Tune-scans for HL-LHC and LHC -...
Transcript of Tune-scans for HL-LHC and 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.
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 2 / 34
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
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Ord. 5 to 13
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1D
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Qy0
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2D
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 3 / 34
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
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 4 / 34
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 ..
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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)
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 5 / 34
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.
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VERT
HOR4.5
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45.
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D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 6 / 34
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
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 7 / 34
DA for case 1): no BB in IR2 and 8
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DA and Chaos HOR @ΣD
DA
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Cha
osV
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T@Σ
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Wst15
the only case when the chaotic border was > 2 at some angles
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 8 / 34
DA for cases 1) and 2). The shift for 2) works – improves DA.
tune-scan A is quite universal
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Horizontal Dynamic aperture
Ver
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Dyn
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Case 2) before shift
Case 1)
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Case 1) needs no shift
Case 2) after shift
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DA
HΣL
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 9 / 34
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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DA and Chaos HOR @ΣD
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Wst1582_bwp
It will further improve for w.p. closer to diagonal —> pages 14+
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 10 / 34
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.
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seed=1
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seed=2
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seed=3
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seed=4
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seed=5
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First 6 seeds for LHC with corrected triplet. Here Qx represents Qx0 (sorry).
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 11 / 34
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
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D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 12 / 34
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
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DA
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(a) HL-LHC
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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:
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Φ
I
nΣ= 3, S=1.3 %
-3 -2 -1 0 1 2 3
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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).
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 13 / 34
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
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 14 / 34
Tune-scan C (2D) 11 angles
∆QBB ' 0.033
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Qy0
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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
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 15 / 34
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).
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 16 / 34
Tune-scan C
extending the domain up and to the right (to capture best-DA region)
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Qx0
Qy0
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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→
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 17 / 34
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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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
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D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 19 / 34
continued Jan 2017
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 20 / 34
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.
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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⇒)
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 21 / 34
DA at nominal tune (no errors)
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D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 22 / 34
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.
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 23 / 34
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
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
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 25 / 34
my result for corr. strengths(comp. with Fig.2 of ref. paper)
Same errors and same correctors used as in ref. paper above
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brho K2L , T�m^1
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brho K5L , T�m^4
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D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 26 / 34
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
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 27 / 34
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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D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 28 / 34
Identify worst seeds
“worst” seeds 38, 7, 5 , 15 and 16
good seed: 2
may be correlated with dr. termsnext ⇒
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 29 / 34
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)
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82, 1< 82, 1< 80, 3< 80, 3<
term A3
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term A4
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term A5
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term A6
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 30 / 34
normal driving terms, Beam1Bad seeds (red) are seen to corresp. to near maxima for B4 (2,2), B6(4,2)
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term B4
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term B5
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term B6
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 31 / 34
Use all 60 seeds. Identify worst for each angle3 new “worst” seeds: 36, 48 and 9
38
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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)
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 32 / 34
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
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 33 / 34
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
D. Kaltchev (CERN-TRIUMF HL-LHC Collab.) Tune-scans for HL-LHC and LHC February 3, 2017 34 / 34