Work in progress: Improved models of collimation margins with TCT damage limit R. Bruce, L. Lari 1 Input and discussions: R. Assmann, A. Bertarelli, C. Bracco, F. Carra, B. Goddard, S. Redaelli, R. Tomas 1. IFIC-CSIC, Valencia, and CERN

Outline Components of collimator margins and influence on performance Failure scenarios to be considered for critical margins Methods for calculating margin from optics errors Pessimistic beta-beat, 90 deg phase advance (used so far) Protect against max escaping amplitude Protect TCT against leakage above damage limit (More) realistic failure scenario with TCT impacts Future work and conclusions R. Bruce,

Collimation system Multi-stage collimation system In case of failures, we must ensure protection of TCTs and aperture Minimum aperture that can be protected imposes limit on β* and therefore luminosity => collimator settings limit luminosity Protection margins include orbit, optics errors, lumi scans, positioning errors and setup errors R. Bruce, σ calculated with emittance = 3.5μm 3 TCP TCS7 Aperture TCS6/ TCDQ TCT TCLA7 beam 5.7 σ n 8.5 σ n 17.7 σ n 9.3 σ n 15.0 σ n 17.5 σ n 5.7 σ n 8.5 σ n 17.7 σ n 9.3 σ n 11.8 σ n 14.1 σ n 4.3 σ n 6.3 σ n 8.3 σ n 7.1 σ n 9.0 σ n 10.5 σ n 6.0 σ n 7.0 σ n 10.0 σ n 7.5 σ n 8.3 σ n 8.4 σ n 2010, β*=3.5m, 3.5 TeV 2011, β*=1.0m, 3.5 TeV 2012, β*=0.6m, 4 TeV Nom, β*=0.55m, 7 TeV 2010, β*=3.5m, 3.5 TeV 2011, β*=1.0m, 3.5 TeV 2012, β*=0.6m, 4 TeV Nom, β*=0.55m, 7 TeV Secondary halo Primary halo Tertiary halo Kicked beam

Considered scenarios for margin calculations: Dump failures For critical margins, consider fast (BLMs cannot save us!) accident scenario where sensitive equipment should be protected: beam dump failure Studied in detail previously (B. Goddard et al) in many references. Some are: LHC project note 293, LHC Design report, CERN-ATS , T. Kramer PhD thesis, TUPEB063 in IPAC10, MOPD48 in HB2010, Evian and Chamonix talks Filling with bunches of the LHC ring has “hole” – abort gap – to allow rise of the 15 dump kickers from zero to full field - standard dump R. Bruce, Abort gap

Considered scenarios for margin calculations: Dump failures Some possible failures kickers fire at the wrong moment 1 or more kickers fire without the others following Kickers fire correctly but abort gap is populated In all cases: One or several bunches see intermediate kicks and can potentially be deflected onto sensitive equipment such as the TCTs or machine aperture – therefore, dump protection (TCDQ-TCSG6) installed We must make sure that collimation hierarchy has sufficient margins so that imperfections don’t expose TCTs or aperture R. Bruce, Protection Beam Aperture Protection Aperture Beam

Margins for optics errors So far: assume most pessimistic β-beat and calculate needed margin Assuming now +10% at location to protect, -10% at protection device (very pessimistic!) Change in margin (in σ) of an aperture is given by Implicit pessimistic assumption: aperture bottlenecks always at 90 deg from kick More detailed model: account for full phase space motion First study on leakage to ring collimators during abnormal dumps, including the actual phase advance with imperfections, done in PhD thesis by T. Kramer (2011) for beam 1 at 7 TeV, nominal machine R. Bruce, Nominal: 7.1 σ distance to the beam +10% β-beat: 6.8 σ distance to the beam -10% β-beat: 7.5 σ distance to the beam Example: Beam

Schematic phase space motion Example: Initial bunch (1) kicked (2), cut by protection device at 94 deg (3) With a favorable phase advance, aperture (4) is not in danger of intercepting remaining beam For a less favorable phase advance (5), a fraction of a bunch can still hit an aperture at the same opening as the protection device Idea 1 - conservative approach: calculate largest amplitude of surviving beam for given halo extension (e.g. 4.3 σ cut by primary collimators) as function of phase advance All sensitive equipment should be at larger amplitudes Idea 2: Based on damage limit, we can calculate margin that limits leakage to acceptable level R. Bruce, Normalized phase space of kicked beam

Idea 1 – largest escaping amplitude Calculation inputs Extension of halo – “radius of disk” Kick amplitude Phase advance kick – protection device Phase advance kick – device to be protected R. Bruce, About 2 σ retraction IR6-TCT needed for complete protection, including errors of deg. on phase and 10% beta-beat. 2.8 σ for protection on all phases. On top of this we should add the orbit! More margin needed than used so far Pessimistic! The TCTs are made to intercept particles and survive a small leakage Standard optimization problem – even analytic solution possible if linear motion is assumed Plot max escaping amplitude vs kick, for nominal phase advance and 4 σ beam extension Lose another ~1 σ if phase errors are considered B1

Idea 2 – keep leakage well below damage limit We have to estimate leakage past dump protection onto TCTs and triplets Two methods considered: Linear phase space integration: extremely fast (~60 ms per congifuration) but collimators treated as black absorbers and neglecting non-linearities Modified SixTrack (see talk L. Lari): including out-scattering from collimators and sextupoles, but slower (3 minutes – hours per configuration depending on statistics) R. Bruce,

