Benchmarking electron-cloud simulations and pressure measurements at the LHC
aa r X i v : . [ phy s i c s . acc - ph ] J un BENCHMARKING ELECTRON-CLOUD SIMULATIONS AND PRESSUREMEASUREMENTS AT THE LHC
O. Dom´ınguez ∗ and F. Zimmermann, CERN, Geneva, Switzerland Abstract
During the beam commissioning of the Large HadronCollider (LHC) [1, 2] with 150, 75, 50 and 25-ns bunchspacing, important electron-cloud effects, like pressurerise, cryogenic heat load, beam instabilities or emittancegrowth, were observed. A method has been developed toinfer different key beam-pipe surface parameters by bench-marking simulations and pressure rise observed in the ma-chine. This method allows us to monitor the scrubbing pro-cess (i.e. the reduction of the secondary emission yield as afunction of time) in the regions where the vacuum-pressuregauges are located, in order to decide on the most appro-priate strategies for machine operation. In this paper wepresent the methodology and first results from applying thistechnique to the LHC.
INTRODUCTION
Since almost 15 years photoemission and secondaryemission had been predicted to build up an electron cloudinside the LHC beam pipe [3], similar to the photo-electroninstability in positron storage rings [4, 5, 6]. The possibilityof “beam-induced multipacting” at the LHC had been sug-gested even earlier [7] extrapolating from observations withbunched beams at the ISR in the 1970s [8]. The electroncloud, at sufficiently high density, can cause both singleand coupled-bunch instabilities of the proton beam [3, 9],give rise to incoherent beam losses or emittance growth[10, 11], heat the vacuum chamber (and subsequently pro-voke a quench in superconducting magnets), or lead to avacuum pressure increase by several orders of magnitudedue to electron stimulated desorption [12]. All these ef-fects eventually lead to luminosity limitations. Specifically,electron-cloud induced pressure rises have been one of themain performance limitations for some accelerators [11].From 1999 onward electron-cloud effects have been seenwith LHC-type beams first in the SPS, then in the PS, andfinally, since 2010, as expected, in the LHC itself. Duringthe early LHC beam commissioning with 150, 75 and 50-ns bunch spacing important electron-cloud effects, such aspressure rise, cryogenic heat load, beam instabilities, beamloss and emittance growth, were observed [13, 14, 15].Several exploratory studies at the design bunch spacing of25 ns were performed during 2011 [16].The LHC mitigation strategy against electron cloud in-cludes a sawtooth pattern on the horizontally outer sideof the so-called beam screen inside the cold arcs, a shieldmounted on top of the beam-screen pumping slots blocking ∗ Email: [email protected]. Also at EPFL, LPAP, CH-1015Lausanne, Switzerland the direct path of electrons onto the cold bore of the mag-nets, NEG coating for all the warm sections of the machine,installation of solenoid windings in field-free portions ofthe interaction region, and, last not least, beam scrubbing,i.e. the reduction of the Secondary Emission Yield (SEY)with increasing electron dose hitting the surface, i.e. as aresult of the electron cloud itself. Beam scrubbing repre-sents the ultimate mitigation of electron-cloud effects ofthe LHC, and it is considered necessary to achieve nominalLHC performance [17].At injection energy (450 GeV), the pressure inside thevacuum beam pipe affects the speed of the electron-cloudbuild up, since the initial electrons are produced by gas ion-ization. However, if there is noticeable multipacting therate of primary electrons does not significantly influencethe final value of the saturated electron density, which isthen determined by secondary emission (multipacting) andby the space-charge field of the electron cloud itself. Insuch case larger vacuum pressures just make the electrondensity reach its equilibrium value faster. This is due to thefact that the energy spectrum of electrons hitting the wall isinsensitive to the pressure [19].Nevertheless, in order to infer the best estimates of thebeam-pipe characteristics, the steady-state vacuum pres-sure of the machine for each stage of observation has tobe introduced as a simulation input parameter, in order tocorrectly account for the multiturn nature of the pressureevolution in a circular accelerator like the LHC. This is dueto the fact that the time constant of the vacuum evolution ismuch longer than the revolution period, while the electron-cloud build-up simulations typically model only a fractionof a turn. According to the vacuum-gauge measurements, asteady-state pressure is normally established a few minutesafter injecting the last bunch train for a given configuration.Since dedicated in-situ measurements of the LHCelectron-cloud density and the LHC vacuum-chamber sur-face properties are not available we are developing amethod to determine the actual surface properties of thevacuum chamber related to secondary emission and to theelectron-cloud build up ( δ max, ε max and R [18]; see Fig. 1for a graphical definition of these three quantities), andtheir evolution in time, based on benchmarking computersimulations of the electron flux on the chamber surfaceusing the ECLOUD code against pressure measurementsfor different beam characteristics. This new method al-lows monitoring the effectiveness of LHC “scrubbing runs”and provides snapshots of the surface conditions around theLHC ring. S e c onda r y e l e c t r on y i e l d , δ Electron energy, E (eV) δ max ε maxR Figure 1: Secondary emission yield for perpendicular inci-dence as a function of primary electron energy, defining theparameters δ max, ε max and R . METHODOLOGY
