This paper presents an intermediate review of the single bunch collective effects in the LHC. It first reviews the LHC impedance budget including all elements for which a design is presently available. Then, based on this updated budget, the corresponding rise times and thresholds for single bunch instabilities are evaluated and discussed

Angal-Kalinin, Deepa

Brandt, D

Vos, L

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHEuropean Laboratory for Particle PhysicsINTERMEDIATE REVIEW OF SINGLE BUNCH COLLECTIVE EFFECTSIN THE LHCD. Angal-Kalinin1, D. Brandt2 and L. Vos2This paper presents an intermediate review of the single bunch collective effects in the LHC. It firstreviews the LHC impedance budget including all elements for which a design is presently available. Then,based on this updated budget, the corresponding rise times and thresholds for single bunch instabilities areevaluated and discussed.1  CERN, Geneva, Switzerland2  On leave of absence from CAT, Indore, IndiaPresented at the Eighth European Particle Accelerator Conference (EPAC)3-7 June 2002 - La Villette, Paris, FranceGeneva, Large Hadron Collider ProjectAdministrative SecretariatLHC DivisionCERNCH - 1211 Geneva 23SwitzerlandLHC Project Report 587Abstract8 July 2002INTERMEDIATE REVIEW OF SINGLE BUNCHCOLLECTIVE EFFECTS IN THE LHCD. Brandt and L. Vos, CERN, Geneva, SwitzerlandD. Angal-Kalinin, On leave of absence from CAT, Indore, INDIAAbstractThis paper presents an intermediate review of the sin-gle bunch collective effects in the LHC. It first reviews theLHC impedance budget including all elements for which adesign is presently available. Then, based on this updatedbudget, the corresponding rise times and thresholds for sin-gle bunch instabilities are evaluated and discussed.1 INTRODUCTIONThe last review of the LHC collective effects dates backfrom 1995 [1]. Although detailed in his content, this reviewwas mainly based on educated guesses, since the design ofmost of the components were not readily available. Despiteof that, the review was a fundamental contribution, con-firming that, provided the impedance could be kept withinthe estimations, the LHC could be safely operated from acollective effect point of view. As the final design of newelements became available, the corresponding impedanceshave been re-evaluated either by applying analytical esti-mations, by RF measurements or by numerical estimationwith the MAFIA code [2]. Whenever applicable, the threesets of results have been used such as to cross-check thevalidity of the results. When this was not possible, then atleast two sets of results were used for the evaluation.As far as collective effects for single bunches are con-cerned, the main parameters are the inductive impedance(Z/n) in the longitudinal plane and the relatively high fre-quency (broad-band) impedance in the transverse planes.The transverse low frequency impedance (resistive wall), ismore relevant for coupled-bunch instabilities and will notbe considered here, however, it is treated in a dedicatedcompanion paper [3].2 LHC BOUNDARY CONDITIONSOriginally, feedback systems for both the longitudinaland the transverse planes were considered. The longitudi-nal system was based on 200 MHz cavities, mainly ded-icated to damp injection transients but which could alsohave been used as feedback cavities, albeit at a reducedstrength. In the meantime, new 200 MHz cavities havebeen proposed, and a dedicated study [4] has demonstratedthat, considering the constraints to be fulfilled in termsof bandwidth and related power requirements, a longitu-dinal feedback system for the LHC with the present designwould be extremely difficult to realize. However, the anal-ysis of the loss of Landau damping at high energy showedthat, even in the absence of longitudinal feedback, a suffi-cient safety margin is provided for the nominal operatingconditions, provided the longitudinal inductive impedance(Z/n) remains smaller than 0.28 Ω. This value thus rep-resents a hard limit for the longitudinal impedance of theLHC machine. In the transverse planes, the main bound-ary condition is to ensure that the transverse broad-bandimpedance remains small enough such that the thresholdfor transverse mode coupling instability is higher than thebunch intensities presently foreseen for the operation of theLHC.3 THE LHC IMPEDANCE BUDGETUp to now, the design of about 90 % of the LHC compo-nents has been finalised. As far as the remaining 10 % areconcerned, we shall include estimations which reflect thebest of our present understanding.3.1 Longitudinal Impedance BudgetThe different elements included in our analysis to com-pute the LHC impedance budget can be grouped as follows:• The LHC beam screen: from a pure layout point ofview, with its length of about 24 km, it is clearly themost important component of the machine. However,as far as the longitudinal impedance is concerned, thebeam screen contributes only via the numerous holesdrilled on its surface. The impedance of these holeshas been evaluated according to the theory presentedin Ref. [5], inserting the corresponding LHC parame-ters. This yields an impedance of (Z/n) = 0.017 Ω.