Higher Gradient Quads for Collider IP R. B. Palmer (BNL), Don - - PowerPoint PPT Presentation

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Higher Gradient Quads for Collider IP R. B. Palmer (BNL), Don - - PowerPoint PPT Presentation

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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

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SLIDE 1

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

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SLIDE 2

Motivation

Luminosity

L = nturns fbunch N2

µ

4πσ2

⊥

L ∝ < B > Pbeam N ǫ⊥ β∗

  • We may have trouble getting N = 2 1012
  • 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

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SLIDE 3

Advances in SC Quadrupole Design

Above magnet now under construction uses conductor performance: LARP Quad Cross sec- tion

3

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SLIDE 4

Reproduce LARP Design

y (mm) B (T) 103 dB/B x (mm) Ni3Sn 50 100 150 25 50 75 Bmax (T) 13.59018 Grad (T/m) 194.3587 (c.f. LARP 200) Pole B (T) 11.2535 j (A/mm2) 666.4 y (mm) x (mm) 25 50 75 25 50 75

  • 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

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SLIDE 5

Optimize radial thickness

y (mm) B (T) 103 dB/B x (mm) Ni3Sn 5 10 15 20 25 5 10 15 Bmax (T) 6.795789 Grad (T/m) 583.1355 Pole B (T) 5.627327 j (A/mm2) 1999.404 y (mm) x (mm) Ni3Sn 10 20 30 40 50 10 20 30 Bmax (T) 10.76 Grad (T/m) 870 Pole B (T) 8.63 j (A/mm2) 1103

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

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SLIDE 6

For different R

  • Optimum always

near dR/R = 2

  • But Large dR/R

more useful at low radii Bpole (T) dR/R .8 2 3 1 4 5 6 7 8 9 20 10

0.5 cm 0.8 cm 1 cm 2 cm 4 cm 6 cm 10 cm

  • 6
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SLIDE 7

Bpole and Gradient vs. R

Pole tip field (T) Inside rad (mm) 63% 45% 33% 20 40 60 3 4 5 6 7 8 9 2 10.0 · · · · ·

  • LARP

+ + + + + dr/r=2.0 dr/r=.5

  • Huge gains if radius reduced

7

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SLIDE 8

Grading super-conductor current densities

B pole=12.8 T Grad=325 T/m 1 10.45 .35 2 10.45 .35 3 15.88 .98 4 15.88 .98 5 12.78 .52 6 12.78 .52 50 100 150 200 25 50 75 100 125 1 2 3 4 5 6

0123567901234555555444332110998 124567901344555555444332110998 34578902345555555544332110998 5678912445556555544432210998 789012334455555554433210098 90122222333444454443221098 0122121212323333332221098 221110111011111212110108 11000099090000000009998 0999888889898999898098 988777777777888788987 87766666666677878987 6655544555567779877 454343445556679876 33322334565788776 2122235556787766 101234556887666 02234568877665 2344678776655 445687766555 66877666554 8776665554 776655544 66555444 5554444 544443 44433 4333 333 33 3

B pole=14.12 T Grad= 367 T/m 1 14.4 1.01 2 14.4 1.01 3 17.3 .965 4 17.3 .965 5 15.0 .988 6 15.0 .988 50 100 150 200 25 50 75 100 125 1 2 3 4 5 6

0124578012455666666655443221099 234678013455666666655443221099 45679023456667666655443221099 6789123556777776665543321099 890134556676777665544321009 01244455566666665554322109 2344444555555555544332109 443333445454444433221109 33222323444433322211009 2211112122232222110009 110000001111221110098 09998999990001100098 9977777788900001098 676565667889991098 55434456797000987 3233447778910987 211345779009887 02346680099877 2456890998776 567800988766 88109887766 0098877665 988776655 87766655 7666555 665554 55544 5444 444 43 3

  • 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

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SLIDE 9

Fields vs radius with grading & dr/r=2.0

Pole tip field (T) Inside rad (mm) 20 40 60 3 4 5 6 7 8 9 2 10.0

  • Zlobin

70% 63% 50% 45% 37% 33% · · · · ·

  • LARP

+ + + + + dr/r=2.0 + + + + + dr/r=.5 un-graded dr/r=2 graded

  • Gain from grading ≈ 10% independent of radius
  • Gain including dr/r=2 greatest for small radii

9

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SLIDE 10

Use of exotic materials for pole tips

Holmium

  • nly 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

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SLIDE 11

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

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SLIDE 12

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

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SLIDE 13

Fields vs radius with 2 cm shield

Pole field (T) Pole Radius (mm) 20 40 60 2 3 4 5 6 7 8 9 10.0

  • Zlobin

LARP Zlobin + 52% + 35% Graded dr/r=2 + 100% + 48% With Gadolinium pole

  • Gain now a factor of 2 for 10 mm
  • Gain a factor of 1.5 for 30 mm

13

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SLIDE 14

field quality

Rad (mm) B (T) 104 dB/B 20 40 60 5 10 15 /10

  • Seems ok (dB/B < 10−4) with square pole end
  • Could be improved with pole shaping

14

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SLIDE 15

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

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SLIDE 16

Baseline final focus with 2cm shield and 50 cm gaps

Radius (m) Length (m) sigmas 4 Ebeam (TeV) 0.75 shield(cm) 2.0 Btip(T) 0.0 fac 1.00 beta IP (mm)=10 pole tip field Nb3Sn emit (micron) = 25 beta max (km) 23.3 beta max (km) 22.5 G(m) L(m) R(cm) (T/m) B1 B2 6.00 1.10 1.76 193 2.7 to 3.4 7.2 0.50 1.20 2.51 187 3.6 to 4.7 8.4 0.50 2.10 3.50 -175 4.9 to 6.1 9.6 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 5 10 15 20 0.000 0.025 0.050 0.075 0.100

  • Betamax=23 km

about correct

16

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SLIDE 17

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

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SLIDE 18

example with 3 m to first quad including gadolinium

Radius (m) Length (m) sigmas 4 Ebeam (TeV) 0.75 shield(cm) 2.0 Btip(T) 1.5 fac 1.00 beta IP (mm)= 5 pole tip field Nb3Sn emit (micron) = 25 beta max (km) 21.8 beta max (km) 20.2 G(m) L(m) R(cm) (T/m) B1 B2 3.00 0.85 1.37 321 4.7 to 4.4 10.8 0.50 0.85 2.16 298 6.3 to 6.4 12.4 0.50 1.65 3.29 -262 8.2 to 8.6 13.8 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 5 10 15 0.000 0.025 0.050 0.075 0.100

  • Betamax=20 km is less than baseline
  • But 5 mm beta star gives twice the luminosity,
  • or half the background and driver requirements

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SLIDE 19

Conclusion

  • 200 T/m Nb3Sn 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

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