Update on slow extraction for PS2: alternative sextupole locations and configurations
12
Update on slow extraction for PS2: alternative sextupole locations and configurations B.Goddard, W.Bartmann, M.Gyr March 26 th 2009
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Update on slow extraction for PS2: alternative sextupole locations and configurations. B.Goddard, W.Bartmann, M.Gyr March 26 th 2009. Considerations. ES to MS phase advance is 78 degrees Need separatrix angle at ES of about 40 degrees - PowerPoint PPT Presentation
Transcript of Update on slow extraction for PS2: alternative sextupole locations and configurations
Update on slow extraction for PS2:alternative sextupole locations and configurations
B.Goddard, W.Bartmann, M.Gyr
March 26th 2009
Considerations• ES to MS phase advance is 78 degrees• Need separatrix angle at ES of about 40 degrees
– Opening at MS and clearance for other separatrix branches• <40° means branch 1 approaches ES• >40° means branch 2 approaches MS
– Phase advance of sextupoles to ES of 110, 230, 350 degrees
-12.0
-8.0
-4.0
0.0
4.0
8.0
12.0
-12.0 -8.0 -4.0 0.0 4.0 8.0 12.0
6pole
ES
3
12
3
2
1
-12.0
-8.0
-4.0
0.0
4.0
8.0
12.0
-12.0 -8.0 -4.0 0.0 4.0 8.0 12.0
ES kick
-12.0
-8.0
-4.0
0.0
4.0
8.0
12.0
-12.0 -8.0 -4.0 0.0 4.0 8.0 12.0
MS
~40°
Zero Dx sextupole locations
• Ideally have resonant 6poles in dispersion-free regions, so that there is no effect on chromaticity
• In PS2 lattice looking for new locations with:– |Dx/x | < 0.1 (compared to peak value of 1.5 and RMS of 0.4)
– Free drift space at least 70 cm …assume 30-40 cm magnet and something for coil ends
– Look for 50, 110, 170, 230, 290 and 350 degree locations (alternately –ve and +ve polarities respectively).
– Phase error within 5-10 degrees acceptable.– Large horizontal beta functions preferred (6pole strength)
• Used most recent lattice including– Chromaticity sextupoles– Correctors– BPMs
Possible locations (mod 60°)
0 200 400 600 800 1000 1200 1400-0.5
0
0.5
1
1.5
2
S [m]
Dx/
sqrt
(bet
x) [
sqrt
(m)]
Horizontal normalised dispersion
normalised Dispersion
DS
ArcRF-LSS IE-LSS
DS
Arc
Smaller Dx/x at 6-poles
• 6 Locations in arcs – 70 cm free drift (MB-MB or MB-corr) – Is this enough space???
• 4 locations in DS (one each) – 80 cm free drift between….
• 11 locations in LSS– 8 in RF straight. – 3 in IE straight.
Locations in lattice
DS location (0.8 m available)Arc location (0.7 m available)
LSS (RF)
Combinations evaluated
• V1: arc locations – Dx of ~0.4m, betx ~20m, 0.7 m space• V2: DS locations – Dx of ~0.2m, betx ~24m, 0.8 m space• V3: RF LSS – Dx of 0m, betx ~20-28m, space OK• V4: mixed locations (2 in DS, 1 per LSS) – Dx of 0 – 0.2m, betx of 9 - 25m
S betx mux to ES Dx DxN DxN PrtAGS target phase Comment[m] Upstream Downstream [m] [deg] [m] [sqrt(m)] [mm] [deg] v1 v2 v3 v446.40 0.18 0.12 24.45 0.689 195.1 -0.21 -0.04 -329.1 190.00 DS -ve127.35 0.10 0.10 19.83 1.444 283.4 -0.37 -0.08 -643.0 290.00 Arc -ve287.41 0.10 0.10 19.82 2.939 105.3 -0.39 -0.09 -669.8 110.00 Arc447.47 0.10 0.10 19.82 4.433 287.2 -0.37 -0.08 -646.4 290.00 Arc -ve 481.90 0.23 0.06 25.05 4.627 217.5 -0.19 -0.04 -301.6 230.00 DS +ve +ve538.00 8.91 0.49 8.93 5.406 297.2 0.00 0.00 -0.4 290.00 RF LSS553.00 0.64 8.26 26.51 5.573 236.8 0.00 0.00 0.5 230.00 RF LSS +ve564.50 0.75 8.65 9.92 5.727 181.4 0.00 0.00 0.9 190.00 RF LSS 591.30 0.76 9.14 26.77 5.926 110.0 0.00 0.00 0.3 110.00 RF LSS +ve617.60 0.76 8.14 18.68 6.106 45.1 0.00 0.00 -0.6 50.00 RF LSS -ve636.90 8.67 0.73 9.90 6.249 353.8 0.00 0.00 -0.9 350.00 RF LSS 648.30 8.18 0.72 26.27 6.401 298.7 0.00 0.00 -0.5 290.00 RF LSS -ve663.60 0.70 8.20 9.21 6.574 236.8 0.00 0.00 0.5 230.00 RF LSS +ve719.70 0.28 0.02 23.92 7.350 317.3 -0.22 -0.05 -355.4 290.00 DS -ve800.55 0.10 0.10 19.83 8.104 45.8 -0.37 -0.08 -643.5 50.00 Arc -ve960.60 0.09 0.11 19.84 9.599 227.7 -0.38 -0.09 -667.2 230.00 Arc1120.67 0.10 0.10 19.82 11.093 49.6 -0.37 -0.08 -646.9 50.00 Arc -ve1155.01 0.14 0.15 24.58 11.286 340.1 -0.21 -0.04 -323.9 350.00 DS +ve +ve1211.00 7.72 0.68 9.20 12.062 60.9 0.00 0.00 -0.5 50.00 IE LSS1310.52 0.09 0.31 9.36 12.916 113.6 0.00 0.00 -0.9 110.00 IE LSS1336.30 0.20 1.70 8.56 13.225 2.4 0.00 0.00 0.4 350.00 IE LSS +ve
Free drift (for 0.5 m) [m] Version
Separatrices (natural chromaticity (dq/Q)/(dp/p) of -1.654)
• V1: arc locations – looks OK• V2: DS locations – 6poles need to be stronger• V3: RF LSS – looks OK – can optimise positions and phases• V4: mixed – very nice straight separatrices and angles
