Electron Cloud: Operational Limitations and Simulations

Electron Cloud: Operational Limitations and Simulations E. Benedetto, D. Schulte F. Zimmermann, CERN, Geneva, Switzerland; G. Rumolo, GSI Darmstadt, Germany

Abstract

(100 turns) growth time for the nominal LHC bunch intensity. We can translate these observations to the LHC, by applying simplified scaling laws. The growth time for the coupled bunch instability can be roughly approximated by [12] γ . (1) τ≈ 2πrp βcρel

The rise times of possible single-bunch and multi-bunch instabilities generated by an electron cloud in the LHC are estimated both by simulations and by extrapolation from SPS measurements. Limits on the allowable integral length with multipacting arise from the heat load (in the arcs), from long-term emittance growth, and from the resulting pressure rise and enhanced background in the experiments. Possible implications on the LHC commissioning strategy are outlined. The simulation codes have been benchmarked against the SPS observations. The remaining discrepancies, uncertainties, and missing input data are highlighted.

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Inserting an average electron density ρel ≈ 3 × 1011 m−3 , a beta function of βSPS ≈ 40 m or βLHC ≈ 100 m, and and a beam momentum of pSPS ≈ 26 GeV/c or pLHC ≈ 450 GeV/c, the 1 ms growth times at injection into SPS becomes 5 ms (50 turns) at injection into the LHC. This growth time is comparable to feedback damping time. If multipactoring occurs only over a fraction of the ring, the growth time is correspondingly longer. A possible enhancing effect from the regular impedance is not considered in this estimate. For the single-bunch instability we assume that the electron cloud reaches saturation everywhere around the ring. Then the threshold estimate for the TMCI-like singlebunch instability is [3]

INTRODUCTION

In this report we first dicuss single- and multi-bunch instability rise times, as well as single-bunch instability thresholds, which permit us to estimate the maximum allowable integral length with multipacting. We next report simulations using the HEADTAIL code [1] which indicate a significant long-term emittance growth. We then examine whether the vacuum pressure in the experimental areas might impose additional constraints and show this not to be the case, thanks to the pumping effects of beam and electrons. After describing recent changes and modifications to the ECLOUD code [2], we present updated heat load estimates for the LHC arcs. Finally, we compare the simulated spatial electron distribution in a dipole field, the electron energy spectrum, the total flux and the heat load with measurements at the SPS. The physics of the single-bunch instability and related simulations were previously described in Refs. [3, 4, 5]. Also the model for the electron-cloud build-up simulations was already presented in Refs. [7, 8, 9]. Subsequent changes to the ECLOUD code are mentioned below.

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Taking the betatron tunes QSPS ≈ 0.003 or QLHC ≈ 0.006, the circumferences CSPS ≈ 6.9 km or CLHC ≈ 27 km, the chamber half apertures (hx hy )SPS ≈ 1.3 × 10−3 m2 or (hx hy )LHC ≈ 4 × 10−4 m2 , thebetafunctions βSPS ≈ 40 m or βLHC ≈ 100 m, and momenta pSPS ≈ 26 GeV/c or pLHC ≈ 450 GeV/c, we find a threshold bunch population of Nthr,SPS ≈ 4 × 109 for the SPS, and Nthr,LHC ≈ 1 × 1011 for the LHC. Hence, the LHC beam is expected to be 25 times more stable vertically than the SPS beam, for the same electron line density. Therefore, there should be no problem, even if several kilometres of the LHC suffer from multipacting. Note that in this section, the term ‘multipacting’ is always meant to imply that the electron cloud density approaches the neutralization level of ρe ≈ Nb /(πb2 Lsep ), where Nb denotes the bunch population, b the beam pipe radius and Lsep the bunch spacing. In the LHC arcs this neutralization density can rise up to about 1013 m−3 .

