Collective effects in the CLIC Beam Delivery System Resistive wall Coupled bunch effects

1. Collectiveeffects in the CLIC-BDSG. Rumolo, N. Mounet, R. Mutzner, R. Tomás in CLIC Workshop 09, 14 October 2009 • Collectiveeffects in the CLIC Beam Delivery System • Resistive wall • Coupledbuncheffects • Single buncheffects • Calculation of thewakefields • Fast ioninstability • Outlook: • multi-bunchsimulations • Single bunchstudy • Ions

2. Collectiveeffects in the BDS The main contributors to collective mechanisms in the BDS are: • Resistive wall wakes of the beam chamber, in general due to the small pipe radius and which can give a large contribution especially in the regions of the final quadrupoles (where the β functions are very large). • Geometric and resistive wall wake fields of the tapered and flat parts of the collimators (pipe radius changes and small apertures). • Ions in the electron line and electrons in the positron line • HOMs and LOMs in crab cavities These collective phenomena result into: • Single bunch effects (both instability and emittance growth). These can be excited by the geometric wakes (short range) as well as the high frequency part of the resistive wall impedance • Coupled bunch effects (unstable coherent motion of the bunch train). Long range resistive wall or narrow band resonator wake fields as well as ions and electrons are the source of bunch to bunch coupling

3. LAYOUT of theBeam Delivery System (3TeV) From R. Tomáset al. CLIC’08 • Resistive wall effects can be strong and cause luminosity reduction • Energy collimation section and FF system with very high beta’s and small apertures • Collimators with low apertures and low conductivity

4. Resistive wall: model z L W(z) s e q • Presentsimulationmodelforthemulti-bunch: • Using a Twissfile of the BDS, an initiallyoffsetbunchtrainistrackedthroughabout 2000 points of the BDS line • All particles in bunchessubsequent to thefirstonefeel a transverse kick in each point resultingfromthesum of theresistive wall contributions (integratedoverthe distance L betweenpoints) of all theprecedingbunches.

5. Long rangeresistive wall effect @3TeV • Coupled bunch resistive wall effects • We assume a constant radius all along the BDS • Chamber radius has been scanned from 2 to 8 mm • For a Cu chamber, the resistive wall effect is completely suppressed for r>4mm, whereas for a StSt chamber at least r=6mm is required (safe choice r=8mm)

6. Long rangeresistive wall effect @1TeV • Coupled bunch resistive wall effects • We assume the same lattice at 1TeV as at 3TeV • Chamber radius has been scanned from 2 to 10 mm • Because of the lower energy (factor 3) the effect becomes more visible even for larger radii. For a Cu chamber, the resistive wall effect is completely suppressed for r>6mm, whereas for a StSt chamber at least r=9mm is required.

7. Long rangeresistive wall effect @500GeV • Coupled bunch resistive wall effects • Simulations have been run with the 500GeV lattice • Chamber radius has been scanned up to 15 mm • Here there is the combined effect of the lower energy (factor 6), the different beta functions and the shorter system. For a Cu chamber, the resistive wall effect is completely suppressed for r>7mm, whereas for a StSt chamber at least r=11mm is required.

8.  b g s LT • Short rangeeffects @3TeV • Single bunch effects • Short range wake fields are both geometric (due to the cross section size variation, when the pipe does not a uniform radius along the line) and due to resistive wall • However, the resistive wall regime is different from the one used for coupled bunch studies and classical formulae are not applicable (see following slides) • The geometric contribution can be minimized with smooth tapering instead of abrupt cross section changes • Extensive studies were done in 2006-2007 in relation with collimators (see the relative EPAC, PAC papers) y Tapered parts contribute to: Geometric wakes Resistive wall wakes Flat part contribute to: Resistive wall wakes

9. Geometricwake For smoothtapering, the kick isgivenby(Stupakov, 1997) In diffractionregime whereas in theintermediateregime, thefollowingformulaholds:

10. Theoretical value Comparingthetheoreticalvaluefromformula in intermediateregimewithW. Bruns‘ Gdfidlsimulations. Theuppercurverepresentsthe probe bunch (normalized to thehighestvalue of thewakeforplottingpurposes) and thelowercurvesarethewakesreferring to thelabelledcases.

