The Fast Ion Instability is believed to be a serious danger for bunch trains propagating in the CLIC electron transfer line and main linac, since it may strongly affect the bunches in the tail of the train if the vacuum pressure is not below a certain threshold. We have developed the FASTION code, which can track electrons through a FODO cell line and takes into account their interactions with the produced (and possibly trapped) ions. We describe how this tool can be used for setting tolerances on the vacuum pressure and for giving specifications for the design of a feedback system

Rumolo, G

Schulte, D

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CERN-AB-2008-027FAST ION INSTABILITY IN THE CLIC TRANSFER LINE AND MAIN LINAC*The Fast Ion Instability is believed to be a serious danger for bunch trains propagating in the CLIC electrontransfer line and main linac, since it may strongly affect the bunches in the tail of the train if the vacuumpressure is not below a certain threshold. We have developed the FASTION code, which can track electronsthrough a FODO cell line and takes into account their interactions with the produced (and possibly trapped)ions. We describe how this tool can be used for setting tolerances on the vacuum pressure and for givingspecifications for the design of a feedback system.EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN   -   AB DepartmentGeneva, SwitzerlandAugust 2008AbstractCERN-AB-2008-027CLIC-Note -748EUROTeV-Report-2008-036*Work supported by the Commission of the European Communities under the 6th Framework Programme“Structuring the European Research Area”, contract number RIDS-011899.G. Rumolo and D. SchulteCERN, Geneva, SwitzerlandPresented atEPAC'08, 11th European Particle Accelerator Conference, Genoa, Italy - June 23-27, 2008FAST ION INSTABILITY IN THE CLIC TRANSFER LINE AND MAINLINAC∗G. Rumolo, D. Schulte, CERN, GenevaAbstractThe Fast Ion Instability is believed to be a serious dangerfor bunch trains propagating in the CLIC electron transferline and main linac, since it may strongly affect the bunchesin the tail of the train if the vacuum pressure is not below acertain threshold. We have developed the FASTION code,which can track electrons through a FODO cell line andtakes into account their interactions with the produced (andpossibly trapped) ions. We describe how this tool can beused for setting tolerances on the vacuum pressure and forgiving specifications for the design of a feedback system.INTRODUCTIONThe residual gases (H2, H2O, CO, N2, etc.) present inthe vacuum chamber of an accelerator are generally re-sponsible for the formation of ion/electron clouds (throughbeam induced ionization), which can have destabilizing ef-fects on the beam. The electrons created by residual gasionization are very likely to be only the initial seed for theformation of electron clouds in hadron/positron machines,because their accumulation is actually dominated by thesecondary emission process and not by trapping. The lightelectrons would in fact be lost between two subsequentbunch passages with the usual bunch spacings, and theywould not accumulate if they did not multiply due to thefact that they can produce more electrons when imping-ing against the inner pipe wall with relatively high ener-gies. On the contrary, the ions created from residual gasionization in an electron machine may be either lost be-tween two bunches or not enough accelerated during onebunch passage as to reach the pipe wall before the nextbunch comes. In the latter case the machine is operat-ing in trapping regime, and the number of ions around thebeam increases linearly with the number of bunches pass-ing through a certain accelerator section. Even in absenceof an amplifying effect, this mechanism can result in a two-stream instability [1]. In circular machines, the ion instabil-ity can be of conventional type, when the number of ionsrapidly increases over all the accelerator because there issimply no long enough gap between two bunches such asto clear the ions from the chamber and reset the accumula-tion process. Every electron ring must be conceived as notto operate in this regime. However, even when the beamstructure is such that there exist more trains of bunches cir-culating in the machine, separated by long enough gaps asto clear the ion cloud in between trains, a strong instabil-∗This work is supported by the Commission of the European Com-munities under the 6th Framework Programme Structuring the EuropeanResearch Area, contract number RIDS-011899.ity could still develop over a train length, which is calledfast ion instability. In the fast ion instability, individualions last only for a single passage of the electron beam andare not trapped for multiple turns. This type of instabilitycan equally occur in a linear machine, because it does notdepend on the periodicity of the structure but only on thepropagation of a train of bunches able to trap ions downa sufficiently long machine. Obviously, this is a head-taileffect, which affects only the bunches in the last part ofa