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Pile-Up density management at HL-LHC and the “crab-kissing’’ scheme

Pile-Up density management at HL-LHC and the “crab-kissing’’ scheme. S. Fartoukh HL-LHC ``brainstorming coordination’’ meeting, 25/07/2013 Acknowledgements : A. Ball, O. Bruning, B. Di Girolamo, L. Rossi. Contents. General considerations  Definition, formulae,...

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Pile-Up density management at HL-LHC and the “crab-kissing’’ scheme

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  1. Pile-Up density management at HL-LHC andthe “crab-kissing’’ scheme S. Fartoukh HL-LHC ``brainstorming coordination’’ meeting, 25/07/2013 Acknowledgements: A. Ball, O. Bruning, B. Di Girolamo, L. Rossi

  2. Contents General considerations  Definition, formulae,... Plan A (baseline  US2) and Plan B ( US1) What are the expectations ? Longer bunches, rectangular distribution  Can we really gain something (from the pile up point of view) ? Leveling, beam-beam, pile-up  What should be an ideal leveling scheme ? New possible baseline(s) for the HW and running scenarios of the HL-LHC  The “crab-kissing’’ scheme Conclusions S. Fartoukh, HL-LHC pile up meeting

  3. General considerations and immediate conclusions (1/7) 2D Pile-up density  2D density of luminosity with  Total number of pile up/collision: 140 @5E34  r:Normalizedlongitudinal distribution (  kernel depending on b*, X-angle, crab-cavity settings,... see later  R : Generalized luminosity loss factor defined such that S. Fartoukh, HL-LHC pile up meeting

  4. General considerations and immediate conclusions (2/7) • Line density and r.m.s. luminous region and • Time density and r.m.s. collision time and S. Fartoukh, HL-LHC pile up meeting

  5. General considerations and immediate conclusions (3/7) A few examples for the kernel function k(z;t)  Example 1: for collision with X-angle and no crabs (fis the Piwinsky angle, sz is the r.m.s. bunch length for Gaussian beam)  Example 2: for collision with X-angle and full-crabbing (neglecting HG effects and crab RF curvature).  Example 3: for collision with X-angle and new crab-kissing scheme (yis the so-called ``Time Piwinsky angle’’) ... see later S. Fartoukh, HL-LHC pile up meeting

  6. General considerations and immediate conclusions (4/7) The kernel function k(z ; t) in the (almost) general case with X-angle, hour-glass effect, and (standard usage of) crab-cavities including RF curvature: qX Half normalized crossing angle  (x,z) beam rotation angle (normalized) from cc in the X-plane  for ho collision w crab-cavity frequency (400 MHz) and  b*in the crossing and parallel sep. plane, respectively S. Fartoukh, HL-LHC pile up meeting

  7. General considerations and immediate conclusions (5/7) Main properties of the kernel function k(z;t)  (for synchronized collisions)  In most cases (but in example 3), the kernel is (nearly) independent of the time, . This has immediate consequences on the peak line Pile-up density which is nearly independenton the shape of the long. distribution, and on the r.m.s. bunch length sz. also R×sz cstat large sz , while loosing performance in addition ! ... So the situation is “mathematically blocked’’ unless changing the kernel from K(z) to K(t) .. S. Fartoukh, HL-LHC pile up meeting

  8. General considerations and immediate conclusions (6/7) Time pile-up distribution  Still with , the situation is qualitatively different for the peak time density (and time density in general): which decreases with the bunch length, gaining up a factor of 2 for rectangular distribution and non-zero Piwinsky angle (see later) .. Which is invariant by translation over the time of the collision, but still with a maximum of events produced at the center of the luminous region S. Fartoukh, HL-LHC pile up meeting

  9. General considerations and immediate conclusions (7/7) The crab-kissing scheme  will transform k(z ; t)  K(z) into k(z ; t) K(t)  .. with the introduction of a time Piwinsky angle y, instead of the stantardPiwinsky angle f:physically a time dependent parallel separation at the IP, adding c.c.’s in the parallel sep. plane (..see later)  ... and therefore transfer the properties of the time densitymt(t) to mz(z) ,and conversely. S. Fartoukh, HL-LHC pile up meeting

