Tune-scans for HL-LHC and LHC - TRIUMFlin12.triumf.ca/text/design_notes/...03-tune_scans_for_HLLHC_2017.pdf · standard MadX-SixTrack-SixDesk env. D. Kaltchev (CERN-TRIUMF HL-LHC

Tune-scans for HL-LHC and LHC

D. Kaltchev

CERN-TRIUMF HL-LHC Collab.

February 3, 2017

D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 1 / 34

Optics configurations usedWhat’s in black is kept constant including β? (leveling scenarios not considered)

HL-LHC V1.2 baseline:

bunch charge Nb=2.2 or 1.1×1011;IR1,5 Xing half-ang = 295 µrad, β?= 15 cmIR8 β? = 3m, Xing half-ang =-135-250=-385 µrad (LHCb spect. pol.=-1)IR2 β? = 10m, hor. sep. = 2 mm, Xing = 170 µrademitn= 2.5 µm, bunch len. = 7.5 cm, ∆p

p =2.7×10−4

25 ns, chrom = 3

LHC V6.503 at peak Lumi 1× 1034

conditions for trackingHirata BB ON, crab cavities OFF or ON with fully crabbing of strong beam

enforced (the default)

standard MadX-SixTrack-SixDesk env.


Tune-scan (TS) conditions

tune-scan A HL-LHC,Nb=1.1×1011, crabs OFF, along line ‖ diag. –>

tune-scan B LHC (to compare with TS A)

tune-scan C HL-LHC,Nb=2.2×1011, crabs ON. It is 2D: looking for a betterw.p. closer to diagonal in yellow –>

(Yannis)

QxBB=Qx0+∆Qx QyBB=Qy0+∆QyQx(y)BB is as reported by MadX or SixTrack with CC on

62.26 62.27 62.28 62.29 62.30 62.31 62.32 62.33

60.26

60.27

60.28

60.29

60.30

60.31

60.32

60.33

Ord. 5 to 13

2

4

6

8

1D

0.300 0.305 0.310 0.315 0.320

0.305

0.310

0.315

0.320

0.325

Qx0

Qy0

012

6

345

2D


Tune-scan AHL-LHC with Nb = 1.1×1011, IP1,5,2,8 and crab OFF

Figure 1 OLD STYLE PLOT: DA-by-angle dep. on perturbed tune

18 azimuthal angles

split into two plots

Nominal HL-LHCfootprint at 2.2 E11

old style plot

< 2010

Tune-scan line

QxBB=Qx0−ΔQ


Tune-scan A

New-style plots: Let’s color intervals between the constant-angle contours.Color Hue is proportional to angle value. Some overlapping unfortunately takes place ..

62.27 62.28 62.29 62.30 62.312

4

6

8

10

QxBB

DA

HΣL

VERT

HOR4.59.

13.518.

22.527.

31.536.

40.545.

49.554.

58.563.

67.572.

76.581.

85.5

Here color Hue is proportional to upper bound of the angle interval (4.5 deg)


Tune-scan A

Keeping all angles, just shortening the Legend (scaling the Hue).

And shifting by the approximately constant BB tune shift ∆Qx = 0.0155.Qx0 is the unperturbed tune.

62.28 62.29 62.30 62.31 62.32 62.332

4

6

8

10

Qx0

DA

HΣL

VERT

HOR4.5

12.6

20.7

28.8

36.9

45.

53.1

61.2

69.3

77.4

85.5


Tune-scan A: when in terms of QxBB explains other cases:Take CC ON, Nb=2.2×1011 for two cases: 1) “no IP8” and 2) “with IP8”.

62.27 62.28 62.29 62.30 62.31QxBB = linearly shifted BB tune

DA

Nb=1.1 IR1,5,8 NO CC

2) Nb=2.2 IR1,5,8 CC ON

1) Nb=2.2 IR1&5, CC ON

HLLHC Lattice cases:

6 / 31

QxBB

Nb=2.2IR1&5

Nb=1.1IR1,5,8

Nb=2.2IR1,5,8

Case 2) needs a litle shift to the right. The result is “best w.p. from TS A”.