2 INSTABILITIES AND ACCEPTABLE ELECTRON-CLOUD DENSITY 2.1

γQs hx hy 2Lsep . βC rp

Scaling Instability Rise Times and Thresholds

The SPS instability observations were analysed and reported by G. Arduini [10] and K. Cornelis [11]. Their main features are that in the horizontal plane a coupled-bunch instability is observed with about 1 ms (50 turns) growth time, that is independent of Nb , whereas in the vertical plane a single-bunch instability occurs, with about ∼2 ms

2.2

Emittance Growth

Simulations in 2002 have revealed a new type of singlebunch instability, which differs from the TMCI-type singlebunch instability considered above. This novel effect mani1

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fests itself in a strong, mostly incoherent emittance growth, which starts at the tail of the bunch, as is illustrated in Fig. 1. Similar simulation results were reported earlier by V. Lotov and G. Stupakov [13] and by Y. Cai [14]. The former two employed a simplified plasma approach enforcing perfect cylindrical symmetry without any azimuthal dependence, which demonstrates that this emittance growth cannot be explained (solely) by dipole wake fields, but must be due to a ‘monopole’ effect. We suspect that the increase of the electron density at the center of the beam during the passage of a bunch induces a large tune shift as well as strong nonlinear forces, which are responsible for the blow up. The effect may then be similar to that of space charge.

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Figure 2: Simulated evolution of LHC emittance vs. time in seconds for a single bunch at injection; the different curves correspond to different electron densities as indicated.

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Figure 1: The product of local transverse beam size and local line density, λ(s)σx (s), as a function of the longitudinal position s after 4 turns, suggesting the existence of a ‘monopole’ instability; this simulation considered a round beam and SPS like parameters.

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Figures 2 and 3 show recent simulations using the HEADTAIL code for the LHC. Only the effect of the electron cloud was included. Space charge and conventional impedances were not taken into account. Other simulation parameters are listed in Table 1. The two pictures refer to injection and top energy, respectively. The various curves refer to different average electron-cloud densities. The growth rates are extremely fast for most of the cases. The saturation after a ten- or twenty-fold increase in emittance is largely due to the finite size of the grid used in the simulation, which extends over ±10σ. The HEADTAIL simulation results for the LHC are summarized in Fig. 4, where the initial emittance growth rates inferred from the simulation are displayed as a function of electron density. There is a steep increase in the growth rate with increasing density. For a constant average density of electrons, the growth rate decreases as we pass from the SPS (one point shown), through the LHC injection towards top energy. Nevertheless, even the smallest growth rates in Fig. 4 represent a significant emittance dilution over the time scale of the LHC injection plateau (20 minutes) or in collision (24 hours). It it peculiar that there is no clear threshold, as one would perhaps expect for the regular space-charge force.

Figure 3: Simulated evolution of LHC emittance vs. time in seconds for a single bunch at injection in collision; the different curves correspond to different electron densities as indicated. Though large, most of the growth rates in Fig. 4 would presumably go undetected in a positron storage ring, where the blow up can be suppressed by radiation damping. There is, however, some circumstantial evidence from PEP-II that the onset of emittance growth lies below the mode coupling threshold, which could be explained by the monopole effect. From the SPS no observations of emittance growth exist over a seconds time scale. Therefore, at present it is difficult to draw any definite conclusion as to whether the simulated emittance growth rates are realistic or not. There are good reasons to believe that the actual growth rates will be smaller than simulated. In the simulations of Figs. 2, 3 and 4, the electrons and the beam have interacted at a single ‘interaction-point’ on each turn around the ring. Using this simplified model the result is assumed to be the same, for example, as if a ten times denser cloud were concentrated over a tenth of the ring circumference. This is not necessarily the case. But, most importantly, the single in2

