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

The HiLumi LHC Design Study is included in the High Luminosity LHC project and is partly funded by the European Commission within the Framework Programme 7 Capacities Specific Programme, Grant Agreement 284404.

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

S. FartoukhHL-LHC ``brainstorming coordination’’ meeting, 25/07/2013

Acknowledgements: A. Ball, O. Bruning, B. Di Girolamo, L. Rossi

S. Fartoukh, HL-LHC pile up meeting 2

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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


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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: Normalized longitudinal distribution (

kernel depending on b*, X-angle, crab-cavity settings,... see later

R : Generalized luminosity loss factor defined such that


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• Line density and r.m.s. luminous region

and

• Time density and r.m.s. collision time

and


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• A few examples for the kernel function k(z;t) Example 1: for collision with X-angle and no crabs (f is 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 (y is the so-called ``Time Piwinsky angle’’)

... see later


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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


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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 independent on the shape of the long. distribution, and on the r.m.s. bunch length sz.

also R×sz cst at large sz , while loosing performance in addition !... So the situation is “mathematically blocked’’ unless changing the kernel from K(z) to K(t) ..

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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 translationover the time of the collision, butstill with a maximum of events produced at the center of the luminous region

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• 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 stantard Piwinsky 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 density mt(t) to mz (z) , and conversely.


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) 7/

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Plan A & Plan B (2/4)Plan A Plan B

# Bunches 2808

p/bunch [1011] 2.2 (1.11 A)

gex,y [mm] 2.5

sz [cm] 7.5 9.0

400 MHz Crab-cavity Yes (12 MV per IR side per beam) No

bb wire compensator A priori not needed Mandatory

Optics type Round Flat

Levelling strategy b* in both planes b* in separation plane only

b* in X plane [cm] from start to end of SB 69 15 50 50

b* in sep. plane [cm] from start to end of SB 69 15 90 10

X-angle [mrad] 590 (12.5 s) 260 (10 s in the plane of biggest b*)

Lumi loss factor (with HG effect & crab RF curvature) from start to end of SB 0.956 0.832 0.742 0.683

Virtual lumi [1034] (including HG and RF curvature effect) 20.1 11.1

Leveled lumi [1034] 5.0 4.0

Tleveling [h] 8.6

Integrated lumi [fb-1 ] for 150 days/year for 40% machine efficiency (TSB/TRUN) 260 210

Average number of pile up events / crossing 140 (200 for “worst collisions”) 110 (165 for “worst collisions”)

r.m.s. luminous region [cm] for minimum b* 4.4 4.4

Max pile up line density reached at the IP [mm-1] for minimum b* 1.27 (1.81 for “worst collisions”) 1.03 (1.47 for “worst collisions”)

r.m.s. collsion time [ps] for minimum b* 163 212

Max pile up time density [ps-1] for minimum b* 0.34 (0.48 for “worst collisions”) 0.21 (0.30 for “worst collisions”)

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Plan A & Plan B (3/4)

4 sz,lum=18 cm

1.25 event/mm (up to 1.8 for “worst collisions”)

4 sz,lum=18 cm

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• Line Pile up density for Gaussian (black) and rectangular

(red) bunch shape of the same r.m.s.

As predicted1. For both plans, no sensitivity of the peak density v.s. bunch shape

2. 20% reduction from Plan A to Plan B but driven by the reduced leveled lumi, not by the increased r.ms. bunch length

Plan A (@ 5E34 sz=7.5 cm) worst case at min. b*

Plan B (@ 4E34 sz=9.0 cm) worst case at min. b*


Plan A & Plan B (4/4)

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• Time Pile up density for Gaussian (black) and rectangular

(red) bunch shape of the same r.m.s.

As predicted1. For both plans, small gain in relative from Gaussian to

rectangular, even more with non-zero Piwinsky angle (Plan B)

2. Sensible gain with the bunch length from Plan A to Plan B, and even more for rectangular shape

0.6 0.4 0.2 0.0 0.2 0.4 0.6

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0.35 0.35 event/ps (up to 0.48 for “worst collisions”)

4 st,lum=650 ps

Plan A (@ 5E34, sz=7.5 cm) worst case at min. b*

4 st,lum=850 ps

Plan B (@ 4E34, sz=9 cm) worst case at min. b*


Longer bunches, rectangular distribution (1/6)

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• General rules for Pile up density w/o crab-kissing scheme1. Line density: nothing to gain with longer or rectangular bunches

2. 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!