Case 2) Case 1) Case as scan was made


DA for case 1): no BB in IR2 and 8

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0 2 4 6 80

2

4

6

8

DA and Chaos HOR @ΣD

DA

and

Cha

osV

ER

T@Σ

D

Wst15

the only case when the chaotic border was > 2 at some angles


DA for cases 1) and 2). The shift for 2) works – improves DA.

tune-scan A is quite universal

0 1 2 3 4 5 6 70

2

4

6

8

Horizontal Dynamic aperture

Ver

tical

Dyn

amic

ape

rtur

e

Case 2) before shift

Case 1)

0 1 2 3 4 5 60

1

2

3

4

5

6

Horizontal Dynamic aperture

Ver

tical

Dyn

amic

ape

rtur

e

7 / 7

Case 1) needs no shift

Case 2) after shift

62.2775 62.2780 62.2785 62.2790Qx

DA

HΣL


DA for case 2) with IR2 added (still at best w.p. from TS A)

some tiny increase in ∆Q from 0.0318 to ∼ 0.033 due to IR2

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0 2 4 6 80

2

4

6

8


DA

and

Cha

osV

ER

T@Σ

D

Wst1582_bwp

It will further improve for w.p. closer to diagonal —> pages 14+


Tune-scan B (LHC as-built with corrected tripl. errors )

Tune-scans for seeds 1–6. Color code is same as above, but only 9 angles.The three resonance dips near 64.31 are known from previous studies.

64.26 64.28 64.30 64.320

2

4

6

8

10

12

14

Qx

DA

HΣL

seed=1

64.26 64.28 64.30 64.320

2

4

6

8

10

12

14

Qx

DA

HΣL

seed=2

64.26 64.28 64.30 64.320

2

4

6

8

10

12

14

Qx

DA

HΣL

seed=3

64.26 64.28 64.30 64.320

2

4

6

8

10

12

14

Qx

DA

HΣL

seed=4

64.26 64.28 64.30 64.320

2

4

6

8

10

12

14

Qx

DA

HΣL

seed=5

64.26 64.28 64.30 64.320

2

4

6

8

10

12

14

Qx

DA

HΣL

seed=6

First 6 seeds for LHC with corrected triplet. Here Qx represents Qx0 (sorry).


Tune-scans A and B comparedTop: HL-LHC, Nb=1.1×1011 BB and Sext. Bottom: LHC, BB+sext and corr. tripl. for seed 1

62.28 62.29 62.30 62.31 62.32 62.332

4

6

8

10

Qx0

DA

HΣL

64.28 64.29 64.30 64.31 64.32 64.332

4

6

8

10

12

14

Qx0

DA

HΣL

seed=1


detour 1/1: Tune-scans A and B, dip locations (X-plane only)It’s a lot easier to explain the dips than the maxima of course..

red only, i.e. DA near HOR plane

62.28 62.29 62.30 62.31 62.32 62.332

4

6

8

10

Qx0

DA

HΣL

(a) HL-LHC

64.28 64.29 64.30 64.31 64.32 64.332

4

6

8

10

12

Qx0

DA

HΣL

(b) LHC

The simple Two-Head-On-IPs BB model HOR plane

only for the perturbed CS invariant (Poincaré surface

of section) seems to explain dip locations. This

invariant, when confirmed with tracking (black dots),

looks like:

-3 -2 -1 0 1 2 3

4.45

4.50

4.55

4.60

Φ

I

nΣ= 3, S=1.3 %

-3 -2 -1 0 1 2 3

24.2

24.4

24.6

24.8

25.0

Φ

I

nΣ= 7, S=0.98 %

Near resonance it begins to oscillate fast. The blue

curves on the right show module of some high-order

Fourier coefficient (C10 used here).


detour 1/2: fast osc. of invariantsample lattice

0.3068 0.3069 0.307 0.3071

0.3072 0.3073 0.3074 0.3075

0.3076 0.3077 0.3078 0.3079

0.308 0.3081 0.3082 0.3083

0.3084 0.3085 0.3086 0.3087


Tune-scan C (2D) 11 angles

∆QBB ' 0.033

0.300 0.305 0.310 0.315 0.320

0.305

0.310

0.315

0.320

0.325

Qx0

Qy0

012

6

345

TS lines

Tune-scan lines parallel to diagonal and approaching it from above:0, 1, 2 . . . , 6 (TS A line is 0 here)

step in tune ∆Qx = 10−3

step in distance to diagonal (yellow) =√

2∆ Qx ' 14× 10−4


Tune-scan C (by TS line)

(a) 1 Dist=10−2 . Min DA is

5.5 at the best w.p. from TS A.

Seen to be near 45-deg plane

(green).

(b) 2 (c) 3 (d) 4

(e) 5 (f) 6 (g) 7 Dist=1.4 × 10−5 . Min

DA grows to 6.5. Seen to be near

VERT plane (blue).


Tune-scan C

extending the domain up and to the right (to capture best-DA region)

0.305 0.310 0.315 0.320 0.325

0.305

0.310

0.315

0.320

0.325

Qx0

Qy0

3.0

4.5

5.0

5.5

6.0

6.5

Min DA over 11 angles. The black dot is “best w.p. from TS C”: (Qx0,Qy0)=(0.316,0.319).

