Higher Gradient Quads for Collider IP R. B. Palmer (BNL), Don Summers (Mississippi) Physics and Detectors FNAL 11/10/09 • Motivation • Super-conductor properties • Cos theta quadrupole optimization • Aside on ”block” design • Grading super-conductor current density (p9) • Use of exotic magnetic materials • Application to Collider final focus • Conclusion 1
Motivation Luminosity N 2 µ L = n turns f bunch 4 πσ 2 ⊥ L ∝ < B > P beam N ǫ ⊥ β ∗ • We may have trouble getting N = 2 10 12 • We may have trouble getting ǫ = 25 10 − 6 m • We may have trouble getting 7% cooling transmission • Look for other ways to recover Luminosity – More proton power (Chuck) – Lower β ∗ <<<<<< 2
Advances in SC Quadrupole Design Above magnet now under construction uses conductor performance: LARP Quad Cross sec- tion 3
Reproduce LARP Design y (mm) B (T) 10 3 dB/B 75 75 y (mm) Ni3Sn Bmax (T) 13.59018 Grad (T/m) 194.3587 50 50 (c.f. LARP 200) Pole B (T) 11.2535 j (A/mm 2 ) 666.4 25 25 0 0 0 50 100 150 0 25 50 75 x (mm) x (mm) • Gradient found of 194 T/m c.f. LARP’s 203 T/m Good enough agreement • Adding wedges would give required field quality but would not significantly change the fields • Note field at all angles • So YBCO is not suitable 4
Optimize radial thickness 10 3 dB/B 15 30 y (mm) B (T) Ni3Sn Ni3Sn 10 20 Bmax (T) 6.795789 Bmax (T) 10.76 Grad (T/m) 583.1355 Grad (T/m) 870 y (mm) Pole B (T) 5.627327 Pole B (T) 8.63 j (A/mm 2 ) 1999.404 j (A/mm 2 ) 1103 5 10 0 0 0 5 10 15 20 25 0 10 20 30 40 50 x (mm) x (mm) Small dR/R=0.5 Large dR/R=2.0 Grad=583 Grad=870 • Max fields higher in dR/R=2.0, current densities lower, but gradient still higher • dR/R=0.5: Radial width of conductor (0.5 cm) much less than LARP (3 cm) • dR/R=2.0: Radial width of conductor (2 cm) still less than LARP (3 cm) but key-stoning is more severe and will need R&D 5
20 For different R ◦ ◦ 10 cm ◦ 6 cm 4 cm ◦ • Optimum always 10 B pole (T) 2 cm near dR/R = 2 9 ◦ • But Large dR/R 1 cm 8 ◦ 0.8 cm more useful at low radii 7 ◦ 0.5 cm 6 5 4 .8 1 2 3 dR/R 6
B pole and Gradient vs. R 2 33% dr/r=2.0 + Pole tip field (T) + + LARP ◦ · 45% + · 10.0 · 9 + 63% dr/r=.5 8 · 7 6 · 5 4 3 0 20 40 60 Inside rad (mm) • Huge gains if radius reduced 7
Grading super-conductor current densities 125 125 3 3 1 10.45 .35 1 14.4 1.01 33 43 333 444 2 10.45 .35 2 14.4 1.01 4333 5444 44433 55544 544443 665554 100 3 15.88 .98 100 3 17.3 .965 5554444 7666555 66555444 87766655 4 15.88 .98 4 17.3 .965 776655544 988776655 8776665554 0098877665 1 5 12.78 .52 1 5 15.0 .988 66877666554 88109887766 3 3 445687766555 567800988766 75 75 2344678776655 2456890998776 6 12.78 .52 6 15.0 .988 02234568877665 02346680099877 101234556887666 211345779009887 2122235556787766 3233447778910987 2 2 33322334565788776 55434456797000987 454343445556679876 676565667889991098 50 50 5 6655544555567779877 5 9977777788900001098 87766666666677878987 09998999990001100098 B pole=12.8 T B pole=14.12 T 988777777777888788987 110000001111221110098 0999888889898999898098 2211112122232222110009 6 6 Grad=325 T/m Grad= 367 T/m 11000099090000000009998 33222323444433322211009 4 4 221110111011111212110108 443333445454444433221109 25 0122121212323333332221098 25 2344444555555555544332109 90122222333444454443221098 01244455566666665554322109 789012334455555554433210098 890134556676777665544321009 5678912445556555544432210998 6789123556777776665543321099 34578902345555555544332110998 45679023456667666655443221099 124567901344555555444332110998 234678013455666666655443221099 0 0123567901234555555444332110998 0 0124578012455666666655443221099 0 50 100 150 200 0 50 100 150 200 • Tables show fraction of short sample currents by block • Without ’grading’ inner blocks run far bellow maximum • Adjusting densities by choice of cable thickness brings all blocks to same level • Field and gradient gain is 10-15 % 8
Fields vs radius with grading & dr/r=2.0 2 37% + 50% dr/r=2 graded + 33% + Pole tip field (T) + + LARP + + ◦ · 70% 45% + Zlobin ◦ · 10.0 + dr/r=2.0 · 9 + 63% dr/r=.5 un-graded 8 · 7 6 · 5 4 3 0 20 40 60 Inside rad (mm) • Gain from grading ≈ 10% independent of radius • Gain including dr/r=2 greatest for small radii 9