3. Performance (leveling time): can only be worst for 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


• Lumi loss factor R vs. r.m.s. bunch length [cm] for Gaussian (black) and Rectangular (red) distribution: Plan A (snapshot @ 15 cm b*)

0.06 0.08 0.10 0.12

0.6

0.7

0.8

0.9

1.0


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!

All effects combined (solid)PlanA-0 (sz=7.5 cm, Gaussian): R = 0.83, Tlevel = 8.6h

PlanA-1 (sz=10 cm, Gaussian): R=0.70, Tlevel = 7.8h

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 !! 7/

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• Lumi loss factor vs. r.m.s. bunch length [cm] for Gaussian (black) and Rectangular (red) distribution: Plan B (snapshot @ min. b*)

0.06 0.08 0.10 0.12

0.60

0.65

0.70

0.75

0.80

0.85

0.90 No HG effect (dotted)

HG effect included (solid)

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

PlanB-0 (sz=9 cm, Gaussian): R = 0.68, Tlevel = 8.6h

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0.2 0.1 0.0 0.1 0.2

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• 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

0.08 0.09 0.10 0.11 0.12

0.9

1.0

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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

PlanA-2 (sz=12.5 cm, Rectangular) 0.81 1.23 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

Plan A

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PlanB-1 (sz=10 cm, Gaussian) 0.89 0.98 event/mm

PlanB-2 (sz=12.5 cm, Rectangular) 0.85 0.95 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

Plan B ... same conclusions

0.08 0.09 0.10 0.11 0.12

1.1

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PlanB-0 (sz=9 cm, Gaussian) 0.95 1.03 event/mm

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• 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)

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0.6 0.4 0.2 0.0 0.2 0.4 0.6

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Plan A0, A1, A2 (5E34) snapshot at min. b*

Plan B0, B1, B2 (4E34) snapshot at min. b*

[ps-1]

[ns]

1 event (in average) every 10 ps for Plan B2 (12.5 cm, rectangular)... but 10 ps is still a rather short time !

12.5 cm (Rectangular)

10.0 cm (Gaussian)

Pan A0:7.5 cm (Gaussian)

Pan B0:9.0 cm (Gaussian)



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Lumi Leveling, Pile up and beam-beam (1/3)• Putting everything in perspective, what should be an

ideal lumi leveling scheme?1. Keep the beam stable

2. Reduce the peak lumi with good dynamic range, in fact the total number of pile-up,

3. at cst and ideally reduced peak line density of pile-up (i.e. at constant or larger luminous region)

4. Easy to operate

5. Ideally with minimal head-on beam-beam tune spread (including contribution of LHcB), or beam-beam driven resonances.


Lumi Leveling, Pile up and beam-beam (2/3)

• Do we have it? NO(T YET) to my humble opinion.

Leveling techniques v.s. Criteria

Crab(std way)

b* Parallel separation Crab-kissing(.. see later )

Beam-stability ?(machine reproducibility

and MO polarity)

?(to be tested with new MO

polarity)

Lumi reduction Pile-up density Operability ?

(machine reproducibility)

Beam-beam ?(DQbb=0.033 with LHCb)

?(a priori bad for resonance

but works for LHCb in 2012)

(at least for DQbb ~ 0.016

including LHCb)

Vote UnanimouslyRejected

Baseline ...by default

Not popular... but might change

To be seen,... but need crabs!

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Lumi Leveling, Pile up and beam-beam (3/3)... up to DQbb= 0.033 with b* leveling in 3 IRs !

