Magnets for muon collider ring and interaction regions V.V. Kashikhin, FNAL December 03, 2009.

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Magnets for muon collider ring and interaction regions V.V. Kashikhin, FNAL December 03, 2009

Transcript of Magnets for muon collider ring and interaction regions V.V. Kashikhin, FNAL December 03, 2009.

Page 1: Magnets for muon collider ring and interaction regions V.V. Kashikhin, FNAL December 03, 2009.

Magnets for muon collider ring and interaction regions

V.V. Kashikhin, FNAL

December 03, 2009

Page 2: Magnets for muon collider ring and interaction regions V.V. Kashikhin, FNAL December 03, 2009.

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Requirements: ring

MC Lattie Design - Y.Alexahin FNAL, November 11 2009

Muon Collider Parameters 10

s (TeV) 1.5 3

Av. Luminosity / IP (1034/cm2/s) 0.8* 3.4

Max. bending field (T) 9.2** 14

Av. bending field in arcs (T) 7.7 12

Circumference (km) 2.6 4

No. of IPs 2 2

Repetition Rate (Hz) 15 12

Beam-beam parameter / IP 0.087 0.087

* (cm) 1 0.5

Bunch length (cm) 1 0.5

No. bunches / beam 1 1

No. muons/bunch (1012) 2 2

Norm. Trans. Emit. (m) 25 25

Energy spread (%) 0.1 0.1

Norm. long. Emit. (m) 0.07 0.07

Total RF voltage (MV) at 800MHz 60 700

+ in collision / 8GeV proton 0.008 0.007

8 GeV proton beam power (MW) 4.8 4.3

-----------------------------------------------------------------------*) With reduction by beam-beam effect**) Not 10T just by mistake

hC

Pfh

Nnf rep

b

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0L

P – average muon beam power (~ )

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Nr

C – collider circumference (~ if B=const)

– muon lifetime (~ )

* – beta-function at IP

– beam-beam parameter

0.5 1 1.5 2

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h

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“Hour-glass factor”

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Requirements: IR

MC Lattie Design - Y.Alexahin FNAL, November 11, 2009

Final Focus Quads 9

Requirements adopted for this design:

full aperture 2A = 10sigma_max + 2cm (Sasha Zlobin wants + 1cm more)

maximum tip field in quads = 10T (G=200T/m for 2A=10cm)

bending field 8T in large-aperture open-midplane magnets, 10T in the arcs

IR quad length < 2m (split in parts if necessary!)

Gradient (T/m) 250 187 -131 -131 -89 82

Quench @ 4.5K 282 209 146 146 (with inner radius 5mm larger)

Quench @ 1.9K 308 228 160 160

Margin @ 4.5K 1.13 1.12 1.12

Margin @ 1.9K 1.23 1.22 1.22

Is the margin sufficient? If not lower beam energy or increase * to allow for smaller aperture

We don’t need 5sigma+ half-aperture, 3sigma+ is enough: can accommodate N=50 m!

No dipole field from 6 to 16.5m, is it worthwhile to create ~2T by displacing the quads?

a (cm)

z (m)

5y

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Baseline conductor: Nb3Sn

Nb3Sn is superior to

NbTi at all fields and temperatures and has a potential for further improvement

Nb3Sn is superior to

HTS at the fields <18T and the liquid helium temperature ―> fits well in the present optics requirements

From P. Lee

Nb3Sn has a lower critical temperature than HTS (18K vs. >85K). However,

our (LARP) experience with measuring thermal margin in Nb3Sn magnets

shows that even the 18K margin is unlikely to be explored in a collider because of the cryogenic constraints

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Thermal potential of Nb3Sn

The 120-mm Nb3Sn quads in the LHC IR

triplets CAN operate at the luminosity of 1036 cm-2s-1 with ~20% margin IF the cryogenic system is able to extract the heat (~3kW per 6-m long Q1 magnet at 1.9K)

But it is an order of magnitude above the available cryogenic capacity

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Average power density (mW/g)

T0=1.9K, SS collar

T0=4.5K, SS collar

T0=1.9K, Al collar

T0=4.5K, Al collar

Operating gradient

V. V. Kashikhin, R. Bossert, G. Chlachidze, M. Lamm, N. V. Mokhov, I. Novitski, A.V. Zlobin, “Performance of Nb3Sn Quadrupole Magnets Under Localized Thermal Load”, CEC/ICMC 2010.