Black dot tested next→


DA at the best w.p. of TS CA sigma gained (compare with page 10)

WnameQxBB/QyBB

dQx/dQy

CHx/CHy

Wst1582_BP62.284/60.2868

0.0324/0.0327

3.26843/2.10872

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0 2 4 6 80

2

4

6

8


DA

and

Cha

osV

ER

T@Σ

D

best w.p. tune scan C

w.p. set to (0.3164,0.3195) with MadX onlyD. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 18 / 34

Tune-scan C (2D) in terms of QxyBB

0.270 0.275 0.280 0.285 0.2900.270

0.275

0.280

0.285

0.290

0.295

0.300

QxBB

QyBB

3.0

4.5

5.0

5.5

6.0

6.5


continued Jan 2017


Tune-scan D (2D), Nb=1.1×1011

So that D is same as A, but crab ON and IR2 ON, or same as C, butNb=1.1×1011.

0.305 0.310 0.315 0.320 0.325

0.305

0.310

0.315

0.320

0.325

Qx0

Qy0

3.0

4.5

5.0

5.5

6.0

6.5

0.305 0.310 0.315 0.320

0.310

0.315

0.320

0.325

0.330

Qx0

Qy0

5

6

7

8

9

Min DA over 11 angles.Left: TS C repeated and Right: TS D

(DA at the nominal tune (red point) will be studied without and with IT field errors⇒)


DA at nominal tune (no errors)

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0 2 4 6 80

2

4

6

8


DA

and

Cha

osV

ER

T@Σ

D

Qone0


Tune-scan C and D shown by TS line

To see the effect of halving Nb.Top: Nb=2.2×1011 Bottom: Nb=1.1×1011

from left to right – approaching the diagonal starting from Dist=0.01.


DA for nominal tune with IT field errorsRef. for corrector limits

A table from HiLumi LHC WP3 page shows max Integrated strengths 1

1Integrated strength is the field at the 50 mm ref radius times the magnetic lengthD. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 24 / 34

https://espace.cern.ch/HiLumi/wp3/SitePages/Home.aspx

IT of IR1/5 correctors as IPAC13 paper (used as reference)

Results taken from ref. paper 2 are: corr. strengths (Fig 2) and integrated mult.field at 5 cm (Table 3).

mT×meter (confirm with prev

page)

2M. Giovannozzi, S. Fartoukh, R. De Maria: SPECIFICATION OF A SYSTEM OF CORRECTORS FOR THE TRIPLETS ANDSEPARATION DIPOLES OF THE LHC UPGRADE, Proceedings of IPAC2013


my result for corr. strengths(comp. with Fig.2 of ref. paper)

Same errors and same correctors used as in ref. paper above

-10 -5 0 5 100

5

10

15

20

25

30

35

brho K2L , T�m^1

a3b3

-600 -400 -200 0 200 400 6000

10

20

30

40

brho K3L , T�m^2

a4b4

-40 000 -20 000 0 20 000 40 0000

10

20

30

40

brho K4L , T�m^3

a5b5

-1 ´ 107 -5 ´ 106 0 5 ´ 106 1 ´ 1070

20

40

60

80

100

brho K5L , T�m^4

a6b6


my result for integrated strengths(comp. with Table 3 of ref. paper) need to explain the difference

correctors, mT.mComputed Specified

3 16 634 15.3 46

norm 5 9.6 256 30.8 862 186 10003 15.1 63

skew 4 11.4 465 12.3 256 5.5 17


DA at nominal tune with IT field errors, no A2, no D1,D2i.e., at the red point for TS D on page 21FIRST 40 seeds

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0 20 40 60 806.

7.

8.

9.

10.

Angle @degD

DA

@ΣD


Identify worst seeds

“worst” seeds 38, 7, 5 , 15 and 16

good seed: 2

may be correlated with dr. termsnext ⇒


skew driving terms, Beam1Relative units. First of pair: IR5. Second of pair: IR1. Where terms is 0, means corrected. Badseeds (red) are seen to corresp. to near maxima for A4 (1,3), A5 all not-corrected – main causefor DA loss and A6 (3,3)

22 2 25

55 5

7

7

7 715

15 15 15

16

1616 1638 38 38 38

82, 1< 82, 1< 80, 3< 80, 3<

term A3

22 2 2

55 5 57

7

7

715

1515

15

16

16

16

16

38 38 38 38

81, 3< 81, 3< 83, 1< 83, 1<

term A4

2

2

2

2

2 25

5

5

5

5 5

7 77 7

7 715

15

15

15

15 1516

16

16

16

16 16

38 38 3838

38 38

84, 1< 84, 1< 82, 3< 82, 3< 80, 5< 80, 5<

term A5

2 22

2

5 55

5

7 7

7

7

15 1515 15

16 16 16

16

38 38

3838

85, 1< 85, 1< 83, 3< 83, 3<

term A6


normal driving terms, Beam1Bad seeds (red) are seen to corresp. to near maxima for B4 (2,2), B6(4,2)