Table 1: Parameters for SPS and LHC emittance-growth simulations using the HEADTAIL code parameter symbol SPS (inj.) LHC (inj.) LHC (coll.) cloud density ρe variable bunch population Nb 1.1 × 1011 beta function βx,y 40 m 100 m 100 m rms bunch length σz 0.30 m 0.13 m 0.077 m rms beam size σx,y 3.0, 2.3 mm 0.884 mm 0.224 mm rms momentum spread δrms 0.002 4.68 × 10−4 1.1 × 10−4 synchrotron tune Qs 0.004 0.006 0.00212 momentum compaction αc 1.856 × 10−3 3.47 × 10−4 3.47 × 10−4 circumference C 6.9 km 26.7 km 26.7 km tunes Qx,y 26.62, 26.58 64.28, 59.31 64.31, 59.32 chromaticity Q0x,y 2, 2 2, 2 2, 2 relativistic factor γ 27.73 479.6 7461 cavity voltage Vrf 1 MV 8 MV 16 MV harmonic number h 4620 35640 35640 teraction point tends to overestimate the emittance growth. This question is currently under investigation. The HEADTAIL code can handle an arbitrary Number of interaction points. We are in the Process of computing the emittance growth as a function of this parameter. In addition, we will increase the number of macroparticles representing the beam or the electrons, in order to rule out numerical noise as the source of emittance growth.

growth is not fully understood (it appears to be an incoherent effect, similar to space charge). A similar blow up has also been seen in other simulations. Studies are ongoing to clarify the origin of this effect and to obtain more reliable numerical predictions, in collaboration with K. Ohmi (KEK) and T. Katsouleas (USC). Running a detailed Simulation using the plasma-modelling code QUICKPIC we can avoid introducing an artificial small number of beamelectron interaction, but describe the real continuous situation. It would be extremely valuable to measure the longterm emittance growth (over minutes or hours) in the SPS or the PS when an electron cloud is present. The electron clou dmust be sustained over the time period of the experiment which could prove difficult, due to rf noise etc.

2.4

Beam and Electron Pumping

While in the SPS the onset of the electron cloud is accompanied by a huge pressure increase, the situation may be different in the LHC, where almost all warm vacuum chambers are coated by TiZrV getter. Since the time of the ISR it is known that ionization by the beam contributes to the pumping [15]. This effect is largest for a getter coated surface, which has a sticking coefficient of 1 for ionized molecules or atoms. Then the linear pumping speed by the beam is

Figure 4: Simulated LHC emittance growth rates in %/s vs. average cloud density, for a single beam-electron interaction point.

Slin,beam = σb Ib /e; .

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The beam pumping amounts to Slin,beam ≈ 0.2 ls−1 A−1 for H2 and 1.3 ls−1 A−1 for methane [16]. Also, and more importantly, the electrons of the electron cloud also ionize the residual gas atoms, and so provide an additional pumping speed

Acceptable Length of Multipacting Section

Concluding the discussions of Sections 2.1 and 2.2, the SPS observations and simple instability scaling laws suggest that the LHC will not observe any instability even if several kilometres of the LHC undergo multipacting. However, even for low average electron densities the simulations show a strong emittance growth, which strongly depends on the electron density, but also on the number of beam-electron interaction points, and on the number of no. macro-electrons. The mechanism of this emittance

Slin,e− ≈ σe Ib /e ,

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since at saturation (near the neutralization level) λe ≈ λb . The electron ionization cross sections at Energies between 10 and 100 eV are ∼ 100 times larger than the ion3

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ization cross section of the ultra-relativistic protons (100– 400 Mbarn instead of 0.4–2 Mbarn). Thus, the estimated electron pumping Slin,beam ≈ 20 ls−1 A−1 for H2 and 130 ls−1 A−1 for methane. This is significant. The implications for the Vacuum pressure are presently under investigation by A. Rossi. The importance of the beam-pumping effect for the LHC straight sections was first Pointed out to us by C. Benvenuti.

