Magnets for muon collider ring and interaction regions V.V. Kashikhin, FNAL December 03, 2009.
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Transcript of 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
2
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
~2
1
4
2
0L
P – average muon beam power (~ )
4
Nr
C – collider circumference (~ if B=const)
– muon lifetime (~ )
* – beta-function at IP
– beam-beam parameter
0.5 1 1.5 2
0.6
0.7
0.8
0.9
h
z /
“Hour-glass factor”
3
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
5x
4
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
5
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
0
20
40
60
80
100
120
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160
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200
220
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Luminocity (x1035 cm−2s−1)
Qu
ench
gra
die
nt
(T/m
)
0 5 10 15 20 25 30 35 40 45 50 55 60
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.
6
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
7
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
8
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?
9
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!
+ =
10
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
11
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
12
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
13
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
14
IR BE1 magnet: FQ zoneFQ optimized for the 1:2 beam ratio. ~Elliptical good field area
Shell magnet Shell/block hybrid
X (mm)
Y (
mm
)
Field quality (10-4)
-60 -40 -20 0 20 40 60-60
-40
-20
0
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40
60
0
1
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5
6
7
8
9
X (mm)
Y (
mm
)
Field quality (10-4)
-60 -40 -20 0 20 40 60-60
-40
-20
0
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40
60
0
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10-3 limit: 118x56mm10-4 limit: 108x26mm
10-3 limit: 120x64mm10-4 limit: 84x37mm
15
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
16
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.
17
BE1 dipole ends
Midplane gap and open aperture are maintained throughout the magnet
18
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
19
IR dipole: forces
23% of total
17% of total6.6% of total
16% of total
20
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
21
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)
22
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