A theoretical and experimental crash program has been set up at CERN to investigate electron cloud effects in the LHC. In particular, I report about recent estimates of the critical secondary-emission yield, versus bunch population and bunch spacing, and ongoing multipacting tests with a coaxial resonator in a strong magnetic field

Ruggiero, F

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHEuropean Laboratory for Particle PhysicsLarge Hadron Collider Project LHC Project Report 166Electron Cloud in the LHCFrancesco RuggieroAbstractA theoretical and experimental crash program has been set up at CERN to investigate electroncloud eects in the LHC. In particular, I report about recent estimates of the critical secondary-emission yield, versus bunch population and bunch spacing, and ongoing multipacting tests witha coaxial resonator in a strong magnetic eld.Presented at the Advanced ICFA Workshop on Beam Dynamics Issues for e+e Factories,Laboratori Nazionali di Frascati - INFN, 20-25 October 1997, Frascati (Rome) - ItalyCERN{SL DivisionAdministrative SecretariatLHC DivisionCERNCH-1211 Geneva 23SwitzerlandGeneva, 4 February 19981 IntroductionSynchrotron radiation from proton bunches in the LHC creates photoelectrons atthe beam screen wall. These photoelectrons are pulled towards the positively chargedbunch. When they hit the opposite wall, they generate secondary electrons which canin turn be accelerated by the next bunch if they are slow enough to survive. Dependingon several assumptions about surface reectivity, photo-emission and secondary-emissionyields, this mechanism can lead to the fast build-up of an electron cloud with potentialimplications for beam stability and heat load on the cold beam screen. In view of the tightdeadline for the design of the LHC cryogenic system, an intensive research program [1]has been set up at CERN to measure the relevant physical quantities and to validateanalytic estimates and simulation results.The linear photon ux due to synchrotron radiation in the LHC is=52p3Nbtsep' 1017photonsm  s; (1)where  ' 1=137 is the ne structure constant,  ' 7000 the Lorentz factor for protons at7 TeV, Nb= 1011the bunch population,  ' 2780 m the bending radius and tsep= 25 nsthe time separation between subsequent bunches. The critical energy of these photonsis "cr= 3=2 3hc= ' 45 eV, i.e., well above the work function for copper (a few eV);photoelectrons are thus created at the beam screen wall and pulled towards the positivelycharged proton bunch. A rst estimate [3] of the corresponding heat load on the beamscreen, based on a photoelectron yield e' 0:02 and an average energy gain from theproton bunch hW i ' 700 eV (in the absence of magnetic eld and for a uniform electroncloud distribution), gave a linear power P = ehW i ' 0:2 W/m comparable to theheat load due to synchrotron radiation. This estimate does not include a possible electroncloud build-up associated with secondary emission, which can signicantly increase thepower deposition and, according to earlier simulations [2], can lead to a very fast horizontalmulti-bunch instability.For a uniform illumination of the beam screen, corresponding to high surface reec-tivity, the average energy gain in a dipole magnet is smaller by a factor two, since only thevertical component of the beam force is eective in accelerating the electrons. Indeed theyspiral along the vertical magnetic eld lines with typical Larmor radii of a few m andperform about a hundred cyclotron rotations during a bunch passage. On the other hand,the heat load in a dipole magnet is drastically reduced if the screen reectivity is muchsmaller than unity: in this case, photoelectrons and secondary electrons are produced onlynear the horizontal plane, where the vertical component of the beam force is very small.For high surface reectivity, the measured photoelectron yield per incident photonmay dier signicantly from the relevant yield per absorbed photon (sooner or laterall photons are absorbed by the beam screen). Therefore simultaneous measurementsof photoelectron yield and reectivity, at grazing incidence angle of 11 mrad, are underway at CERN using synchrotron light from the EPA machine, with critical energy of45 eV. Recent results [4] for copper coatings with dierent surface preparations indicatea rather high photoelectron yield per absorbed photon e' 0:15  0:20, however thereectivity drops from 80% for smooth surfaces down to about 5% for a surface roughnessof a few m.In kick approximation, the maximum energy gain of an electron initially at restwith radial oset a from the beam axis is independent of the bunch length and givenby "max= 2mec2Nb2r2e=a2, where c is the speed of light, methe electron mass and re10.0 0.5 1.0 1.5 2.0Initial Radius (cm)0246Energy Gain (keV)Energy Gain of Stationary Electron (No Magnetic Field)LHC: σ⊥=0.2 mm, σl=7.7 cm, N=1.05×1011Rectangular BunchGaussian BunchEnergy for Single KickPotential Energy (Rectangular)Figure 1: Electron energy gain (keV) versus initial radial oset (cm) for the LHC: the solidcurve diverging at small radial osets is the kick approximation, the two lower curves referto Gaussian and rectangular longitudinal bunch distributions. Here the peaks