2.5

LHC Electron-Cloud Build Up

The ECLOUD simulation parameters for the LHC are summarized in Table 2. In the LHC simulations, we interpolate critical input parameters, like the photon reflectivity R, the energy of the maximum secondary emission yield max, and the primary rate of photo-electrons dλe /ds, linearly as a function of the maximum secondary emission yield, δmax , between their canonical values prior and after surface conditioning. This interpolation is displayed in Fig. 5.

Vacuum Pressure in LSS and Background

Calculations in 2002 [17] indicated about 10 nTorr pressure in the long straight sections of LHC, if an electron cloud builds up, while the LHC experiments now desire a pressure of 1 nTorr or below. Relief comes from the fact that most of the warm straight sections will be coated by TiZrV getter and the 2002 SPS experiments showed a complete absence of multipacting in regions with NEG coating. In addition, the LHC vacuum calculations are being updated so as to include correct outgassing rates of NEG and, more importantly, the pumping by beam and by the electrons, discussed in the previous section. Since it now looks probable that the electron cloud will even improve the vacuum pressure, there no limit on the acceptable multipacting from this point of view.

Table 2: Parameters of electron-cloud simulations used to model the LHC arcs prior to and after surface conditioning. parameter symbol initial final bunch intensity Nb 1010 –1.8 × 1011 rms transverse size σx,y 0.3 mm rms bunch length σz 77 mm chamber half apertures hx,y 22, 18 mm max. sec. em. yield δmax 1.9 1.1 energy at max. yield max 240 170 photon reflectivity R 10% 5% primary el. rate dλe /ds 1230 615 [10−6 m−1 ]

3 UPDATED ELECTRON-CLOUD SIMULATIONS FOR THE LHC 3.1

Recent Changes to ECLOUD code

At the beginning of 2003, we have performed a number of changes to the ECLOUD code. The most important ones are: • we found and corrected factor 2 error in beam field for elliptical chamber with image charges; • we removed the cos θ dependence of the yield component describing the elastic reflection; • we modified and speeded up numerical solutions for dipole and quadrupole fields;

Figure 5: Linear interpolation of photon reflectivity R, primary photo-electron rate dλe /ds, and energy at max. sec. em. yield max as a function of δmax , for LHC heat-load simulations.

• we removed several inconsistencies near beam-pipe wall in space-charge calculations, making the calculation now perfectly symmetric; • for the moment we approximate LHC arc chamber by a pure ellipse, since using the inscribed ellipse only for image-force calculations gave rise to inconsistencies in the vicinity of the wall;

The build-of of an electron cloud along an LHC bunch train (batch) is simulated by the ECLOUD code. Results for different bunch intensities both in dipoles and field-free regions are displayed in Figs. 6 and 7. At first the electron density increases as a function of bunch intensity; it then reaches a maximum for bunch intensities between about 8 × 1010 and 1011 , and for higher bunch intensities it decreases again. This non-monotonic dependence might be related to the ‘lock-out’ regime postulated by S. Heifets [18].

• we dynamically increase the maximum and miminum allowed macro-electron charges to avoid crashes by overflow. The last change should also enable simulations for larger values of δmax (say above 2.0). 4

Figure 6: Electron line density vs. time during the passage of a batch in an LHC dipole, for δmax = 1.3, max = 187.5 eV and different bunch intensities.

Figure 8: Average LHC arc heat load simulated in 2002 and cooling capacity as a function of bunch population Nb .

Figure 7: Electron line density vs. time during the passage of a batch in an LHC field-free arc region, for δmax = 1.3, max = 187.5 eV and different bunch intensities.

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Figure 9: Average LHC arc heat load simulated in 2003 and cooling capacity as a function of bunch population Nb .

Heat Load R. Cimino [19] with the parametrization used at the moment, and an alternative model containing an exponentially decaying component centred at 0 eV with a width of 10 eV. In this second model the probability of elastic reflection always approaches 1 at zero energies, whereas in our present parametrization this probabililty varies roughly between 0.2 and 0.6 depending on the value of δmax . The head loads for these two alternative parametrization are different, and the present description is the more optimistic one.