train, whereas the bunches in the head are totally unaf-fected.CLIC is an electron-positron linear collider designed tohave main linacs of about 20 km, and equally long beamtransfer lines to transport both electrons and positrons fromtheir sources to the interaction point [2]. Trains of 311 veryshort bunches spaced by less than 1 ns will have to propa-gate through these structures to reach the interaction pointwith the required features to achieve the nominal luminos-ity. Therefore, there are the basic conditions for a poten-tial fast ion instability both in the long transfer line and inthe main linac (for electrons), if trapping occurs and if theresidual gas pressure is high enough as to produce enoughions to excite an unstable motion. The goal of this paperis to assess the pressure thresholds both in the transfer lineand in the main linac, above which the fast ion instabilitysets in. For this purpose we have developed the FASTIONcode, which is described in the Section II and subsequentlyapplied to CLIC in Section III. Conclusions as well as aview on the future work are given in Section IV.THE FASTION CODEThe FASTION code has been developed at CERN to de-scribe in detail ion generation and interaction with an elec-tron bunch train along a linear machine. In the model, bothions and electrons are treated as macroparticles. The basicprinciple of the code is illustrated in Fig. 1. The electronbunches are made to interact with the ions, as they are gen-erated bunch by bunch, twice per FODO cell (at the pointsof maximum and minimum beta functions). They are trans-ported down the line using linear transfer matrices betweenthe selected interaction points. In the latest version of thecode, the lattice can be passed to the code through an exter-nal Twiss file (compatible with either the PLACET [3] orthe MAD-X structure) and the interaction points are thendefined by the locations specified in this file. Accelerationcan be included by means of the variation of the relativisticgamma along the line. In ideal conditions, this results in abeam size change (usually shrinking) compatible with thedesigned beta function variation along the line and conser-vation of the normalized transverse emittances. Ions of dif-ferent species (desired number specified in the input file)are generated proportionally to their partial pressures andionization cross sections. They are subsequently trackedalong the train passage according to their masses.ionelectronBunch nF O D OCell jsxyFigure 1: Principle of the FASTION code.The main default outputs of the FASTION code include:• Snap shots of the bunch by bunch centroids and emit-tances in the two transverse planes at all the interac-tion points chosen in the line. An unstable motion willbe revealed by an exponential correlated growth of thecentroid motion in the bunches located at the tail ofthe train. Emittance growth can accompany this typeof coherent instability.• Sample trajectories of ions from their generation to theend of the train passage to be able to check whetherthey are trapped. In the case of changing energy alongthe line, these sample trajectories are saved up to 10times along the full line in order to check on the trap-ping condition at several locations (as the beam sizemay change a lot due to acceleration).• Ion distributions in x and y after each bunch passageat the beginning of the line (also up to 10 points alongthe line in case of acceleration).APPLICATION TO CLICThe Long Transfer LineThe parameters of the CLIC long transfer line are sum-marized in Table 1.Table 1: Parameters used in our study: the transfer lineEnergy p0 (GeV) 9Norm. transv. emitt. x,y (nm) 680, 10Bunch length σz (ps) 0.15Bunch spacing ΔTb (ns) 0.667Bunch population N 4× 109Number of FODOs NFODO 500Number of bunches Nb 300FODO length LFODO (m) 40Phase advance φFODO (o) 70Gas pressure PH2O,CO (nTorr) 1, 1Ioniz. cross sect. σH2O,CO (MBarn) 2, 2Analytical evaluations of the ion effect are reported inthe companion paper [4]. Ions are trapped in the long trans-fer line, as Figs. 2 depict. We see horizontal and verticaltrajectories of two sample ions of different species, whichare essentially sinusoidal oscillations with frequencies de-pending on the mass of the ions and on the plane we areobserving (the beam has almost two orders of magnitudedifferent emittances in the two planes).