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Magnet design concept

Based on the well known and proven (now also for Nb3Sn)

shell-type magnet technology

Avoid dumping all the heat in the cryogenic system by opening the midplanes, using absorbers, optimizing magnet length, etc.

Uniform assumptions for all magnets: Jc(12T,4.2K)=2700A/mm2, scaled with the operating temperature as necessary. Cu/nonCu ratio 1.17. These parameters were achieved in the Nb3Sn conductors for LARP

Use HTS only where Nb3Sn cannot work

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IR quadsMAGNET REFERENCE NAME PARAMETER UNIT

Q1 Q2 Q3

Coil cross-section plot -

Coil aperture mm 80.00 110.00 160.00 Yoke IR mm 83.50 98.50 123.50 Yoke OR mm 200.0 250.0 300.0 Bare cable width mm 16.019 Bare cable mid-thickness mm 1.437 Cable keystoning angle deg 0.750 Cable insulation thickness mm 0.150 Operating gradient T/m 250 193 130 Operating current kA 16.61 15.80 14.17 Quench* gradient @ 4.5K/1.9K T/m 281.5 / 307.6 209.0 / 228.4 146.0 / 159.5 Quench* peak field @ 4.5K/1.9K

T 12.76 / 13.95 13.19 / 14.42 13.49 / 14.75

Quench* current @ 4.5K/1.9K kA 18.90 / 20.82 17.26 / 19.04 16.17 / 17.86 Inductance @ op. gradient mH/m 3.574 6.582 12.882 Stored energy @ op. gradient kJ/m 493.0 821.6 1391.8 Field reference radius mm 27 37 53

b6 - 0.0000 0.0000 0.0001 b10 - -0.0341 0.0019 0.0020 b14 - -0.8615 0.0901 0.0864

Harmonics @ ref. radius & low field

b18 - -0.0632 -0.3714 -0.4198 Fx total MN/m 1.79 2.37 2.79 Fy total MN/m -2.18 -2.89 -3.38

Octant forces @ op. gradient

F IL/OL MN/m 1.29 / 1.28 1.61 / 1.79 2.06 / 1.93

* Jc(12T, 4.2K) = 2700A/mm2, Kcu/nonCu = 1.17

90-mm Nb3Sn

quads were tested by LARP

120-mm quad will be tested next year

There are certain issues, but the way is more or less clear

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Opening midplane in cos-theta coil

Field quality gets destroyed quickly as the midplane gap increases

But, is there way to approach the ideal field with such geometry?

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Analytical concept of an open midplane dipole

Let’s consider the following two statements:

“Cos-theta” magnet cannot be made with an open midplane

Technology used for the “cos-theta” magnets cannot be applied in the open midplane magnets

- Somewhat true

- Fundamentally wrong!

+ =

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Open-midplane ring dipole

Based on two double-shells to minimize the number of splices

Keystoned cable to ease winding of coil ends

Aperture available for the beam – 60mm

Bop~10T with ~15%

margin at 4.5K.