A firm commissioning constraint is the heat load deposited on the cold bore of the arc chamber. Figures 8 and 9 show average LHC arc heat loads simulated in 2002 with those obtained by the upgraded ECLOUD code, respectively, as a function of bunch intensity for two different values of δmax . Also indicated is the available cooling capacity, which decreases for higher intensities due to the enhanced heating by synchrotron radiation and image currents. The threshold at which the simulated heat load surpasses the cooling capacity has increased by about 25% for δmax = 1.1 compared with the 2002 simulation. For a well-conditioned surface with δmax ≈ 1.1 we can now reach the ultimate LHC intensity of 1.7 × 1011 protons per bunch. On the other hand, the intensity threshold for δmax = 1.3 has decreased by about 10-20%.

3.4

4 COMPARISON SIMULATIONS - SPS OBSERVATIONS It is of fundamental importance to cross-check and calibrate the electron-cloud observations against the SPS experiments. A good agreement will lend more confidence in our ability to extrapolate to LHC conditions. We can compare the following points:

Modelling Low-Energy Elastic Reflection

The modeling of the elastic electron reflection between 0 and 10 eV is still subject to considerable uncertainties. Figure 10 compares recent measurements by I. Collins and

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Figure 11: Simulated electron flux vs. horizontal position x for a bunch intensity of Nb = 1.2 × 1012 , two different magnetic field strengths and two different sources of primary electrons, i.e., on the wall (as for photo-electrons) or inside the beam (modelling ionization electrons).

and In addition, we assume that the rms energy spread and rms bunch length are constant, equal to δrms ≈ 0.0013 and σz ≈ 0.315 m, respectively. Finally, at the strip detector the optical functions are βx ≈ 91 m, βy ≈ 24 m, and |Dx | ≈ 0.79 m. Combining these data, we compute the beam sizes as functions of intensity, which are used in the ECLOUD simulations. They are displayed in Fig. 4. The strip detector is installed in an MBA chamber. This chamber is rectangular, with full widths equal to 152 mm and 35.3 mm. For the simulation we adopt the electron emission parameters inferred from the in-situ measurement after the 2002 SPS scrubbing run, namely δmax = 1.6 and max = 240 eV. Finally, we assume a residual carbonmonoxide gas pressure of 50 nTorr and an ionization cross section of 2 Mbarn, which translates into a primary electron generation rate of dλe /ds ≈ 2.5 × 10−7 m−1 per proton.

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the stripes and the associated flux. Figure 12 unveils the sensitivity to rather small changes in the vertical magnetic field, and the effect of a change in the maximum secondary emission yield. The latter does not affect the position of the stripes, but alters the overall electron flux to the wall. Figure 13 compares stripe positions measured in 2001 and 2002 as a function of bunch intensity with those computed by 2002 and 2003 simulations. Evidently the results from the upgraded ECLOUD code in 2003 are much closer to the measurement. As also shown, increasing the field from the nominal value of 100 G to 150 G would give nearly perfect agreement with the measured stripe position. However, we should point out that the field of 100 G is believed to be the correct value, and that there are several other parameters which we could adjust instead of the magnetic field to obtain a similarly good agreement, e.g., the incident energy at the maximum emission yield, max , the bunch intensity, the transverse beam size or the bunch length.

Position of Stripes

Figure 11 illustrates that the primary-electron source distribution — and, if the primary electrons are launched inside the beam volume, also the precise value of the magnetic field —, are important for determining the position of 6

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Figure 14: Simulated electron energy distribution for a dipole field. Figure 12: Simulated electron flux vs. horizontal position x for a bunch intensity of Nb = 1.2 × 1012 , two different magnetic fields and two different yields δmax . 25

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Figure 13: Horizontal position of the electron stripes measured in 2001 and 2002 (M. Jimenez), compared with simulations in 2002 and 2003 vs. bunch intensity. The effects of altering the magnetic field and using different maximum emission yields are also shown.