The pressure increase due to an electron cloud can berelated with the electrons hitting the chamber wall as ∆ P = kT R η e ( E ) φ e ( E ) dES eff , (1)where k denotes Boltzmann’s constant, T the temperature, S eff the pumping speed, η e the electronic desorption co-efficient and φ e the flux of electrons hitting the chamberwall. The quantities η e and S eff cannot be introduced inthe present electron cloud simulation codes, but assumingthat the pressure increase is proportional to the electron fluxhitting the chamber wall, pressure measurements for dif-ferent bunch train configurations (e.g. with changing spac-ing between trains or with a varying number of trains in-jected into the machine) can be benchmarked against simu-lations by comparing ratios of observed pressure increasesand of simulated electron fluxes at the wall, respectively.The idea of the benchmarking using ratios goes back to anearlier study for the SPS (serving as LHC injector) wherethe electron-cloud flux could be measured directly [20]. Inthe LHC case, no electron-cloud monitor is available, butinstead the measured increase in the vacuum pressure istaken to be a reliable indicator proportional to the electronflux on the wall.We face a four-parameter problem. The steps followedin the benchmarking are the following:(1) We fix two of the parameters, namely the pressure(using the measured value) and ε max (set to 230 eV, whichseems to be a good first estimate according to past surfacemeasurements and some previous simulation benchmark-ing ). Several studies (e.g. [21]) reveal an evolution of the value of ε maxwith the scrubbing process. This evolution depends on the scrubbing tech-nique (either using an electron gun or a real beam) and several parameterssuch as the roughness of the surface, the previous surface treatment, theelectrons energy, etc. Simulations depend indeed on this parameter. Fur-ther investigation is currently ongoing to infer its evolution in the LHC. (2) We simulate the electron cloud build up for differentbunch configurations using the ECLOUD code, scanningthe other two parameters, δ max and R , in steps of 0.1 and0.05 respectively. Smaller steps introduce statistical noisewhich needs to be controlled by smoothing techniques.(3) For each bunch configuration we plot the simulatedelectron flux φ i above a 2D grid spanned by δ max and R .(4) We fit the flux simulated on the grid to a third orderpolynomial and then form the ratio of simulated fluxes (thatis, dividing the polynomials) for two different bunch con-figurations [the fluxes and not their ratio are fitted in orderto suppress the effect of statistical fluctuations].(5) Comparing the latter ratio with the experimental ratioof measured pressure increases yields a curve in the δ max- R plane (see Fig. 2). Different configurations yield differentcurves in that plane.(6) If the measurements contain sufficient informationand the simulation model is reasonably accurate we expectto obtain a unique intersection between lines correspondingto different bunch configurations. This crossing point thendefines the solution for δ max and R . φ b / φ a δ max R φ b / φ a Figure 2: Example of a 3D surface of simulated fluxesfor the case φ b /φ a (red) cut by a plane surface (blue) atthe value equal to the ratio of the corresponding measuredpressures ( P b /P a = 161 . ). The bottom plane shows thecontour of the intersection between both surfaces (green).We apply this methodology for certain LHC regions inwhich pressure gauges and vacuum pumps are located.Normally these are installed in short beam-pipe modulesmade from copper-coated stainless steel mounted betweentwo NEG coated pipes (7 m long each), with a good pump-ing and (after activation) low secondary emission yield, sothat we may assume that the pressure rise measured at agauge is the result of the electron cloud produced exclu-sively within the gauge’s vacuum module. The modulevacuum chamber is round with 80 mm diameter. In thefollowing we only present results for one ionization gauge.Results for other gauges look similar. ESULTS
Until now we have processed 4 sets of measurementsobtained during the conditioning of the machine throughbeam scrubbing. All of these have been recorded at a beamenergy of 450 GeV with either 50-ns or 25-ns bunch spac-ing for the first 3 sets and the last set, respectively.We have used two kinds of beam configurations, withvarying spacing between successive bunch trains (alsocalled “batches”) and varying number of batches, respec-tively. Table 1 lists the parameters for the three sets ofmeasurements with 50 ns bunch spacing.Table 1: Parameters used in the simulations for the differentsets of measurements with 50 ns bunch spacing. In sets 2and 3 there is an additional space of 225 ns between thetwo (set 2) or three trains (set 3) of 36 bunches injectedsimultaneously.