22

2 25

5

5 57 7 7 715

15

15 15

16 1616 1638

38

38 38

83, 0< 83, 0< 81, 2< 81, 2<

term B3

2 2 2 2

2

25 5 5 5

5

5

7 7 7 7

7

715 15 15 15 15

1516 16 16 16

1616

38 38 38 3838

38

84, 0< 84, 0< 80, 4< 80, 4< 82, 2< 82, 2<

term B4

2 22

2

2

2

5 5

5

5

5

57 7

7

7

7

715 15

15

15

15

15

16 1616

16 16 1638 3838

38

38

38

85, 0< 85, 0< 83, 2< 83, 2< 81, 4< 81, 4<

term B5

2 2 2 2

2

2

2

2

5 5 5 5

5

5

5

57 7 7 7

7

7

77

15 15 15 15

15

1515

15

16 16 16 1616

16

16

16

38 38 38 38 38

3838

38

86, 0< 86, 0< 80, 6< 80, 6< 84, 2< 84, 2< 82, 4< 82, 4<

term B6


Use all 60 seeds. Identify worst for each angle3 new “worst” seeds: 36, 48 and 9

38

7

5

7

3838

36

15

16

48

9

5

2

highest |dr. term|found on the next plots

ang [deg] seed dr. term7.5 38 A5 (2,3)15 7 A6 (3,3) and B6 (4,2)22.5 5 B4 (2,2)30 7 3,3 and 4,237.5 38 A5 (2,3)45 38 A5 (2,3)52.5 36 B6 (2,4) ?60 15 A5 2,367.5 16 A4 (1,3) ? check75 48 B3 (3,0) and B5 (3,2)82.5 9 A5 (2,3)


skew

55

5 57

7

7 79

99 9

1515 15 15

16

1616 16

36

36

36 3638 38 38 3848

4848 48

82, 1< 82, 1< 80, 3< 80, 3<

-100

-50

0

50

100

150term A3

55 5 57

7

779

99

915

1515

15

16

16

16

1636

3636

3638 38 38 384848

4848

81, 3< 81, 3< 83, 1< 83, 1<-1. ´ 10-9

-5. ´ 10-10

0

5. ´ 10-10

1. ´ 10-9

1.5 ´ 10-9

term A4

5

5

5

5

5 57 7 7 7

7 7

9

9

9

9 9 915

15

15

15

15 1516

16

16

16

16 163636

36

36

36 36

38 38 3838

38 38

48

48

48

48 48 48

84, 1< 84, 1< 82, 3< 82, 3< 80, 5< 80, 5<-1 ´ 1010

-5 ´ 109

0

5 ´ 109

1 ´ 1010term A5

5 55

5

7 7

7

7

9 9

9

915 1515 15

16 16 16

16

36 36 3636

38 38

3838

48 48 4848

85, 1< 85, 1< 83, 3< 83, 3<

-2 ´ 1013

0

2 ´ 1013

4 ´ 1013

6 ´ 1013

term A6


normal

55

5 57 7 7 7

9 9

9 915

15

15 1516 16

16 16

36

36 36 3638

38

38 3848

48

48 48

83, 0< 83, 0< 81, 2< 81, 2<

-150

-100

-50

0

50

100

term B3

5 5 5 55

5

7 7 7 7

7

79 9 9 9 9

9

15 15 15 15 15 1516 16 16 1616

16

36 36 36 36 36 3638 38 38 38 38

38

48 48 48 4848

48

84, 0< 84, 0< 80, 4< 80, 4< 82, 2< 82, 2<

-0.0010

-0.0005

0.0000

0.0005

0.0010term B4

5 5

5

5

557 7

7

7

7

79 9

99 9

915 15 15

15

1515

16 1616

16 16 1636 36 3636

36

36

38 38 3838

38

3848 4848

48

48

48

85, 0< 85, 0< 83, 2< 83, 2< 81, 4< 81, 4<

-5 ´ 109

0

5 ´ 109

1 ´ 1010term B5

5 5 5 5

5

5

5

57 7 7 7

7

77

79 9 9 9 9

9

9

9

15 15 15 15

15

1515

1516 16 16 16

16

16

16

16

36 36 36 3636

36

36

36

38 38 38 38 3838

3838

48 48 48 48

4848 48 48

86, 0< 86, 0< 80, 6< 80, 6< 84, 2< 84, 2< 82, 4< 82, 4<-3 ´ 1014

-2 ´ 1014

-1 ´ 1014

0

1 ´ 1014

2 ´ 1014

3 ´ 1014

term B6


Documents

Tune-scans for HL-LHC and LHC - TRIUMFlin12.triumf.ca/text/design_notes/...03-tune_scans_for_HLLHC_2017.pdf · standard MadX-SixTrack-SixDesk env. D. Kaltchev (CERN-TRIUMF HL-LHC