-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
-40
-20
0
20
40
60
80
100
-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
-40
-20
0
20
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60
80
100
-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
-40
-20
0
20
40
60
80
100
-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
-40
-20
0
20
40
60
80
100
V2 V3V1
V4
Other sextupole locations for orthogonal “steering” of separatrix angle
• Locate pairs of sextupoles at phases of 15° around the ideal phase locations of 50, 110, …, 350 deg
• Then possible to adjust by 15 degrees the phase advance at the ES by varying the powering of the two families
22
2 3cos3sin
nxn
nxneffS
nxn
nxn
xeff
3cos
3sinarctan
3
1
Note 1: need twice as many magnets and power supplies…
Note 2: required strength needs to be a factor of 2 higher to get the full tuning range…
Note 3: larger range possible if supplies are bipolar…-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
25 30 35 40 45 50 55 60 65 70 75Effective 6pole phase [deg]
S/S
0
S 70 deg
S 30 deg
-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
-40
-20
0
20
40
60
80
100
Separatrix angle steering
• Tried with 4 magnets arranged in 2 families at (120 –15) deg and (230 +15) deg– In reality would use 8 separately powered magnets
-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
-40
-20
0
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100
-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
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0
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100
-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
-40
-20
0
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100
-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
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0
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-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
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-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
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0
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-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
-40
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-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
-40
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0
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-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
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0
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-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
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-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
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0
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-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
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-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
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0
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-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
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0
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-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
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-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
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0
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Conclusions
• Suitable “0 Dx” locations for resonant extraction sextupoles – 4 positions in DS, 6 in arcs, 8 in RF-LSS, 3 in IE-LSS– Several configurations of sextupoles possible
• Critical issue is magnet (+coil end) length needed– If feasible in 0.7 m drift, many possibilities in arcs, DS and LSS– If in 0.8 m drift, only 4 DS locations and LSS– If >0.8 m needed, only LSS
• Separatrix angle adjustment at ES is possible– Divide 4 sextupoles into 8 magnets at 6015°– Increases required strength by factor of about 2
• Other issues should be considered– Lattice tuning accomplished where? Need to go from ~13.32 to
13.333 : would like to keep phase advances to ES fixed. – Servo-quadrupole for modulating spill – strength to be defined– Situation with chromaticity sextupoles ON to be evaluated
