aug 29, 2006s. kahn -- 50 t hts solenoid1 a proposal for a 50 t hts solenoid steve kahn muons inc....

Aug 29, 2006 S. Kahn -- 50 T HTS Solenoid 1

A Proposal for a 50 T HTS Solenoid

Steve Kahn

Muons Inc.

August 29, 2006


Alternating Solenoid Lattice for Cooling

• We plan to use high field solenoid magnets in the near final stages of cooling.

• The need for a high field can be seen by examining the formula for equilibrium emittance:

• The figure on the right shows a lattice for a 50 T alternating solenoid scheme previously studied.

From R. Palmer


A Proposal for a High Field Solenoid Magnet R&D

• The availability of commercial high temperature superconductor tape (HTS) should allow significantly higher field that can produce smaller emittance muon beams.

• HTS tape can carry significant current in the presence of high fields where Nb3Sn or NbTi conductors cannot.

• We would like to see what we can design with this commercially available HTS tape.


Comparison of JE for HTS Conductors

We have chosen to use Bi2223 since it is available as a reinforced tape from AMSC

The conductor can carry significant current at very high fields. NbTi and Nb3Sn can not.


Properties of American Superconductor’s High Temperature Superconductor Wire

•6% more current per turn

•10 % more turns per radial space

Parameter High Current Wire

High Strength Wire

Compression Tolerant Wire

High Strength Plus Wire

Je amp/mm2 161 113 100 133 Thickness, mm 0.22 0.3 0.3 0.27

Width, mm 4 4.2 4.85 4.2 Max Tensile Strength

(77º K), MPa 65 300 280 250

Max Tensile Strain (77ºK)

0.10% 0.35% 0.30% 0.4%

Max Compressive Strain (77º K)

0.15% 0.15%

Min Bend Radius, mm 50 25 25 19 Max Length, m 800 400 400 400

Spliceable no yes yes yes

New and Improved High Strength Plus Tape

High Strength Tape used for calculations


Cross Sections of AMSC HTS Tape

High Strength Tape

High Compression Tape

High Current Tape

React and Wind


Some Mechanical Properties of Oxford BSSCO-2212

Young’s Modulus

E~51-63 GPa

Ultimate Strength~130 MPa

Strain Degradation at 0.4%

Wind and React


Why Do We Want to Go to Liquid Helium?

Field Scale Factor vs. Temperature

0

0.5

1

1.5

2

2.5

3

3.5

0 10 20 30 40 50 60 70 80

Temperature, K

Field

Sca

le Fa

ctor

Parallel

Perpendicular

The parallel field orientation is the most relevant for a solenoid magnet.

Previous calculations had used the perpendicular field. (We can view this not as a mistake, but as a contingency).


Current Carrying Capacity for HTS Tape in a Magnetic FieldScale Factor is relative to 77ºK with self field

4.2 K Scale Factor

0

1

2

3

4

5

6

0 5 10 15 20 25 30

Field, T

Scale

facto

r

4.2K par

4.2K perp


A Vision of a Very High Field Solenoid

• Design for 50 Tesla.• Inner Aperture Radius: 2.5 cm.• Axial Length chosen:0.7 meter• Use stainless steel ribbon between layers of HTS tape.

– We will vary the thickness of the SS ribbon.– The SS ribbon provides additional tensile strength

• HTS tape has 300 MPa max tensile strength.• SS-316 ribbon: choose 660 MPa (Goodfellow range for

strength is 460-860 MPa)• Composite strength = SS SS + (1-SS) HTS (adds like

parallel springs).• We use the Jeff associated to 50 Tesla.

– We operate at 85% of the critical current.• All parameters used come from American Superconductor’s Spec

Sheets.


Constraining Each Layer With A Stainless Steel Strip

• Instead of constraining the forces as a single outer shell where the radial forces build up to the compressive strain limit, we can put a mini-shell with each layer. Suggested by R. Palmer, but actually implemented previously by BNL’s Magnet Division for RIA magnet. (See photo)


Using Stainless Steel Interleaving for Structural Support of 40 Tesla Magnet

• Case 1: Use constant thickness interleaving between layers for structural support.

– The high strength HTS tape comes with ~2.7 mils stainless steel laminated to the tape. Additional SS is wound between the layers.

– The effective modulus of the HTS/SS combination increases with increased SS fraction.

• Figure shows strain vs. radial position for a 40 Tesla magnet.

– The maximum strain limit for the material is 0.4%.

• This is achieved with 5 mil SS interleaving.

• The use of constant thickness SS interleaving is not effective for magnets with fields much above 40 Tesla.