Use of exotic materials for pole tips Holmium only becomes ferromagnetic below 20K and saturates at about 4 Tesla . http://en.wikipedia.org/wiki/Holmium~~ http://www.stanfordmaterials.com/ho.html Phys. Rev. 109 (1958) 1547 http://prola.aps.org/pdf/PR/v109/i5/p1547\_1 Dysprosium Becomes ferromagnetic below 85K and saturates at maybe 3.5 Tesla Physica B211 (1995) 345 ”Magnetically aligned polycrystalline dysprosium as ultimate saturation ferromagnet for high magnetic field polepieces” http://dx/doi.org/10.1016/0921-4526(94)01059-A Gadolinium Saturates at 3.2 T at 80 deg K http://en.wikipedia.org/wiki/Gadolinium $130/kilogram The Curie point is described as a phase transition. http://en.wikipedia.org/wiki/Ferromagnetic 10
Use of Holmium for pole within conductors e.g. Argonne NIM A313 (1992) 311; http://accelconf.web.cern.ch/AccelConf/p95/ARTICLES/FAQ/FAQ09.pdf Rad=1.5 cm Bpole=5.25 T Grad-350 T/m Argonne Design For our design: 0-5% gain 11
Use of Exotics if inner shield required • Because of decay electron halo, we may need some shielding - assumed 2 cm • Having ferromagnetic poles passing through this shielding would add signifi- cantly to the gradient • The shielding, and poles, can not be at 4 deg for the heat load • 70-80 degrees is probably ok • That rules out Holmium, but leaves Gadolinium and Dysprosium as possibles • Little or no gain from Holmium pole because gradient limited by conductor far from pole • But significant gain from Gadolinium through shield 12
Fields vs radius with 2 cm shield + 48% With Gadolinium pole + 35% Graded dr/r=2 10.0 9 LARP 8 Zlobin Pole field (T) ◦ ◦ 7 6 + 100% Zlobin 5 ◦ 4 + 52% 3 2 0 20 40 60 Pole Radius (mm) • Gain now a factor of 2 for 10 mm • Gain a factor of 1.5 for 30 mm 13
field quality 15 10 4 dB/B 10 B (T) 5 /10 0 0 20 40 60 Rad (mm) • Seems ok ( dB/B < 10 − 4 ) with square pole end • Could be improved with pole shaping 14
Summary file graded holmium Gadolinium t/R Bmax Grad gain conductor pole tip T T/m % 40snh2 no no no 0.5 11.7 264 40snh1 no no no 1.0 13.9 305 15 40snh no no no 2.0 15.9 317 20 40snh yes no no 2.0 15.9 365 38 40snhb yes yes no 2.0 13.0 360 36 40snhc yes yes yes 2.0 13.0 424 60 • Many modest gains reach a substantial increase in Gradient • Gains are greater for smaller radii 15
Baseline final focus with 2cm shield and 50 cm gaps sigmas 4 Ebeam (TeV) 0.75 shield(cm) 2.0 Btip(T) 0.0 fac 1.00 0.100 beta IP (mm)=10 G(m) L(m) R(cm) (T/m) B1 B2 pole tip field Nb3Sn 6.00 1.10 1.76 193 2.7 to 3.4 7.2 Radius (m) emit (micron) = 25 0.50 1.20 2.51 187 3.6 to 4.7 8.4 beta max (km) 22.5 0.50 2.10 3.50 -175 4.9 to 6.1 9.6 0.075 beta max (km) 23.3 0.50 2.10 3.56 -174 5.6 to 6.2 9.7 0.50 2.20 3.62 173 5.2 to 6.3 9.7 0.050 0.025 0.000 0 5 10 15 20 Length (m) • Betamax=23 km about correct 16
Betamax with other magnets & distance to first quad Dist (m) 1 3 6 Baseline 17 25 Optimized 13 18 ” + Gadolinium 7.3(16) 10(20) 16 Numbers are for β ∗ of 10 mm except Numbers in parentheses are for β ∗ =5 mm 17
example with 3 m to first quad including gadolinium sigmas 4 Ebeam (TeV) 0.75 shield(cm) 2.0 Btip(T) 1.5 fac 1.00 0.100 beta IP (mm)= 5 G(m) L(m) R(cm) (T/m) B1 B2 pole tip field Nb3Sn 3.00 0.85 1.37 321 4.7 to 4.4 10.8 Radius (m) emit (micron) = 25 0.50 0.85 2.16 298 6.3 to 6.4 12.4 beta max (km) 20.2 0.50 1.65 3.29 -262 8.2 to 8.6 13.8 0.075 beta max (km) 21.8 0.50 1.65 3.38 -259 9.4 to 8.8 13.9 0.50 1.74 3.51 256 8.9 to 9.0 14.1 0.050 0.025 0.000 0 5 10 15 Length (m) • Betamax=20 km is less than baseline • But 5 mm beta star gives twice the luminosity, • or half the background and driver requirements 18
Conclusion • 200 T/m Nb 3 Sn Quad under construction by LARP Using this material: • Optimized designs give ≈ 20% gradient gains • With exotic materials give ≈ 36% gradient gains • If shields needed inside quads then gains of ≈ 60% achieved • Use of such quads could lower β ∗ in collider ring • To Do – Magnet simulations using code like OPERA for magnet material saturation – MARS study of needed shielding 19
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