Parameters Leveling with c.-c. Leveling with b*

# bunches 2808

bunch charge [1011] 2.2

emittance [mm] 2.5

r.m.s. bunch length [cm] 7.5

full X-angle [mrad] 590

initial b* [cm] 15 72

c.-c. initial voltage [MV] - 6.6 12.5

initial Piwinsky angle 4.76 0

initial lumi loss factor 0.21 1.0

levelled lumi [1034cm-2s-1] 5.0

initial luminous region [cm] 1.1 4.3

initial bb tune shift for 3 IRs(IR1, IR5 & IR8)

0.016 (0.011+2×0.0025)

0.033 (3×0.011)

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The crab-kissing scheme (1/10)

• No change in the X-plane with full-crabbingX

Z

x2x1

Z1 Z2

ax1-ax2 =2 Qx : full normalized X-angle with ax1+ax2 0

ax1=Qx :(x-z) normalized rotation angle for B1 ax2= - Qx :(x-z) normalised rotation angle for B2


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The crab-kissing scheme (2/10)• Assuming CC in the parallel separation planeY

Z

Y2Y1Z1

Z2

a||1=a|| :(y-z) normalized angle for B1 a||2=a|| :(y-z) normalized angle for B2

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)


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The crab-kissing scheme (3/10)

• Everything could also be combined in the X-planeX

Z

x2x1

Z1

Z2

ax1

ax2

ax1-ax2 =2 Qx : full normalized X-angle

BUT ax1+ax20 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.


• 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

The crab-kissing scheme(4/10)

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Term from CC in anti-phase in the || plane NOT (yet) in the HL-LHC baseline

Term coming from CC in phase in the X plane HL-LHC baseline


The crab-kissing scheme(5/10)• Analytical expressions for Gaussian and Rectangular distributions

neglecting HG effect and c.-c. RF curvature (wsz/c<< 1) Quantity Gaussian (rms sz) Rectangular (half-length L= 3×sz)

r

f(Standard Piwinsky angle in X-plane)

for full crabbing for full crabbing

RX(Standard loss factor)


y(“Time” Piwinsky angle in || plane)

RII(“Time”loss factor)

at high y

R(Total loss factor)


(Line pile up density) Gaussian independent of y !

Reopen the path for lumi leveling with crab-cavities

Rectangular at high y and full crabbing ! ... and reducing the peak density

Peak line density for full crabbing in the X-plane (f=0)

at high y Reduced by a factor of 2 w.r.t. Gaussian of the same r.m.s.

... Leveling the peak density starting at L=1E35!?

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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 for1. Lumi leveling at reduced line pile up density and reduced DQbb

2. Or “peak line density leveling” at increased lumi and reduced DQ bb


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The crab-kissing scheme(6/10)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:

z [cm]

[mm-1]

1.28 event/mm and slum= 4.4 cm


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The crab-kissing scheme(7/10)• Case 2: example of HL-LHC possible newlineHH RF (8 MV) for rectang. bunches with s z=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 !


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The crab-kissing scheme(8/10)• Case 2a1 Leveling @ 5E34, first with b* in || plane

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Beginning of Fill: L=5E34HH RF voltage [MV] 8

CC voltage in X plane [MV] 8

CC voltage in || plane [MV] 4

b* in X plane [cm] 30

b* in || plane [cm] 74

Full X angle [mrad] 400

Bunch length r.m.s. [cm] 9.0

Min b* reached : L=5E34HH RF voltage [MV] 8




b* in || plane [cm] 7.5



CC off in || plane L=5E34HH RF voltage [MV] 8







End of leveling ..back to case 1HH RF voltage [MV] 0







with , L= 15 cm and =2.5

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Time

(No gain in DQbb)


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The crab-kissing scheme(9/10)• Case 2a2 Leveling @5E34, first with b* in X plane

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Beginning of Fill: L=5E34HH RF voltage [MV] 8







Min b* reached : L=5E34HH RF voltage [MV] 8







CC off in || plane L=5E34HH RF voltage [MV] 8







End of leveling ..back to case 1HH RF voltage [MV] 0








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DQbb reduced but big b* aspect ratio “Anti-ATS” needed


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The crab-kissing scheme(10/10)• Case 2b Leveling instead at 1.28 event/mm

0.2 0.1 0.0 0.1 0.2

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Beginning of Fill: L=9.9E34HH RF voltage [MV] 8







2MV in || plane : L=7.2E34HH RF voltage [MV] 8







0 MV in || plane : L=5.6E34HH RF voltage [MV] 8







L=5.0E34 ...back to case 1HH RF voltage [MV] 0








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L1035 i.e. mtot =280!!


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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

1. Integrated performance (in case of short fill)

2. Lumi (or peak density) leveling,

3. 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.

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

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