correspondto electrons temporarily trapped in the bunch potential, performing an integer number ofoscillations plus one quarter [5].its classical radius. For a photoelectron starting at the wall a ' 2 cm of the LHC beamscreen, "max' 200 eV and the corresponding travel time to the opposite wall is about 5 ns,i.e., signicantly less than the 25 ns bunch spacing. When the next bunch arrives, thereis a relatively uniform distribution of photoelectrons (plus secondary electrons) in thescreen cross section: the energy gain can reach a few keV and these fast particles hit veryquickly the screen walls, producing low energy secondary electrons. However, for a correctmodelling of the electron motion during the bunch passage [5] one has to cut the bunchinto several transverse slices (typically 50). This is important for electrons near the beamaxis, when the energy gain in kick approximation is largely overestimated (see Fig. 1),and is a key ingredient in all recent simulations of the electron cloud dynamics [6, 7, 8].2 Electron cloud build-up and critical secondary electron yieldHere I shortly review the theory of electron cloud build-up recently developed atCERN by G. Stupakov [9] and use his quasi-analytic results to discuss the dependence ofthe critical secondary emission yield cron the bunch population Nband bunch separa-tion Lsep= ctsep.The average number of secondary electrons emitted when a primary electron ofenergy W hits a metal surface with incidence angle  from the normal can be written [10]SEY(W; ) =maxcos hWWo; (2)where the maximum yield max, corresponding to a primary electron energy Wotypicallyaround 400 eV, is a characteristic of the metal (max= 1:3 2:5 for copper, depending onsurface preparation), while h is a universal function having the following phenomenologicalexpression:h() = 1:11  0:351  e 2:3 1:35: (3)2With some simplifying assumptions about the shape of the beam screen (circularwith radius a) and the velocity distribution of the secondary electrons (half-Maxwellianwith characteristic energy Ws= mv2s), it is possible to solve analytically the Vlasovequation describing the free drift of these electrons along the vertical magnetic eld linesin a bending dipole. The initial phase space distribution for secondary electrons producedat the screen wall with vertical coordinate yo(x) =pa2  x2isf(o)e(x; y; v) = no(x)s2mWse mv2=2Ws(y  yo(x)); (4)where no(x) denotes the initial electron surface density at the screen wall projected onthe horizontal plane (particles per unit area in the horizontal plane) and the velocityv > 0 is directed from the wall towards the beam axis. The vertical drift velocity alongthe magnetic eld lines is vy= vyo=a and the evolution of the electron cloud densityne(x; y; t) during the time interval between two subsequent bunches is given byne(x; y; t) =2no(x)tvsyo(x)=a" y   yo(x)tvsyo(x)=a!+  y + yo(x)tvsyo(x)=a!#; (5)where () = (1=p2) exp( 2=2) and the two terms in square brackets account forelectrons drifting away from the upper or lower parts of the screen walls, respectively.Combining the energy gain from the next bunch W (x; y) = "maxa2y2=(x2+ y2)2, in kickapproximation and in presence of a vertical magnetic eld, with the secondary electronyield given by Eq. (2), one gets the `second generation' electron surface densityn1(x) =Zyo(x) yo(x)dy SEY(W (x; y); (x))ne(x; y; tsep): (6)Here (x) = arccos(yo(x)=a). Although the kick approximation fails for electron energieslarger than about 1 keV, the corresponding secondary emission is a smooth function of Wat such energies and the error is not expected to be signicant. Note that Eq. (6) is validassuming that the surviving rst generation electrons hit the screen wall instantaneouslyafter the passage of the next bunch.Build-up of the electron cloud will take place if n1(x) > no(x), i.e., if max> cr(x)wherecr(x) =(Zyo(x) yo(x)dy h (W (x; y))ayo(x)ne(x; y; tsep)no(x)) 1: (7)This denes a critical value cr, weakly dependent on the horizontal position x along thebeam screen cross section, for the maximum secondary electron yield: if maxis smallerthan the critical value, there is no spontaneous amplication of the electron cloud density.1)For nominal LHC parameters (Nb= 1011, Lsep= 7:5 m) and assuming a typical secondaryelectron energy Ws= 10 eV, one nds a minimum crof about 1.35, in agreement withsimulation results [8]. Such a low value for maxis not easy to achieve. As shown in Fig. 2,however, crincreases signicantly for larger bunch spacings and has a weak dependenceon the bunch population. Therefore, as a possible back-up solution, one could envisage todouble the LHC bunch spacing.1)The denition of crdoes not include space charge eects, which can be neglected at the beginningof the electron cloud build-up. An approximate analytic solution of the Vlasov equation is possible,however, even including space charge [9]. It would be interesting to extend this approach to takeinto account the eect of the resistive wall wakeeld, which might play a signicant role during theinter-bunch gaps.31 2Nb ê1011123dcritCritical value of maximum SEY dmax vs bunch population NbLsep= 7:5 mLsep= 15 m5 10 15Lsep @mD123dcritCritical value of maximum SEY dmax vs bunch spacing LsepNb= 1011Nb= 5 