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Electron Flux

Figures 18 and 19 compare the measured and simulated fluxes for an MBA chamber with and without magnetic field, respectively. Only electrons of energy larger than 20 eV are included. The measured flux stays well belowthe simulation by factors of about 6 and 35 for the dipole and field-free region, respectively. Some of the difference may be attributed to energy and momentum acceptance of the stripe detector, whose minimum value might have been as high as 30 eV and which in addition depends on the angle of incidence. In this context we note that in a 100-G field the cyclotron radius is ρ ≈ 750 µm at 5 eV and 3.4 mm at 100 eV. These values are comprable to the chamber hole radius of1 mm. Another reason could be the partial suppression of the cloud build up by the many holes in the beam pipe at this detector. While the above effects may explain the factor of 6 discrepancy for the dipole, it appears unlikely that they can

Energy distribution

Figures 14 and 15 show the simulated enery spectrum of impinging electrons and the SPS measurements, respectively. In both cases, electrons with energy below 300 eV Are not displayed, since these annot be measured with the present apparatus. We should point out that in the simulation the overwhelming majority of electrons belongs to this low-energy range. The simulation exactly reproduces the peak at 200 eV for the nominal magnetic field of 100 G. Therefore, we should try to adjust one or several of the other candidate parameters to perfectly match the stripe location and the energy spectrum. The same measurements and simulations were conducted without the dipole field. The results are displayed 7

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Figure 18: Measured and simulated electron flux to wall during the passage of 1–3,4 batches in a 100-G dipole field The measured data were provided by M. Jimenez. The simulation assumed: δmax = 1.4, max = 240 eV, Nb = 1011 , σz = 0.315 m, σx = 3.29 mm, σx = 1.57 mm, 100 or 0 G field, MBA chamber; only electrons with energy larger than 20 are counted.

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account for the factor 35 difference without magnetic field. Perhaps some physics input is missing to correctly describe the situation without the controlled external field.

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Figure 19: Measured and simulated electron flux to wall during the passage of 1–3,4 batches in a field-free region. The measured data were provided by M. Jimenez. Simulation assumed: δmax = 1.4, max = 240 eV, Nb = 1011 , σz = 0.315 m, σx = 3.29 mm, σx = 1.57 mm, 100 or 0 G field, MBA chamber; only electrons with energy larger than 20 are counted.

Table 3 compares the heat loads measured in the warm calorimeters 1 and 2 with simulation results obtained in the year 2002. The different cases correspond to different numbers of consecutive 72-bunch batches, two different calorimeter chamber geometries, and two magnetic field configurations (100-G dipole field, and field-free region). Inmost cases, the simulations and measurements look consistent, within the large scatter of the experimental data points. We can also compare simulated and measured heat loads for a cold environment, namely the cold prototype vacuum chamber COLDEX. This comparison is shown in Figs. 20 and 21. Within the large fluctuation of the experiment, measurement and simulations appear consistent.

bility, with regard to coupled or single-bunch instabilities. Also the pressure in the experimental regions does not impose any limitation on the multipacting, as the pumping (ionization) by the electron cloud in conjunction with the getter coating of the chamber wall will decrease the vacuum pressure rather than degrade it, when electrons are present. However, one aspect of the simulation is not yet understood and, if confirmed, could lead to a much tighter tolerance on the acceptable average electron density. This is the rapid emittance growth seen in the HEADTAIL simulation even for moderate electron densities. So far there

5 CONCLUSIONS In the LHC several kilometres of beam pipe with electron multipacting are unlikely to compromise the beam sta8