• The 200 MHz RF cavities: these 4 units will be usedto accommodate the beam emittance coming from theSPS as well as to damp injection errors. With an es-timated (Rshunt/Q) of 192 Ω per unit, this yields animpedance of about 0.045 Ω for the 4 units. Actually,the effective impedance is expected to be smaller thanthis value. For this reason, the value included in theimpedance budget amounts only to 30 % of that, i.e.0.015 Ω.• The 400 MHz RF cavities: these 8 units composethe core of the LHC RF system. With a (Rshunt/Q)of 44.5 Ω per unit, this corresponds to an effectiveimpedance of 0.01 Ω.• The experimental chambers: the respective contribu-tions vary a lot, due to the very different design. Interms of impedance, ATLAS is rather optimal, witha very smooth vacuum chamber. Its contribution istherefore negligible. The design of CMS is welladvanced and its contribution has been estimated to0.0005 Ω for the experiment. TOTEM, when operat-ing (i.e. in closed position) should increase the contri-bution by about the same amount, namely 0.0006 Ω.For ALICE, the final design is not yet available, butthe present estimation amounts to 0.001 Ω. Finally,the contribution from LHCb is by far the most impor-tant, amounting to 0.0085Ω (of which more than 80%are due to the vertex detector in closed position).• The shielded bellows: due to the very high number ofthese elements, the design phase was particularly crit-ical. As a result of an intense and successful optimi-sation campaign, the impedance of the 1700 shieldedbellows could be kept as low as 0.01 Ω.• The unshielded bellows: such elements are extremelyunfavourable from an impedance point of view, anda special effort was made to avoid such componentswhenever possible. As a result, their number could berestricted to a few elements in the surroundings of theLHC experiments. Their total length is expected to bearound 3 m, with an impedance of 0.005 Ω.• The vacuum valves: another element whose occur-rence in the machine is high. The valves with an in-ner radius of 31.5 mm will be connected to the nor-mal vacuum chamber (radius of 40 mm) by two taperswith a slope of 15 degrees. For 350 units per ring, thisyields an impedance of 0.005 Ω.• The Beam Position Monitors (BPMs): there are ba-sically three different types of monitors in the LHC,namely the button electrodes monitors which are in-stalled in the arcs of the machine and are thus by farthe most numerous, some strip lines monitors installedin the warm parts of the machine and finally some”hybrid” monitors (combination of strip lines and but-tons) also foreseen for the straight sections. In total,there will be more than 500 BPMs per ring, with animpedance estimated to be 0.002 Ω.• The re-combination chambers: these are specialchambers (8 in total) where the beams, which travel ina common vacuum chamber around the experiments,are separated to go in the two separate rings. Thesechambers required a dedicated optimisation in orderto avoid the presence of trapped modes. In total, there-combination chambers are expected to contributefor 0.001 Ω.• Special equipment: Special components like the injec-tion and dump kickers, the septa and the TDI are notexpected to contribute significantly to the longitudinalimpedance budget, since they are equipped with a thinmetallic layer on their inner surface.A few important elements are still missing from this list,namely those for which the conceptual design is still miss-ing. These are essentially the collimators and the specialequipment for beam instrumentation. As far as the collima-tors are concerned, we assumed that i) they will be mountedon the conventional vacuum chamber (radius 40 mm), ii)the inner radius will be around 8 mm at injection and iii)the transitions will be tapered with a slope ranging between10 - 15 degrees. For 20 collimators, the correspondingimpedance is estimated to 0.004 Ω. At this point, it is im-portant to stress that, in case the material retained for thesecomponents would be an insulator, then it is mandatory tohave a thin metallic layer (a few microns) deposited on theinner surface, in order to guarantee for the low inductancequoted here. Given our present information, a guess for thebeam instrumentation is even more difficult. Our presentestimation relies on 24 units per ring, with an inner radiusof 40 mm, an outer radius of 60 mm and conventional ta-pers for the connections. Such a system would yield animpedance of about 0.001 Ω.The longitudinal impedance budget summarising the de-scription given above is presented in Table 1.Table 1: Estimated impedance budget for the LHC in thelongitudinal plane.Element Number or (Z/n)length [mΩ]Beam screenpumping holes 24 km 17200 MHz cavities 4 15400 MHz cavities 8 10Exp. chambers 5 11Shielded bellows 1700 10Unshielded bellows 3 m 5Vacuum valves 350 5Collimators 20 4Beam monitors 500 2BI instruments 24 1Re-comb. chambers 8 1Total 81As can be seen from Table 1, the total estimated longi-tudinal impedance is slightly less than the 0.1 Ω defined asthe objective two years ago. However, this