-60-40-20 0 20 40 60 0  50  100  150  200  250  300<x> (μm)Bunch indexH2OCO-6-4-2 0 2 4 6 8 0  50  100  150  200  250  300<y> (μm)Bunch indexH2OCOFigure 2: Horizontal and vertical trajectories of two sample ions(generated at the first bunch passage) as the 300 bunches of theelectron beam go through the chanber.Trapping is a condition which may easily translate intobeam instability if the residual gas pressure in the vacuumchamber is too high. In fact, the simulation shows that par-tial pressures of 1 nTorr for both H2O and CO (or N2, sincethey have the same mass number) are sufficient to drive theelectron beam unstable in the vertical plane. The instabil-ity manifests itself with both coherently growing verticalcentroid motion and emittance growth in the second part ofthe bunch train. Figures 3 display several snapshots alongthe line of both vertical centroid and emittance bunch bybunch. The centroid motion exhbits clear frequencies onwhich it is excited (depending on the ion oscillation fre-quencies), whereas the emittance growth amounts to about50% for bunches in the second half of the train and hassome peaks of 100% increase for a few bunches in the verytail of the train.The main result of this study is that in the long transferline a vacuum better than 1 nTorr is required against fast ioninstability. This poses a serious constraint on the design ofthe vacuum system.The Main LinacThe parameters of the CLIC main linac are summarizedhere below in Table 2.Table 2: Parameters used in our study: the main linacEnergy p0 (GeV) 9 to 1500Norm. transv. emitt. x,y (nm) 680, 10Bunch length σz (ps) 0.15Bunch spacing ΔTb (ns) 0.667Bunch population N 4× 109Number of bunches Nb 311Gas pressure PH2O,CO (nTorr) 10, 10Ioniz. cross sect. σH2O,CO (MBarn) 2, 2Length L (km) 20.5The lattice with the increasing beta functions is de-scribed through a PLACET output file. which is used asan auxiliary FASTION input file (from which also the en-ergy information can be taken). In this case the situation ismore complex than in the transfer line, because trapping,-10-5 0 5 10 15 0  50  100  150  200  250  300<y> (μm)Bunch number1st FODO100th FODO200th FODO300th FODO400th FODO500th FODO 5 10 15 20 25 30 0  50  100  150  200  250  300ε y (nm)Bunch number1st FODO100th FODO200th FODO300th FODO400th FODO500th FODOFigure 3: Vertical centroids and emittances of the 300 electronbunches at six locations along the transfer line.which certainly occurs at the beginning of the main linac,can be lost along the way, as the beam size shrinks. Thishas a stabilizing effect, because it limits the ion accumula-tion around the beam, and adds up to the other stabilizingmechanism coming from the beam becoming stiffer.The fact that trapping is lost along the line can be seen look-ing at the distribution of ions (for example, in the verticaldirection) after the first and last bunch of the train at the endof the main linac (plotted in Figs. 4). While at the begin-ning of the linac the produced ions remain relatively closeto the beam up to the passage of the last bunch, at the end ofthe line they tend to spread much farther off the beam cen-ter. Therefore, the effect of their interaction with the beam(which at the same time has become transversely smallerand more energetic) becomes very weak.It should be not be surprising that the electron beam inthe main linac is much more stable against fast ion mecha-nisms than in the transfer line, and the vacuum constraint inprinciple much more relaxed. First signs of fast ion insta-bility appear for a residual gas pressure of about 50 nTorrand the instability becomes strong at 100 nTorr (see Fig. 5),hinting that even a vacuum of few 10−8 Torr could be tol-erated. Attention has to be paid to the fact that, since oneof the reasons why the beam gets more stable is the loss oftrapping, reducing the bunch charge can have the effect ofmaking the beam more unstable, since it would restore trap-ping where it would have been lost with a higher charge.For example, simulations were run at 50 nTorr and it wasobserved that the beam would become significantly unsta- 0.0001 0.001 0.01 0.1 1 10 100-1.5 -1 -0.5  0  0.5  1  1.5(a.u.)y (mm)dNi/dy, end of Linac, first bunchdNi/dy, end of Linac, last bunchFigure 4: Ion distributions in y after the first and last bunch of atrain, taken at the end of the linac.-0.01-0.005 0 0.005 0.01 0  50  100  150  200  250  300  350<y> (μm)bunch numberp=100 nTorrEnd of linacMiddle of linacBeginning of linacFigure 5: Snap shots of the bunch by bunch vertical centroiddistributions along the main linac.ble for numbers of electrons per bunch between 10 8 and109, but it would be quickly stabilized outside of this range.CONCLUSIONSFast ion instability simulations were run with a newly de-veloped code (FASTION) both for the CLIC long transferline and for the main linac. The main purpose was to pindown vacuum constraints for both lines. The outcome ofthe study is that in the tranfer line a vacuum in the order of10−10 Torr is required to ensure beam stability, whereas thetolerance seems to be relaxed in the main linac due to thehigher energy and to the loss of trapping (p < 10−8) Torr).However, one has to bear in mind that in this simulation wehave ignored both the effect of rf fields on the ions and theeffect of field ionization, which can be specially importantin the second part of the linac.REFERENCES[1] T. Raubenheimer and F. Zimmermann, Phys. Rev. E 52,5487–5498 (1995)[2] CLIC parameters 2008, CERN CLIC Note, edited byF. Tecker, to be issued[3] D. Schulte, T. E. D’Amico, G. Guignard, and N. Leros,CERN Report No. CERN/PS-2001-028 (AE)[4] J.-B. Jeanneret et al., in these proceedings

Fast Ion Instability in the CLIC Transfer Line and Main LINAC

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