Set 1 Set 2 Set 3 of bunches 36 72 (2x36) 108 (3x36)per batch of batches 1 - 5 1 - 14 1 - 12Batch spacing 2.0 - 6.0 4.850 0.925( µ s)Av. bunch 1.1 1.21 1.15population( ppb)At the beginning of a scrubbing run in April 2011, twoexperiments were carried out (both corresponding to set 1listed above). In the first we injected batches in pairs withvarying batch spacing (6 µ s, 4 µ s and 2 µ s). Each pair ofbatches was separated by 11.5 µ s (a time considered longenough to clear any electron cloud). Figure 3 shows thepressure increases observed during this first experiment,including an additional first, shorter 12-bunch batch intro-duced for machine-protection reasons (and where no pres-sure increase can be appreciated). In the second experimentwe injected an increasing number of batches at a batch-to-batch distance of 2.125 µ s (up to 5).Figure 4 depicts the results obtained for both experi-ments. We could conclude that the solution is around δ max = 1 . and R = 0 . . We have to take into accountthat there are large uncertainties in the measured pressurevalues as well as in the estimated bunch population. Ac-cording to simulations, such uncertainties can lead to a mis-match between lines and prevent a single unique intersec-tion, as seen for this example. The value of δ max = 1 . is in agreement with an estimate from the CERN vacuumgroup, which expected an initial value between 1.6 and1.9 [22, 23]. In addition, the value R = 0 . is in agree-ment with several high precision measurements, both re-cent (e.g. [24]) and old (e.g. [25]).After a few days of surface conditioning, double batchesof 36 bunches each separated by 225 ns were injected ata distance of 4.85 µ s (up to 14). This corresponds to the : :
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00 04 : : N b ( ⋅ ppb ) P r e ss u r e ( ⋅ - m ba r) N b VGI.141.6L4.B
Figure 3: Beam intensity and pressure at the gaugeVGI.141.6L4.B during the first experiment on 6 April2011. Every step in the beam intensity (red curve) indi-cates the injection of a new batch. R δ max Φ / Φ =40.6 Φ / Φ =101.0 Φ / Φ =161.0 Φ µ s / Φ µ s =0.477 Φ µ s / Φ µ s =0.118 Figure 4: Combinations of δ max- R values characteriz-ing the chamber surface, obtained by benchmarking ratiosof observed pressure increases against ratios of simulatedelectron fluxes, for measurements on 6 April 2011.set 2 of experimental data. A similar experiment (set 3)took place in mid May 2011 but using triple batches in-stead, again separated by 225 ns, at a distance of 925 ns(up to 12). Figure 5 shows the results obtained in thesecases. It is worth noting that for these last two cases we ob-serve parallel lines instead of a clear intersection betweenthe lines. This is due to the loss of sensitivity to the effectof the 225 ns gap between 36-bunch batches, that appearswhen the double (or triple) batches are injected together in-stead of one after the other. Indeed the lines should be iden-tical under some plausible simplifying assumptions. Theconclusion is that it is necessary, during the same experi-ment, to take two sets of measurements with different batchspacings, in order to obtain lines of different slope whichuniquely intersect and yield the desired parameter informa-tion.A new measurement, with varying spacing betweenbatches, has been carried out at the end of the 2011’s pro- R δ max φ / φ =18.54 φ / φ =63.15 φ / φ =78.54 R δ max φ / φ =26.69 φ / φ =66.00 φ / φ =82.57 φ / φ =87.47 φ / φ =92.37 Figure 5: Combinations of δ max- R values characteriz-ing the chamber surface, obtained by benchmarking ratiosof observed pressure increases against ratios of simulatedelectron fluxes, for LHC measurements taken on 11 April(top) and 19 May 2011 (bottom).ton run (end October). On this occasion the bunch spacingwas reduced to 25 ns. Table 2 shows the parameters usedin this case and Fig. 6 depicts the result obtained for thisexperiment.Table 2: Parameters used in the simulations for the mea-surements with 25 ns bunch spacing. Set 4 of