Linear phase space integration Each collimator makes cut in the initial phase space (before kick). In linear approximation Impacting intensity is integral of bunch distribution over phase space area outside a TCT but inside all upstream collimators. Using adaptive Monte-Carlo integration in Mathematica. R. Bruce, Example: β*=60cm, all TCTs and IR6 TCSG at 7.1 σ, IR7 not shown. Kick amplitude = 7.1 σ Beam hitting TCT About 6 permille assuming Gaussian

Comparison integration-SixTrack Modified SixTrack (L. Lari – see next talk): Gaussian bunch tracked from IR1, kicks from all MKD implemented and can be set independently Benchmark on dummy case: Agreement within a few percent R. Bruce,

Studied failure scenario Several bunches in a train should be studied – each bunch sees different kick during the rise of the dump kickers Standard asynchronous dump – 1 bunch at 50 ns, 2 bunches at 25 ns at dangerous phases Single module pre-fire: slower rise of kick if only 1 kicker starts => more bunches affected. Worst case? Doing phase space integration for all kicks and summing the result – for now studying 50 ns and β*=60cm R. Bruce, Thanks to B.Goddard for data file

Scan over optics errors Errors on beta function and phase advance should be considered Optics errors measured, but measurement uncertainty similar to measurement (~10% β-beat). Future optics errors unknown Therefore sampling 1000 random optics configurations For each optics: scan over TCT retraction. For each TCT retraction: sum of leakage over bunches Doing phase space integration for all cases– in total TCT leakage calculated in configurations in 2 hours on desktop computer R. Bruce, TCDQ IR1 TCTH

Scan over optics errors – 0.05% bins R. Bruce,

Margins with allowed (small) leakage to TCTs For each TCT retraction, calculating the smallest leakage higher than 99% of all optics configurations Talk A. Bertarelli in MPP workshop: Above 5e9 7 TeV, the TCT suffers plastic deformations Above 2e10 7 TeV, particle detachment occurs, polluting surrounding elements – must be avoided! Between 5e9 and 2e10, we can recover by moving TCTH vertically to use an undamaged surface – no major intervention required to recover Present 0.55 σ margin is well below damage operation was safe! R. Bruce, Leakage (in fraction of 1 bunch) hitting the TCT, summed over all bunches during pre-fire of one kicker – 4 TeV, 50 ns, β*=60cm Assuming bunch population of 1.7e11 p. Other failure types still to be studied, as well as 25ns and smaller β*. preliminary 7 TeV Plastic deformation limit 7 TeV limit for spray of tungsten particles – 5 th axis still usable 4 TeV

Worst-case scenario R. Bruce, NominalWorst-case of 1000 random configurations As by-product, we can estimate impacts on a TCT in a realistic worst-case scenario Taking worst case of 1000 random optics error configurations + additional orbit shift in IR7 (VERY pessimistic!)

Worst-case scenario As function of kick amplitude, dangerous bunches have kicks of 5-10 σ. TCT losses reach maximum at about 7 σ kick (~50% escapes dump protection). Using modified SixTrack, cross- checked with phase space integration – excellent agreement! Summed over all bunches, about 30% of one bunch hits the TCT To be studied: Can we have an even worse case with another combination of dump kickers firing?

SixTrack loss maps (L. Lari) Loss maps show drastic increase of losses at TCT compared to nominal configuration R. Bruce, Optics and orbit imperfections – worst bunch Reference case – dump in perfect machine Preliminary L. Lari

TCT impacts from SixTrack per bunch R. Bruce,

Impacts on IR1 TCT from SixTrack TCT impacts concentrated on one jaw with impact parameter mm Inelastic interactions extracted, summed over all bunches Next: FLUKA + Autodyn in collaboration with MME? Inelastic interactions on TCT from SixTrack (L. Lari)

Future work New iteration of margin calculations with new damage limit with realistic TCT impact distribution. Quantify ratio to damage limit to be used for margins We should extend the study to include other dump failure scenarios 25 ns other β*-values - phase advance conditions different! ATS optics? Checks of margin TCT-triplet – what is the triplet damage limit? Implications on margin TCT-triplet? Can we gain margin in terms of optimized phase advance? Optics by S. Fartoukh with 90 instead of 94 deg phase advance from dump kicker to TCDQ to be checked. Can we optimize phase advance to critical TCTs as well? Drawback: how accurately can we actually correct the phase advance in the machine? Realistic? R. Bruce,

Summary Collimator margins in hierarchy should be as small as possible for optimizing luminosity without compromising protection of TCTs and triplets More detailed model of optics margins presented: keep leakage to the TCT below damage level considering realistic optics conditions Two methods – SixTrack and linear phase-space integration – in agreement. Integration method very fast – can efficiently treat very large parameter sets With 50 ns and β*=60cm, we were well below limit for plastic deformation in 2012 in agreement with previous pessimistic model. If we can tolerate damage where 5 th axis can be used to recover, margin could be decreased. Proposed more realistic multi-bunch failure scenario for TCT impacts with imperfect optics, simulated with SixTrack Future work: extend study to other optics and failure scenarios. Iterate on TCT damage limit with realistic impact distributions. Comments and suggestions welcome! R. Bruce,

Backup R. Bruce,