A Slightly More Aggressive Approach

• We can vary the amount of stainless steel interleafing as a function of radius.– At small radius where we have smaller stress, we could use a

smaller fraction of stainless steel. (See previous slide)– In the middle radial region we would use more stainless where

the tensile strength is largest.• Following this approach we can build a 50 Tesla solenoid.

– I will show you results for two cases:• Case 2: 40 Tesla solenoid with SS interleaving varied to

achieve 0.4% strain throughout.• Case 3: 50 Tesla solenoid with SS interleaving varied to

achieve 0.4% strain throughout.• A 60 Tesla solenoid may be achieved by increasing the current as

the field falls off with radius by using independent power supplies for different radial regions.


Varying SS Interleaving to Achieve Maximum Strain

• The thickness of the stainless steel interleaving is varied as a function of radius so as to reach the maximum allowable strain through out the magnet.– This minimizes the outer

solenoid radius (and consequently the conductor costs).

– This also brings the center of current closer to the axis and reduces the stored energy.

– This is likely to increase the mechanical problems.


Case Comparisons

• The tables on the left summarize the parameters and results of the three cases presented.– The analysis assumes the

solenoid length is 70 cm– The top table shows the

dimensional parameters:• Inner/outer radius• Conductor length and

amp-turns.– The bottom table shows the

results from the magnetic properties:

• Stored energy• Radial and Axial Forces

Parameter Case 1 Case 2 Case 3

Stainless Steel width 5 mil fixed

variable variable

B0 tesla 40 40 50

Inner Radius, mm 25 25 25

Outer Radius, mm 200 168 224

Conductor Length, km 60.0 46.7 59.9

Current, mega-amp-turns 23.56 23.20 29.73

Parameter Case 1 Case 2 Case 3 Stainless Steel width 5 mil fixed variable variable

B0, tesla 40 40 50 Bdl, tesla-m 29.58 29.12 37.32

Stored Energy, mega joules 11.0 7.8 20.5 Total Radial Force,

mega newtons 201 173 340

Axial End Force, mega newtons

-16.5 -11.9 -30.5


Comments on Stored Energy

• The 70 cm length was chosen to be consistent with the range of ~100 MeV muon. It is also the minimum solenoid length where there is some “non-fringing” central field.

• The stored energy of the 50 Tesla magnet (case 3) is 20 Mega-Joules (for 70 cm).– This can be compared to 7 Mega-Joules for the 10 m long LHC

2-in-one dipole.• The LHC quench protection system actually handles a string

of dipoles in a sextant (?).• There are differences between HTS and NbTi that need to be

considered for quench protection.– HTS goes resistive at a slower rate than NbTi.– A quench propagates at a slower velocity in HTS than for NbTi.– We will have to design a quench protection for the HTS system

to determine how to protect the magnet in case of an incident.


What about Axial Forces?

• There is a significant contribution to the axial forces from the fringing radial fields at the ends.– In the 50 Tesla solenoid

shown we will see a fringing field of 9 Tesla

– We have seen that there is a total axial compressive force at the center of ~30 Mega-Newtons.


More on Compressive Forces

• The top figure shows the Lorentz force density at the end of the solenoid as a function of radius for the three cases.

– The axial pressure on the end is P=JBrt where t is the tape width. This peaks at 10 MPa.

• The lower figure shows the Lorentz force density along the length for the peak radial position.

– It is largest at the end and falls to zero at center as expected.

• These stresses are not large. Do we have to worry about compressive strain along the axial direction?

– The maximum allowable compressive strain for the tape is 0.15%.

0.00E+00

5.00E+08

1.00E+09

1.50E+09

2.00E+09

2.50E+09

3.00E+09

0 0.05 0.1 0.15 0.2 0.25

Radius, m

Case 1

Case 2

Case 3

Maximum Axial Forces Along Z

0.00E+00

5.00E+08

1.00E+09

1.50E+09

2.00E+09

2.50E+09

3.00E+09

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Axial Position, m

Case 1

Case 2

Case 3


Formulate R&D Plan

• Initial measurements of material properties.– JC measurements under tensile and compressive strain.– Modulus measurements of conductor.– Thermal cycling to 4K.

• Formulate and prepare inserts for high field tests.– Design insert for test in 30 Tesla magnet.

• This magnet has a reasonable size aperture.– At 30 Tesla, some part of the insert should be at the strain limit.

• Initial testing of insert can be performed with FNAL 16-17 T solenoid.

– Can increase current in lower field magnet so that JB can still be significant for testing.

– Program for conductor tests at 45 Tesla.• 45 Tesla magnet has limited aperture (3.1 cm).• It has a warm aperture.

• Formulate and simulate a quench protection scheme.

aug 29, 2006s. kahn -- 50 t hts solenoid1 a proposal for a 50 t hts solenoid steve kahn muons inc....

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