bunches 72per batch of batches 2batch spacing ( µ s) 1.0, 2.0, 3.0, 4.0bunch population 1.1, 1.0, 1.0, 1.1( ppb)Although we are not yet able to extract a unique value for δ max and R , we can clearly see evidence for conditioning,as the solution for later cases tends towards lower δ maxvalues. Figure 7 summarizes the approximate time evolu-tion of δ max in the “warm-warm” transition regions wherepressure gauges are located.We can see that the evolution of the conditioning for 50-ns and 25-ns beams looks as expected, with δ max approach-ing the simulated multipacting thresholds for 50-ns or 25-ns bunch spacing (both also indicated in the figure), re- R δ max φ µ s / φ µ s =0.462 φ µ s / φ µ s =0.282 φ µ s / φ µ s =0.256 Figure 6: Combinations of δ max- R values characteriz-ing the chamber surface, obtained by benchmarking ratiosof observed pressure increases against ratios of simulatedelectron fluxes, for LHC measurements taken on 25 Octo-ber 2011. In this case a value ε max = 260 eV has beenassumed, as it gives a better fit to the data. This could be asign of variation of ε max during the scrubbing. δ m a x date δ max
50 ns threshold25 ns threshold
Figure 7: Approximate time evolution (from April to Octo-ber 2011) of δ max in the uncoated warm straight sections(chamber radius 40 mm). The lowest values reachable withscrubbing corresponds to the 25-ns multipacting threshold,for a reflectivity R of 0.2. The first injection of a beam with25-ns bunch spacing beam took place on 29 June 2011.spectively, as asymptotic limit. All these facts instill someconfidence in the method and support its potential use as atool for monitoring the surface conditioning through beamscrubbing.The evolution in the uncoated straight sections goes froman initial value of δ max ≈ . at the beginning of the scrub-bing run in April 2011 to δ max ≈ . when the experi-ments with 25 ns were carried out. The points shown for11 April and 19 May 2011 have been obtained by assumingthe value of an average line in Fig. 5 at R = 0 . . ONCLUSIONS
In 2010 and 2011 first electron-cloud effects have beenobserved with proton beams in the LHC. Rapid surfaceconditioning has allowed reducing the bunch spacing fornominal operation from 150 ns over 75 ns down to 50 nswithout any significant perturbation from electron cloud.Thanks to the benchmarking of vacuum observationsagainst simulations described in this paper, we have beenable to monitor the evolution of δ max during machine con-ditioning in the warm straight sections of the LHC. The ob-servable considered is the pressure increase resulting fromthe electron cloud, which is taken to be proportional tothe electron flux impinging on the vacuum chamber walls.Namely, by benchmarking the ratios of experimental pres-sures and of simulated electron fluxes for different beamconfigurations (e.g., for varying spacing between bunchtrains or varying number of batches) we can then pin downthe value of the maximum secondary emission yield as wellas the reflection probability for low-energy electrons. Ap-plying this method to each of the different measurementsets available so far provides clear evidence for surfaceconditioning in the uncoated warm regions of the LHC,from an initial maximum secondary emission yield of about1.9 down to about 1.35, with R ≈ . , as can be seen inFig. 7.In order to reach the design LHC bunch spacing of 25 nsin physics operation, further conditioning of the secondaryemission yield is still required. According to some esti-mates [26], approximately 2 weeks of machine time wouldbe required to achieve these values, since the scrubbing ef-fect reduces with decreasing δ max. ACKNOWLEDGEMENTS
The authors would like to thank G. Arduini, V. Baglin,G. Bregliozzi, G. Iadarola, G. Lanza, E. M´etral, G. Ru-molo, M. Taborelli and C. Yin-Vallgren for relevant and al-ways enriching discussions and experimental data as wellas all the machine operators for the support they providedwith the machine operation during the experiments.