1010Figure 2: Minimum value of the critical secondary electron yield given by Eq. (7), for acircular screen of radius a = 2 cm and a secondary electron energy Ws= 10 eV, versusbunch population (left) and bunch spacing (right). The solid and dotted curves correspondto a bunch spacing of 7.5 m and 15 m (left) or to a bunch population of 1011and 5 1010(right), respectively.3 Multipacting testsThe secondary electron yield and its possible reduction by a strong dipole magneticeld can be inferred from the multipacting level reached under suitable conditions in aresonant coaxial setup. Measurements of photoelectron yield and of multipacting rise timemay also be possible using UV light (e.g., from a Xe ash lamp mounted near or inside thecoaxial tube) and applying a DC-voltage between inner and outer conductors of the coaxialstructure. Comparing experimental results and predictions of computer simulations willalso provide a very useful `calibration' for the numerical results concerning heat load onthe LHC beam screen.                                                                        100WTEFLON TEFLONAMPLIFIERIN OUT DIR. COUPLERAM INOUTGENERATORFUNCTION TRIGGERREFLECTEDGENERATORSIGNAL SCOPE1ΜΩ or 50ΩSOURCEDC-+100κΩFORWARD TRANSMITTEDRESISTOR PROBE50κΩFigure 3: Experimental setup for multipacting tests. Using a coaxial resonator we canreach high electric elds and RF-voltages between the inner and outer conductor, in-spite of the limited power of the wide-band amplier: for a Q of 1000 and a charac-teristic impedance of about 100 , a power of 100 W corresponds to a peak voltage ofp100 W 100 1000 ' 3 kV.Multipacting tests have been successfully performed at CERN [11] using the coaxialsetup shown in Fig. 3. We have developed a simple and reliable technique, based onamplitude modulation of the input signal, to detect electronically the onset of multipacting4and to monitor the eld level in the resonator. An example of multipacting signature isshown in Fig. 4a: no reected signal (upper trace) is present until the amplitude modulatedinput signal reaches a threshold value. Meanwhile the transmitted signal (lower trace)increases and then becomes constant in the multipacting range. We observe a negative low-frequency signal superimposed on the `resistor probe' RF signal from the inner conductor,as in the lower trace of Fig. 4b, and thus the electric potential of the inner conductor tendsto become negative during multipacting. Although the sign of this low-frequency signalbecomes positive with a strong magnetic eld, as shown in Fig. 4c, the multipactingthresholds at room temperature are qualitatively similar to those measured during recentcold tests, with a dipole magnetic eld up to about 7.5 T. This seems to exclude anysignicant reduction of the secondary electron yield by a strong magnetic eld over mostof the outer tube surface, where the eld is not strictly parallel to the metal.a) 100 V, W =  28:2 dBmH: 50 ms/div, Vtb: 100-200 mV/divb) 0 kA, W =  21:2 dBmH: 5 ms/div, Vtb: 200-5000 mV/divc) 10 kA, W =  21:2 dBmH: 5 ms/div, Vtb: 500-1000 mV/divFigure 4: Multipacting tests in a resonant coaxial setup: with 100 V DC-bias and nomagnetic eld (a), in a cryostat at 1.8 K without magnetic eld (b) and with a dipoleeld of 7.3 T (c). The generator signal, with frequency around 480 MHz and power W ,is amplitude modulated at 3 Hz (a) or at 30 Hz (b)-(c) and amplied at maximum gain( 60 dB). The upper trace is the reected signal attenuated by 40 dB and measuredwith a 50  load, the lower trace is the transmitted signal (a) or the `resistor probe'signal (b)-(c) measured with a 1 M load.References[1] F. Ruggiero, World-wide web page on Electron Cloud in the LHC,http://wwwslap.cern.ch/collective/electron-cloud/.[2] F. Zimmermann, A Simulation Study of Electron-Cloud Instability and Beam-Induced Multipacting in the LHC, CERN LHC Project Report 95 (1997).[3] O. Grobner, Beam Induced Multipacting, CERN LHC Project Report 127 (1997),presented at the IEEE Particle Accelerator Conference, Vancouver, 1997.[4] I.R. Collins and O. Grobner, private communication (October 1997).[5] J.S. Berg, Energy Gain in an Electron Cloud During the Passage of a Bunch, CERNLHC Project Note 97 (1997).[6] F. Zimmermann, Electron-Cloud Instability and Beam-Induced Multipacting in theLHC and in the VLHC, SLAC-PUB-7664 (1997), presented at the workshop MBI'97,KEK, Tsukuba, Japan, 1997 and contributions to these proceedings.[7] M.A. Furman, Comments on the Electron-Cloud Eect in the LHC Dipole BendingMagnets, LBNL 40914/CBP Note-241 (1997), presented at the workshop MBI'97,KEK, Tsukuba, Japan, 1997 and contributions to these proceedings.5[8] O. Bruning, Simulations for the Beam-induced Electron Cloud in the LHC liner,CERN LHC Project Note 102 and LHC Project Report 158 (1997).[9] G. Stupakov, Photoelectrons and Multipacting in the LHC: Electron Cloud Build-up,CERN LHC Project Report 141 (1997).[10] H. Seiler, Secondary electron emission in the scanning electron microscope,J. Appl. Phys. 54, 11 (1983).[11] F. Caspers, J.-M. Laurent, M. Morvillo, and F. Ruggiero, Multipacting tests with aresonant coaxial setup, CERN LHC Project Note 110 (1997).6

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