  10. Plan A & Plan B (1/4) • Two main scenarios, with (Plan A) or w/o crab-cavities (Plan B) both, with lumi leveling using b* at slightly different value (5E34 and 4E34, resp.)  giving the same leveling time (8.6 h)  giving the same size of the luminous region: sz,lum 4.5 cm r.m.s. and similar peak line pile-up density (d<m>/dz)max 1.0  1.3 event/mm (i.e. 1.4 1.8 event/mm for the “worst collisions”) 1) Plan A (US2) : 400 MHz crab-cavities & round optics (15 cm b*) with • Gaussian distribution of nominal bunch length (7.5 cm r.m.s.) • Full crabbing (full crab-voltage) to reduce the 2D pile up density with head-on collisions (but maximize as well the head-on bb tune shift) 2) Plan B (US1) : BB wire compensator & flat optics (50/10 cm b*) with • Gaussian distribution of increased bunch length (9 cm r.m.s. as in 2012) • Not more than 10 s X-angle in the plane of biggest b* (instead of 15-16 s needed w/o BB wire compensator) S. Fartoukh, HL-LHC pile up meeting

  11. Plan A & Plan B (2/4) S. Fartoukh, HL-LHC pile up meeting

  12. Plan A & Plan B (3/4) • Line Pile up density for Gaussian (black) and rectangular (red) bunch shape of the same r.m.s. 1.25 event/mm (up to 1.8 for “worst collisions”) Plan A (@ 5E34 sz=7.5 cm)  worst case at min. b* Plan B (@ 4E34 sz=9.0 cm)  worst case at min. b* 4 sz,lum=18 cm 4 sz,lum=18 cm  As predicted • For both plans, no sensitivity of the peak density v.s. bunch shape • 20% reduction from Plan A to Plan B but driven by the reduced leveled lumi, not by the increased r.ms. bunch length S. Fartoukh, HL-LHC pile up meeting

  13. Plan A & Plan B (4/4) • Time Pile up density for Gaussian (black) and rectangular (red) bunch shape of the same r.m.s. 0.35 event/ps (up to 0.48 for “worst collisions”) Plan A (@ 5E34, sz=7.5 cm)  worst case at min. b* Plan B (@ 4E34, sz=9 cm)  worst case at min. b* 4 st,lum=650 ps 4 st,lum=850 ps  As predicted • For both plans, small gain in relative from Gaussian to rectangular, even more with non-zero Piwinsky angle (Plan B) • Sensible gain with the bunch length from Plan A to Plan B, and even more for rectangular shape S. Fartoukh, HL-LHC pile up meeting

  14. Longer bunches, rectangular distribution (1/6) • General rules for Pile up density w/o crab-kissing scheme • Line density: nothing to gain with longer or rectangular bunches • Time density: some gain for longer Gaussian bunches for the peak time density, strongly amplified for rectangular shapes with non-zero Piwinsky angle ... but the collision time seems too short anyway to be usable! • Performance (leveling time): can only be worstfor longer bunches (if keeping them long for the full coast), due the degradation of the loss factor R: - from crab RF curvature for Plan A - from the Piwinsky angle for Plan B - from hour-glass effects for both Plans S. Fartoukh, HL-LHC pile up meeting

  15. Longer bunches, rectangular distribution (2/6) • Lumi loss factor Rvs. r.m.s. bunch length [cm] for Gaussian (black) and Rectangular (red) distribution: Plan A (snapshot @ 15 cm b*) No Hour-Glass (HG), nor crab-cavity RF curvature effect  No sensitivity (R=1) HG effect only (dotted-dashed) RF curvature effect only (dotted)  400 MHz crabs does not fit! PlanA-0 (sz=7.5 cm, Gaussian): R = 0.83, Tlevel= 8.6h All effects combined (solid) PlanA-2 (sz=12.5 cm, Rectangular, with additional HH RF): R=0.53, Tlevel= 6.4h ! Bunch much too long w.r.t. lRF/4 !! PlanA-1 (sz=10 cm, Gaussian): R=0.70, Tlevel= 7.8h S. Fartoukh, HL-LHC pile up meeting