Midplane gap:

Coil-coil – 30mm

Clear – 20mm

As the conductor is removed from the coil midplanes, it can no longer be referred to as the “cosine-theta” geometry. Although it may look that way, the optimization employs different (from the “cosine-theta”) criteria to compensate for the missing turns

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Combined-function ring dipole

Different left and right gaps to create gradient

Asymmetric coils to optimize the field quality (work in progress)

The B/G ratio is built into the design, but can be adjusted for the specific requirements

Bop~10T, Gop~23T/m with ~15% margin at 4.5K

Midplane gap:

Coil-coil – 30/42mm

Clear – 20mm

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Ultimate case – gradient C-dipole Naturally provides dipole

field and relatively large gradient

Bop~10T, Gop~50T/m with ~10% margin at 4.5K

Midplane gap:

Coil-coil – 60mm

Clear – 50mm

BUT the quadrupole component CANNOT be reversed without reversing the dipole OR reversing the open midplane

It is a limitation of that design,… but before we discard it – would anyone be interested in such magnet?

By

x

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IR BE1 magnet

One of the most challenging magnets in the list: large midplane gap and unusual aperture requirements

Same concept as for the ring dipole, but field quality optimized for the vertically elongated beam

Two double-shells or shell/block hybrid

Bop ~ 8T with ~22% margin at

4.5K in either case.

Midplane gap:

Coil-coil – 60mm

Clear – 50mm

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IR BE1 magnet: FQ zoneFQ optimized for the 1:2 beam ratio. ~Elliptical good field area

Shell magnet Shell/block hybrid

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Field quality (10-4)

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10-3 limit: 118x56mm10-4 limit: 108x26mm

10-3 limit: 120x64mm10-4 limit: 84x37mm

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IR BE1 magnet: iron yoke

800-900 mm outer diameter is required to contain the flux

Can be reduced if fringe field is not a concern

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Coil ends

Shell type geometry allows the “traditional” coil ends even in case of the open midplane magnet.

Benefits:

The winding stresses are minimized as the cable takes the most natural position corresponding to the minimum strain energy;

All conductors are contained within the cylindrical shells that allows the same mechanical structure throughout the coil. It avoids structural discontinuity between the straight section end ends that may cause premature quenches and degradation;

The end length in minimized;

30+ years of polishing this type of superconducting technology starting from Tevatron and continuing in LARP.

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BE1 dipole ends

Midplane gap and open aperture are maintained throughout the magnet

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IR dipole structural analysisAssumptions and

constraints:

Coil elasticity modulus is 40GPa

Coil can move within its envelope and separate from the collar

All prestress is provided by the collar

The collar is registered with respect to the vertically split iron yoke using two keys (per quadrant)

No thermal contraction was considered

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IR dipole: forces

23% of total

17% of total6.6% of total

16% of total

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Shell type IR dipole The mechanical structure is not

optimized

If the coil motion is unrestricted, the stresses approach 300MPa in the coil corners and the maximum vertical displacement is 335 m

If the inner layer spacer is locked with respect to the collar, the stresses are below 200 MPa and the maximum vertical displacement is 240 m

It may be possible to reduce the stress to 150MPa (considered the reversibility limit for Nb3Sn) after the shim and keys

geometry is optimized

However, the Nb3Al conductor having

the stress tolerance up to 500MPa can work right away

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Hybrid IR dipole

The hybrid allows vertical support at the center of the coil midplane

The peak coil stress is ~120MPa and the maximum vertical displacement is ~260 m (no spacer locking is needed)

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SummarySome of the ring and IR magnets were preliminary studied:

The aperture and gradient requirements for the IR quadrupoles are close to those considered by LARP. These magnets can directly benefit from the LARP experience.

The open midplane ring dipole can provide the required field with a sufficient margin. Can be made as the combined function magnet with both midplanes open or as a C-type magnet

Because of the large midplane gap and unusual aperture requirements, the open midplane IR dipole appears to be one of the most challenging magnets

Two IR dipole concepts based on shell and shell/block geometry were considered:

- The good field quality can be obtained within the vertically elongated area in either design

- The stresses approach 200MPa in the shell type design, but may be reduced after optimization of the support structure. The stresses in the hybrid are comfortably low

The shell type magnet technology is an attractive option for either type of the open midplane magnet