Table 3: Comparison of measured and simulated heat loads for the warm calorimeters WAMPAC1 and WAMPAC2 in the SPS (the respective vertical chamber half apertures hy are indicated in the table); the different rows show results for different numbers of LHC batches; all simulations were performed in 2002, considered a bunch population Nb = 1011 , a gap of 8 missing bunches between trains, and assumed δmax = 1.4 and max = 240 eV. detector WAMPAC1 (hy = 70 mm) no field WAMPAC2 (hy = 18 mm) no field WAMPAC2 (hy = 18 mm) with field

trains 1 2 3 4 1 2 3 1 2 3 4

heat (W/m) sim. meas. 0.00026 0.028 0.030 0.278 0.110 0.501 1.363 0.180 >1.94 0.0012 0.394 0.160–0.450 1.339 0.150

Figure 21: Simulated heat load in the cold vacuum chamber of the COLDEX experiment as a function of bunch intensity for 1, 2 and 3 batches. The simulation parameters were σx = 3.5 mm, σy = 1.6 mm, σz = 0.3 m, δmax = 1.4, max = 240 eV, dλe /ds = 2.5 × 10−7 m−1 per proton, hx = 42 mm, hy = 33 mm, Lsep = 7.48 m; elastic electron reflection was included. to the code, the computed heat loads for the LHC arcs agree within ±20 % with the earlier simulations. The exact parametrization of elastic reflection between 0 and 10 eV is still uncertain. If it needs to be modified, the predicted heat load will be altered, perhaps substantially. A detailed comparison of simulations and SPS observations demonstrates that the simulated horizontal position of multipacting electrons now is in good agreement with the measurement. The position can be fine-tuned at the 10% level by adjusting one of 4 or 5 sensitive parameters. The simulated and measured energy spectra of impinging electrons resemble each other, for both dipoles and field-free regions. Below 30 eV the electrons are not measured by the experiment. In the simulation an overwhelming number of electrons is found at these low energies. The simulated electron flux computed from electrons above 20 eV agrees within a factor of 5 or 6 with the measured flux, during the passage of up to 4 batches. The difference may partly be due to the restricted acceptance of the strip detector. For a field-free region, the difference is yet another factor of 5 larger, and it it not clear if this can still be explained by the detector acceptance. Perhaps more likely, we are facing a qualitative discrepancy between measurements and simulations for a field-free region, which might indicate that some physics is missing in the simulation. The measured and simulated heat loads for the SPS calorimeters are roughly consistent within the large fluctuation of the measurement. In the near-term future we will continue to improve the ECLOUD and HEADTAIL codes. In particular, we plan to modify the calculation of the electron impact angles in ECLOUD and to determine the image charge for the exact geometry of the LHC arc chamber, instead of for an inscribed ellipse. Further we will attempt to speed up

Figure 20: Measured heat load in the cold vacuum chamber of the COLDEX experiment as a function of bunch intensity for 1, 2 and 3 batches. The simulation parameters were σx = 3.5 mm, σy = 1.6 mm, σz = 0.3 m, δmax = 1.4, max = 240 eV, dλe /ds = 2.5 × 10−7 m−1 per proton, hx = 42 mm, hy = 33 mm, Lsep = 7.48 m; elastic electron reflection was included. is only little experimental evidence to support such effect, but on the other hand we also have no demonstration that it does not exist. Experimental studies of the emittance growth are highly encouraged, though storing an LHC-like proton beam for several seconds in the presence of an electron cloud may prove difficult to realize prior to LHC commissioning. The LHC arc heat load predictions are presently being updated by simulations with the upgraded ECLOUD code. Despite of substantial corrections and modifications 9

the computation for quadrupole fields by piece-wise integration in a locally constant field. For the HEADTAIL code, we explore the sensitivity of The emittance growth to a number of simulation parameters, so as to quantify artificial noise contributions due to the finite number of macroparticles and interaction point. We are also incorporating quadrupole wake fields in order to model the effect of collimator wake fields with and without an electron cloud. Finally, we plan to cross-calibrate the HEADTAIL simulations with the continuous plasma code QUICKPIC.