  16. Longer bunches, rectangular distribution (3/6) • Lumi loss factor vs. r.m.s. bunch length [cm] for Gaussian (black) and Rectangular (red) distribution: Plan B (snapshot @ min. b*) No HG effect (dotted) HG effect included (solid) PlanB-0 (sz=9 cm, Gaussian): R = 0.68, Tlevel= 8.6h PlanB-1 (sz=10 cm, Gaussian): R = 0.65, Tlevel= 8.2h PlanB-2 (sz=12.5 cm, Rectangular, with additional HH RF): R = 0.54, Tlevel= 7.0 h S. Fartoukh, HL-LHC pile up meeting

  17. Longer bunches, rectangular distribution (4/6) • Line pile up density... do we gain something?  Only slightly at the beginning of SB (large b*), not in the end, because the line density varies like 1/R/sz  cst in a regime where b*/sz  1 Plan A PlanA-0 (sz=7.5 cm, Gaussian) 1.10  1.27 event/mm PlanA-1 (sz=10 cm, Gaussian) 0.90  1.14 event/mm Max line density [mm -1] vs. sz [cm] at the End (solid) and Beginning (dashed) of stable beam, for Gaussian (black) and Rectangular (Red) distribution PlanA-2 (sz=12.5 cm, Rectangular) 0.81  1.23 event/mm S. Fartoukh, HL-LHC pile up meeting

  18. Longer bunches, rectangular distribution (5/6) Plan B ... same conclusions PlanB-0 (sz=9 cm, Gaussian) 0.95  1.03 event/mm PlanB-1 (sz=10 cm, Gaussian) 0.89  0.98 event/mm Max line density [mm -1] vs. sz [cm] at the End (solid) and Beginning (dashed) of stable beam, for Gaussian (black) and Rectangular (Red) distribution PlanB-2 (sz=12.5 cm, Rectangular) 0.85  0.95 event/mm S. Fartoukh, HL-LHC pile up meeting

  19. Longer bunches, rectangular distribution (5/6) • Time pile up density...do we gain something?  Definitely YES because the time density varies like 1/sz (more or less independently of the geo loss factor R) [ps-1] Pan A0: 7.5 cm (Gaussian) Pan B0: 9.0 cm (Gaussian) 10.0 cm (Gaussian) 12.5 cm (Rectangular) [ns] Plan A0, A1, A2 (5E34)  snapshot at min. b* Plan B0, B1, B2 (4E34)  snapshot at min. b*  1 event (in average) every 10 ps for Plan B2 (12.5 cm, rectangular) ... but 10 ps is still a rather short time ! S. Fartoukh, HL-LHC pile up meeting

  20. Lumi Leveling, Pile up and beam-beam (1/3) Putting everything in perspective, what should be an ideal lumi leveling scheme? Keep the beam stable Reduce the peak lumi with good dynamic range, in fact the total number of pile-up, at cst and ideally reduced peak line density of pile-up (i.e. at constant or larger luminous region) Easy to operate Ideally with minimal head-on beam-beam tune spread (including contribution of LHcB), or beam-beam driven resonances. S. Fartoukh, HL-LHC pile up meeting

  21. Lumi Leveling, Pile up and beam-beam (2/3) Do we have it?NO(T YET) to my humble opinion. S. Fartoukh, HL-LHC pile up meeting

  22. Lumi Leveling, Pile up and beam-beam (3/3)... up to DQbb= 0.033 with b* leveling in 3 IRs ! S. Fartoukh, HL-LHC pile up meeting

  23. The crab-kissing scheme (1/10) X ax1=Qx:(x-z) normalized rotation angle for B1 ax2= - Qx:(x-z) normalised rotation angle for B2 x1 x2 Z1 Z2 No change in the X-plane with full-crabbing Z ax1-ax2 =2Qx: full normalized X-angle with ax1+ax2  0 S. Fartoukh, HL-LHC pile up meeting

  24. The crab-kissing scheme (2/10) Y a||1=a|| :(y-z) normalized angle for B1 a||2=a|| :(y-z) normalized angle for B2 Assuming CC in the parallel separation plane Z1 Y1 Y2 Z Z2  Reduce the collision time (too short anyway) and therefore the lumi and bb tune shift, w/o reducing the size of luminous region, i.e. at cst or improved (see later) pile up density.  Flat optics, e.g. 30/7.5 cm (SLHCPR049) more favorable to mitigate the CC voltage needed  Typically 4MV@ b*=7.5 cm in the || plane (flat optics) and 6MV @ b*=15 cm (round optics) S. Fartoukh, HL-LHC pile up meeting

