0 at fixed Nb and b correspondseffectively to a coasting beam, hence only a static electroncloud can develop in this limit. The condition 0 < κ ¿ 1correspondsto aregimein which thebeam and theelectroncloud (or, at least, most of the electrons in the cloud) areweakly coupled hence an analytic approach may be fruit-ful. In the high-current limit of a bunched beam, κ À 1,theelectronscross thechamber so quickly under theactionof a single bunch that an electron cloud in the usual senseis not well defined.As a first approximation, the electron cloud distributionis computed in steady state for a coasting beam in a cylin-drical chamber of radius large compared with the trans-verse beam dimensions. The electrons move in the com-bined potential of the beam and the space charge of thecloud. The requirement of zero radial electric field at thewall yields an averageelectron-cloud densityn0 =Nbπb2sb, (3)corresponding to the average beam neutralization condi-tion. Thechargedistribution isgiven by aBoltzmann form,n(r) ∝ exp(−U(r)/T ) where U is the self-consistentbeam-cloud potential and T is a temperature. For abunched beam with κ ¿ 1, an electron takes, on aver-age κ−1 bunch passages to cross the chamber. Since thisis a large number, its motion can be taken to be sensi-bly random. Thermalization of the electrons takes placewithin some distance from the beam. Even if the lin-ear bounce frequency of an electron within a bunch isÀbunch frequency, such electrons can still be described bythe Boltzmann distribution due to randomness of the elec-tron motion. Assuming that an electron that hits the cham-ber wall is absorbed, equating the average energy gainfrom a bunch-electron kick with the average energy lostby an electron hitting the wall defines the cloud temper-ature T in steady state. This calculation also yields theenergy spectrum of the electrons hitting the wall. Photo-electronsand secondary electronsareattracted towards thebeam. These newly-generated electrons produce jets thatmay have higher density than the average n0. The calcu-lation shows that these jets significantly increase the clouddensity near the chamber center. Once saturation level isachieved, which takes a few bunch passages, the newly-generated photoelectrons and secondary electrons are re-pelled by the potential and are sent back to the chamberwall. This implies that the level of thedensity at saturationis fairly independent of the photoelectron and secondaryyield. Multipacting does not change the temperature muchbut rather affects the distribution of electrons only in thevicinity of the wall. This explains why the average densityof the cloud is close to that given by the beam neutralitycondition. The analysis also yields the long-range wakeand thecorresponding linear growth rateof coupled-bunchinstability.This qualitative analysis for κ ¿ 1 was applied to theNLC Main Damping Ring, for which κ = 0.28. Goodgeneral agreement is found with availablesimulations.Electron Cloud Updated Simulation Results for thePSR, and Recent Results for the SNS. The LBNLelectron-cloud code POSINST, which was initially devel-oped to study the ECE in the PEP-II positron beam start-ing in 1995, has been recently applied to the electron-cloud instability seen at the Proton Storage Ring (PSR)ring at LANL, and to the storage ring of the SpallationNeutron Source (SNS), presently under construction atORNL. The physical model embodied by this code is sim-ilar to that of the code ECLOUD, described above. How-ever, the secondary emission process is somewhat differ-ent. An improved, complete, model for this process, in-cluding detailed descriptionsof thethreemain componentsof the emission spectrum (true secondary, rediffused andbackscattered electrons) has been recently included in thecode. The code has been benchmarked against measure-ments at the PSR obtained by means of dedicated electronprobes which measure the flux, time structure, and energyspectrum of the electrons striking the chamber walls. ThePSR contains a single proton bunch of full length ∼ 60m and energy 1.735 GeV in a stainless steel chamber of 5cm radius and 90 m ring circumference. The simulationsshow very clear trailing-edge beam-induced multipacting(BIM), in good agreement with measurements. This effectwas clearly seen in a digital simulated movie of the elec-tron cloud build up and dissipation during two bunch pas-sages. Theelectrons that arepresent in thechamber duringthe beam gap typically have low energy; they are capturedadiabatically by the beam during the passage of its leadingedge, and released with equally low energy towardstheendof the trailing edge. Theseelectrons, therefore, do not con-tribute to trailing-edge BIM. However, the electrons thatare generated from stray protons hitting the chamber dur-ing the bunch passage, especially those produced near thepeak of the bunch current, are captured non-adiabatically     and are released at high energy soon after the passage ofthe peak of the bunch, and contribute strongly to trailing-edge BIM. This phenomenon leads to a strong sensitivityof the electron-wall current (and hence the electron distri-bution) to the longitudinal profile of the bunch. The time-energy joint electron spectrum is in good qualitativeagree-ment with measurements, although the quantitative agree-ment iswithin a factor ∼ 2, assuming apeak SEY valueof2. Preliminary simulations for the SNS show that an aver-age electron line density of ∼ 150 nC/m may be reachedin a field-free region, leading to a significant tune shift dueto beam neutralization. Due to an unexpectedly large elec-tron multiplication during the passage of the SNS beam,simulations have have so far used a low number of seedmacroparticles per bunch passage, leading to poor statis-tics for peak SEY values above 1.3. The code will soon beimproved to deal with this problem.3 ACKNOWLEDGMENTSI am grateful to G. Rumolo for his effective job as theScientific Secretary of Session III, and to F. Zimmermannfor organizing such an informativeworkshop.4 REFERENCES[1] O. Gröbner, “Bunch-Induced Multipactoring,” Proc. 10thIntl. Accel. Conf., Serpukhov, 1977, p. 277.5 DISCLAIMERThisdocument waspreparedasanaccount of work spon-sored by the United States Government. While this docu-ment isbelieved to contain correct information, neither theUnited StatesGovernment nor any agency thereof, nor TheRegents of the University of California, nor any of theiremployees, makes any warranty, express or implied, or as-sumes any legal responsibility for the accuracy, complete-ness, or usefulness of any information, apparatus, product,or processdisclosed, or representsthat itsusewould not in-fringeprivately owned rights. Referenceherein to any spe-cific commercial product, process, or service by its tradename, trademark, manufacturer, or otherwise, doesnot nec-essarily constitute or imply its endorsement, recommenda-tion, or favoring by the United States Government or anyagency thereof, or The Regents of the University of Cali-fornia. Theviewsand opinionsof authorsexpressed hereindo not necessarily stateor reflect thoseof theUnited StatesGovernment or any agency thereof, or The Regents of theUniversity of California.Ernest Orlando LawrenceBerkeley National Laboratoryis an equal opportunity employer.

This is a summary of the talks presented in Session III "Simulations  of Electron-Cloud Build Up" of the Mini-Workshop on Electron-Cloud Simulations  for Proton and Positron Beams ECLOUD-02, held at CERN, 15-18 April  2002

Furman, M.A.

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