[12] F. Zimmermann and G. Rumolo, “Two-Stream Problems in Accelerators,” presented at APAC’01, Beijing, September 17–21, CERN SL-2001-057 (AP). [13] V. Lotov and G. Stupakov, “Single-Bunch Instability of Positron Beams in Electron Cloud,” EPAC 2002, Paris, La Villette (2002). [14] Y. Cai, “Emittance Growth Due to Electron Cloud in Positron Ring,” Proc. ECLOUD’02, CERN, Geneva, April 15-18, CERN-2002-001 (2002). [15] C. Benvenuti, M. Hauer, “ISR Performance Report,” ISRVA/CB/sm (1976).

6 ACKNOWLEDGEMENTS

[16] O. Gr¨obner, “Vacuum Stability with Beam Pumping,” CERN Vac.T.N. 98-23 (1998).

It is a pleasure to thank Gianluigi Arduini, Giulia Bellodi, Cristoforo Benvenuti, Paolo Chiggiato, Roberto Cimino, Ian Collins, Karel Cornelis, Noel Hilleret, Miguel Jimenez, Adriana Rossi, and Francesco Ruggiero for stimulating discussions, useful informations, and for sharing beam observations and laboratory data.

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[17] A. Rossi, G. Rumolo, F. Zimmermann, “A Simulation Study of the Electron Cloud in the Experimental Regions of the LHC,” ECLOUD’02 Workshop, CERN, April 15–18, 2002, published in CERN-2002-001 (2002). [18] S. Heifets, “Qualitative Analysis of the Electron Cloud Effects in the NLC Damping Ring,” Proc. ECLOUD’02, CERN, Geneva, April 15-18, CERN-2002-001 (2002).

REFERENCES

[19] I. Collins and R. Cimino, private communication (2003).

[1] G. Rumolo and F. Zimmermann, “Practical User Guide for HEADTAIL,” SL-Note-2002-036 (2002).

[20] N. Hilleret, private communication (2003).

[2] G. Rumolo and F. Zimmermann, “Practical User Guide for ECloud,” SL-Note-2002-016 (AP) (2002). [3] K. Ohmi and F. Zimmermann, “Head-Tail Instability caused by Electron Cloud in Positron Storage Rings”, Phys. Rev. Letters 85, p. 3821, also KEK preprint, and CERN-SL-2000-015 AP (2000). [4] K. Ohmi, F. Zimmermann, E. Perevedentsev, “Wake Field and Fast Head-Tail Instability caused by an Electron Cloud,” Physical Review E 65, 016502 (2002). [5] G. Rumolo and F. Zimmermann, “Theory and Simulation of Electron-Cloud Instabilities,” Proceedings of Chamonix XI, CERN-SL-2001-03 (DI) (2001). [6] G. Rumolo, F. Zimmermann, “Electron-Cloud Simulations: Beam Instabilities and Wake Fields,” ECLOUD’02 Workshop, CERN, April 15–18, 2002, published in CERN-2002001 (2002). [7] F. Zimmermann, “Electron Cloud Simulations for SPS and LHC”, Proceedings of Chamonix X, CERN-SL-2000-07 (DI) (2000). [8] F. Zimmermann, “Electron Cloud Simulations: An Update”, Proceedings of Chamonix XI, CERN-SL-2001-03 (DI) (2001). [9] F. Ruggiero, G. Rumolo, F. Zimmermann, “Simulation of the Electron-Cloud Build Up and Its Consequences on Heat Load, Beam Stability and Diagnostics,” Proc. ICAP 2000, Darmstadt, and CERN-SL-2000-073 AP (2000). Physical Review Special Topics – Accelerators and Beams 2, 012801 (2001), Erratum-ibid. 029901 (2001) [10] G. Arduini, “Electron Cloud and Ion Effects,” EPAC 2002, Paris, La Villette (2002). [11] K. Cornelis, “The Electron-Cloud Instability in the SPS,” Proc. ECLOUD’02, CERN, Geneva, April 15-18, CERN2002-001 (2002).

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