  25. The crab-kissing scheme (3/10) X x2 x1 Z2 ax2 Z1 Everything could also be combined in the X-plane ax1 Z ax1-ax2 =2Qx: full normalized X-angle BUT ax1+ax20  Would typically require 6MV more for only one of the two beams (b*@=15cm, round)  But creating a net dissymmetry between beams .. I do not like, although I do not have (yet) a stronger argument. S. Fartoukh, HL-LHC pile up meeting

  26. The crab-kissing scheme(4/10) Term coming from CC in phase in the X plane  HL-LHC baseline Term from CC in anti-phase in the || plane  NOT (yet) in the HL-LHC baseline The new kernel function with CCs in X and || planes ... Neglecting HG effect, and crab-RF curvature (cos(x)=1,sin(x)=x), the first term is 1 for full crabbing in the X-plane, and the second term is S. Fartoukh, HL-LHC pile up meeting

  27. The crab-kissing scheme(5/10) Analytical expressions for Gaussian and Rectangular distributions neglecting HG effect and c.-c. RF curvature (wsz/c<< 1) S. Fartoukh, HL-LHC pile up meeting

  28. The crab-kissing scheme(6/10) For Gaussian bunch distribution (no HH RF)  crab-cavities in the || plane are back for lumi leveling, w/o impacting on the line pile up density and at reduced DQbb(not discussed in further details here) For rectangular bunch distribution (HH RF)  crab-cavities in the || plane are back for Lumi leveling at reduced line pile up density and reduced DQbb Or “peak line density leveling” at increased lumi and reduced DQ bb S. Fartoukh, HL-LHC pile up meeting

  29. The crab-kissing scheme(6/10) [mm-1] 3 main cases being simulated by ATLAS and CMS Case 1 : HL-LHC baseline (or plan B w/o crab but flat optics and BB wire compensators)  Very good approximation (in black dashed line) with a Gaussian: 1.28 event/mmand slum= 4.4 cm z [cm] S. Fartoukh, HL-LHC pile up meeting

  30. The crab-kissing scheme(7/10) Case 2: example of HL-LHC possible newline HH RF (8 MV) for rectang. bunches with sz=9 cm (30 cm full length)  2 cc modules in the X-plane (8 MV), 1 module in the || plane (4 MV)  flat optics (b*=30 cm in X-plane, 7.5 cm in the || plane) with 12s=400 mrad full crossing angle (optimistic BB wire certainly needed) Two possible running scenarios:  Case2a: Leveling at constant lumi (5E34), first with b* in || or X planes, then zeroing the 4MV of the CC in the || plane.  Case2b: Leveling at constant peak density (1.28 event/mm), only with the CC in the || plane, starting directly with min b* .. giving L=1E35 ! S. Fartoukh, HL-LHC pile up meeting

  31. The crab-kissing scheme(8/10) Case 2a1 Leveling @ 5E34, first with b* in || plane (No gain in DQbb) Time with , L= 15 cm and =2.5 S. Fartoukh, HL-LHC pile up meeting

  32. The crab-kissing scheme(9/10) Case 2a2 Leveling @5E34, first with b* in X plane DQbb reduced but big b* aspect ratio  “Anti-ATS” needed Time with , L= 15 cm and =2.5 S. Fartoukh, HL-LHC pile up meeting

  33. The crab-kissing scheme(10/10) Case 2b Leveling instead at 1.28 event/mm L1035 i.e. mtot =280!! Time with , L= 15 cm and =2.5 S. Fartoukh, HL-LHC pile up meeting

  34. Conclusions • For scenarios with 140 pile up/Xing, a peak line pile up density of 1.28 event/mm is reached at a time or another during the leveling process.  The Phase II detectors shall be ready to digest this number. • Crab-cavity in the parallel sep. plane offered however a wonderful tool to make the best use of this number for • Integrated performance (in case of short fill) • Lumi (or peak density) leveling, • Beam-beam tune shift with 3 IRs running (presently a bet for HL)  Crabs are a keystone for the HL-LHC performance (virtual lumi), but to have more we have to pay more: in crab-modules or BB-wire or MS magnets, BUT also RF (HH system) and cryo for scenarios @ 10E35. S. Fartoukh, HL-LHC pile up meeting

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