11. Resistive wall wake in thevariousranges Long range(traditional, canbefound in all text books) × z‘ ds wrw × z‘ Intermediateand shortrangew or w/o a.c. conductivity(calculatedstartingfromthepaper of K. Bane & M. Sands,‘95) Short range part, atand kt depend on relaxation time (a.c. conductivity)

12. A PLACET moduleapplyingkicksfromgeometric and resistive wall wakes to thebunchparticles was built and implementedintothecode Comparisonof calculation ofusingtheintermediaterangewakefunction... ...byits integral overthebunchwithsometypical CLIC numbers... ... with MATHEMATICA or... ...withPLACET module

13. A. Latina, GR, D. Schulte, EPAC 2006

14. Using PLACET withthewakefields of thecollimators, theluminosityreductioncurveswerecalculatedfor: Verticaljitter Collimatormisalignment: collimatorsareverticallyoffsetonebyone, obviouslyonlytheeffect of theverticalcollimatorsisvisible. Morerecentevaluationspresentedby J. Resta-Lopeztoday

15. Resistive wall impedances and wakefields Therearenewformulaeforthetransverseresistive wall impedance of a chamber wall with an arbitrarynumber of conductivelayersextendingover a finite length (E. Métral, N. Mounet) Theformulaearevalidforarbitrarybeamenergy, in all frequencyregimes and includetheeffects of acconductivity at high frequency Low frequency regime, imaginary part does not depend on s, real part has opposite dependence than traditional Traditional regime, goes like s-1/2 Peak in high frequency regime, curve also depends on the relaxation time of the metal

16. Resistive wall impedances and wakefields Ifweassumethesame material (sameconductivity and samerelaxation time) and different radii, wecanseethedependence on thechambersize in the different frequencyregimes. Expected: scalinglike b-3 in the „traditional“ regime, like b-2 in lowfrequencyfortheimaginarypart (image charges).

17. Resistive wall impedances and wakefields • Fromfrequencydomain to time domain to find thewakes • Short range: over a bunchlength • Long bunchregime: over a trainlength, sampledwiththebunchspacing • N. Mounetdeveloped an algorithm to carry out theinverseFouriertransform of theimpedancefunctions (whichextendover a hugefrequencyrange) based on separatedpolynomialinterpolations of theexactimpedancefunctionover a suitablenumber of frequencysubsets (Impedance Meeting, CERN, 27.08.2009) W s d W[(j-k)d]N(kd)<x>(kd) W(z-z‘)l(z‘)<x>(z‘)dz‘

18. Resistive wall impedances and wakefields • Short rangewakefieldsforcopperandstainlesssteel(CLIC-BDS bunch ≈0.6ps) • Theshapedependsboth on theconductivity and on therelaxation time • For higherconductivity (Cu) theexpected high frequencyoscillatorybehaviorappearsoverthebunchlengthweareconsidering

19. Resistive wall impedances and wakefields Long rangewakefieldsforcopperand stainlesssteel(CLIC-BDS bunchtrain ≈150ms) How it decays between subsequent bunches How it decays between subsequent bunches

20. Resistive wall impedances and wakefields Short and longrangewakefieldsforgraphite (lowerconductivity) How it decays between subsequent bunches How it decays within one single bunch • Lowerconductivityisimportantforcollimators: • For themultibunch: • Overthetrainlengththebehaviordiffersquite a lot fromthe traditional RW • Theshortrangeregimemaybecomesignificanteven in thebunch to bunch • For thesinglebunch, itisimportant to knowtherelaxation time.

21. Comments on the fast ioninstability • Considerations on the fast ioninstabilityforthe BDS (electrons) • 2km of untrappedionsareunlikely to makethebeamunstableforreasonablylowpressurevalues • Assumingvacuumpressures up to 100nTorr (CO and H2O), thebeam was notfound to beunstable in FASTION simulations • However, the FASTION simulation was donewithoutfieldionization (seetalk on ‚Vacuumspecificationsforthe CLIC linacs‘)..... • Thenewmodel of fieldionization, whichcalculatesthecriticalareafromtheregion in whichtheelectricfieldexceedsthethresholdvalue to ionize 1/10 of themolecules, cangiveionizationratestwoorthreeorders of magnitudehigher. • To bechecked: whatfraction of the BDS cangiverise to significantfieldionization

22. Future Plans • Refinecoupledbunchinstabilitysimulationswithresistive wall • Implement a realisticaperturemodelforthe BDS in thecode • Usethecorrectresistive wall wakefields(expectednot to make a large differenceforthepiperesistive wall in multi-bunchregime, butpotentiallyaffectingboththecollimatorwakefields in multi-bunch and thesinglebunch in general) • Implementtheeffect of collimators (which also requirestheuse of Yokoyafactorsdue to theflatdesign of collimators, as opposed to theroundbeamchamber) • Improvesinglebunchsimulations, donewith PLACET • Geometricwakefields: use EM simulationcodes in time domain, e.g. CST Particle Studio, to calculatethem (not trivial due to theshortbunches) and importthem as tablesinto PLACET • Resistive wall wakefields: usethecorrectcalculation, i.e. implementthemoduleforthewakefieldcalculation (N. Mounet, J. Snuverink) into PLACET • Possiblyintegratesingle-bunch and multi-bunchsimulations • Check forpossibleionissues • Check howmuch of the BDS canbeaffectedbyfieldionizationand calculatethecriticalareas • Run BDS simulationswithfieldionization