positive resultshould not be misinterpreted, in the sense that the quotedimpedance budget reflects our estimations, which need tobe confirmed once the final equipment becomes available.Consequently, it seems reasonable to assume a value of0.1 Ω for the evaluation of the longitudinal thresholds forstability.3.2 Transverse Impedance BudgetIt is essential to stress that the transverse impedancebudget discussed in this section refers to the broad-bandimpedance of the machine (relatively high frequency, i.e.several GHz) and does not include the (low frequency) re-sistive wall contribution, which is presented in a compan-ion paper [3], since the resistive wall effect is more relevantfor coupled-bunch instabilities. Except for the BPMs forwhich the values are taken from a dedicated evaluation [6],the transverse impedance is derived from the longitudinalvalues according to the simple relation:ZT =2Rb2× (Zn)where R is the LHC radius and b the inner radius of thevacuum chamber. Furthermore, we shall restrict ourselvesto quote the values for the vertical plane, since it is themore critical for the present evaluation. The correspondingresults are presented in Table 2.Table 2: Estimated impedance budget for the LHC in thevertical plane.Element Inner radius β/βav ZT[mm] [kΩ/m]Beam screenpumping holes 18 1.25 500200 MHz cavities 50 3 155400 MHz cavities 150 2.9 11Shielded bellows 20 1.25 265Vacuum valves 40 1.25 35Collimators 8 4.3 2300BPMs [6] 25 1.25 300BI instruments 40 2.15 12Total 3578As can be seen from the Table, the transverse contribu-tion is largely dominated by the elements whose structureis in the direct vicinity of the beams, such as the collima-tors. Some of the elements contributing in the longitudi-nal plane, like the re-combination chambers, the unshieldedbellows and the experimental chambers have been omittedin this list. Indeed, their contribution is expected to be neg-ligible, mainly because they are located at positions withrelatively small beta functions. TOTEM has also been leftout, since, at injection, the experiment will not be in closedposition. To summarise, the estimated LHC broad-bandimpedance will be rounded up to 4 MΩ/m. Actually, thisvalue has still to be multiplied by the average beta functionβav which had been taken equal to 70 m in the above es-timations. This yields a value of 280 MΩ, which will beused for the computation of the instability thresholds.4 THRESHOLDS FOR INSTABILITIESFor the impedances quoted above, the stability thresh-olds for the longitudinal microwave instability, the loss ofLandau damping in the longitudinal plane and the trans-verse mode coupling instability (TMCI) have been evalu-ated both at injection and at top energy. For the sake of sim-plicity, we shall quote only the lowest threshold obtained ineach case. The corresponding thresholds are presented inTable 3.Table 3: Thresholds of stability (maximum bunch popu-lation) for the LHC for both the longitudinal and verticalplanes.Injection Injection Top Energy450 GeV 450 Gev 7 TeVRF type [MHz] 200 400 400RF Volts [MV] 3 8 16Total bunch length [m] 0.7 0.464 0.3Sync. tune Qs [×103] 2.55 5.88 2.12Worst case TMCI TMCI LandauNthb [×10−11] 7.5 11.5 6.7These thresholds have to be compared with the bunchintensities foreseen for the operation of the LHC, namely1.1×1011 for the nominal scheme and 1.7×1011 for the so-called ultimate configuration. As can be seen from it, asubstantial safety margin is provided for all the cases con-sidered.5 CONCLUSIONSFor the evaluation of single bunch instabilities, the mostimportant ingredients are the longitudinal impedance (Z/n)and the high frequency broad-band transverse impedance.In a first step, the main components contributing to theseimpedances have been identified, and the correspondingimpedance budgets have been established. Based on thesebudgets, the stability thresholds for the microwave insta-bility, the loss of Landau damping and TMCI have beenevaluated and found to be higher than the bunch intensitiespresently foreseen for LHC operation. From these results,it can be concluded that single bunch effects are not ex-pected to be a problem for the LHC operation.6 REFERENCES[1] F. Ruggiero, “Single-Beam Collective Effects in the LHC”,CERN SL/95-09 (AP), June 1995.[2] R. Klatt et al., ”MAFIA - A Three Dimensional Electro-magnetic CAD Systems for Magnets, RF Structures, andTransient Wake-Field Calculations”, Proceedings of the 1986Linear Accelerator Conference, Stanford Linear AcceleratorCentre report SLAC-303 (June 1986), p.p. 276 - 278.[3] D. Angal-Kalinin and L. Vos, “Coupled Bunch Instabilities inthe LHC”, These Proceedings.[4] D. Boussard, D. Brandt and L. Vos, “Is a Longitudinal Feed-back System Required for LHC?”, LHC Project Note 205,1999.[5] R. L. Glu¨ckstern, “Coupling Impedance of Many Holes in aLiner within a Beam Pipe”, CERN SL/92-06 (AP), 1992.[6] D. Brandt, B. Spataro and L. Vos, “Impedance of the LHCArc Beam Position Monitors”, LHC Project Note 284, 2002.

Intermediate Review of Single Bunch Collective Effects in the LHC

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