# Presentation: 795606

## High Field Solenoid Discussions at BNL

- Steve Kahn
- Muons Inc.
- Nov 9, 2005

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## 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 15 T alternating solenoid scheme previously studied.

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## 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.

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Properties of American Superconductor’s High Temperature Superconductor Wire

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Cross Sections of HTS Tape

- High Strength Tape

- High Compression Tape

- High Current Tape

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

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

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Fit to High Field to Extrapolate Beyond 27 T

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Different Approaches

- We have examined several different approaches.  Each approach is tailored to a different desired field.
- A hybrid design where a HTS insert is placed inside a Nb3Sn Solenoid
- The Nb3Sn outsert provides 14 T and the HTS insert provides the last 6 T to achieve 20 T solenoid.
- A design where HTS tape is interleaved with constant thickness stainless steel tape to mitigate strain on the HTS.  We think that we can achieve 40 T with this scheme.
- If we vary the thickness of the stainless steel tape as a function of radial position we can possibly achieve 50 T.
- If we vary the current density as a function of the radial position we may possibly achieve 60 T.
- Examining these different approaches will be the scope of the Phase I proposal.

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Building a High Field Solenoid from HTS Conductor

- We shall look at two examples to build a 20 Tesla solenoid.
- One example is built entirely with HTS conductor.
- The other is a hybrid solenoid with a HTS insert surrounded by a outsert solenoid made with Nb3Sn conductor.
- The hybrid design is chosen since HTS conductor is very expensive.  Generating 14 T of the field with the less expensive Nb3Sn makes the magnet more affordable.
- We have chosen the *high strength* HTS conductor.
- The inner radius is the minimum bend radius:  25 mm
- The current density is determined by the 20 T field needed on the inner surface:  254 amp/mm2
- The outer radius of the all HTS solenoid is determined by the total current necessary to make 20 T:  88 mm.
- In both these cases the radial forces are contained by an outer Stainless Steel Shell.

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Case 2: Hybrid Magnet with Outer Nb3Sn Coils and Inner HTS Coils

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Hybrid Case with Outer Coils Made of Nb3Sn and Inner Coils of HTS

- This case uses Nb3Sn superconductor for the region where the field is less than 14 Tesla.
- The upper figure shows a contour plot of BZ.  The lower figure shows a contour plot of BR.

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Case 2: Summary of Parameters for Hybrid Magnet

- Maximum Stress determined by integrating radial force density.
- Note that Inner and Outer Stored Energy are that part of the total energy associated to those coils.  They are not that which comes from powering the coils separately.

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## How Do We Constrain the Radial Force?

- Suppose we try to constrain the radial force with a stainless steel shell.
- Stainless Steel 316 Tensile Strength: =460-860 MPa.
- Choose =700 MPa.
- Radial stress from superconductor: P =84 MPa
- Superconductor outer radius: 88 mm.
- The constraining shell needs to be at least 10.6 mm thick.
- This is possible!

- p

- w

- w=Pr

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Case 2 :  Hybrid Magnet Radial Containment

- Based on the radial stress from the HTS we would require a stainless steel containment shell with thickness of 4 mm.
- Based on the radial stress from the Nb3Sn we would require a stainless steel containment shell with thickness of 8.5 mm.
- This approach is limited by the maximum compressive stress the the conductor can take.
- We think that we can get to 27 T by this approach.
- There are uncertainties about the material properties that might further limit this.

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Case 3: 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)

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## A Vision of a Very High Field Solenoid

- Design for 40 Tesla.
- Inner Aperture Radius: 2.5 cm.
- Axial Length chosen: 1 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 40 Tesla.
- We operate at 85% of the critical current.
- All parameters used come from American Superconductor’s Spec Sheets.

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Case 3: Using Stainless Steel Interlayer

- The figure shows tensile as a function of the radial position for the cases of 1.5 and 2 mil stainless steel interleaving tape which will take some of the stress.  These stresses are calculated for a 40 Tesla solenoid!
- The effective modulus for the HTS/SS combination increases with increased SS fraction:
- 90 GPa for no SS
- 96 GPa for 1.5 mil SS
- 98 GPa for 2 mil SS
- 101 GPa for 3 mil SS
- 104 GPa for 4 mil SS
- 110 GPa for 5 mil SS
- The maximum strain limit for this material is 0.35%.
- With 4 mil Stainless Steel we have achieved 40 Tesla!

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## 40 Tesla Solenoid Parameters When Varying the Stainless Steel Fraction

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## A Slightly More Aggressive Approach

- Bob Palmer has suggested that 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 Bob finds that he can build a 60 Tesla solenoid.  (We need to check this but it seems plausible).
- I was only able to achieve 50 T.
- A 60 Tesla solenoid will require significantly more HTS and will consequently cost more.

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Case 4b: Naively Increasing The Field to 50 T

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Case 5: Vary SS Thickness to Achieve 50 T

- HTS Length: 7.27105 m
- HTS Cost: M$ 14.6

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Case 5: Varying SS Thickness in Different Radial Regions to Achieve 50 Tesla

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Can We Do More?

- So far we have used a constant current density in each layer.
- This current density is determined by the field of the solenoid on the inner surface.  We know that the field drops as radius in the conductor region.
- We could put different radial regions on different power supplies and increase the current as the field drops.
- This could increase the field of the magnet.
- This will reduce the amount of HTS (and cost) needed.

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Can We Do More (Continued)

- We could use some other material other than Stainless Steel.  We are limited by the stainless steel modulus.  A higher modulus would reduce the strain allowing us to increase the field.
- Possibilities include Chromium:
- Modulus: 279 GPa   (Stainless Steel was 200 GPa)
- Strength:  689 MPa (for Hard Cr) (Stainless Steel was 460-860 MPa)
- Stainless Steel is probably easier to work with than Chromium (??)
- Iridium:           Not cheap
- Modulus: 528 GPa
- Strength: 1200 Mpa
- Molybdenum:    Not cheap and probably not available in practical form
- Modulus: 325 GPa
- Strength:  650 MPa

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Some Material Properties That We Need to Know

- What is Jeff for fields B>27 Tesla?
- Could this be done at the NHMFL in Florida?
- What are the moduli of this anisotropic material along the three principle axes?
- Does the American Superconductor know this or could we measure it?
- What are the compressive strain/stress limits along each of the three principle axes?
- What are the current carrying aspects under these limits.
- What are the temperature expansivity along these three principle directions?
- Are there fatigue issues associated with repeated cycling of the magnet?
- American Superconductor had observed cycling issues with associated with He getting into the current carrying region.  This may have been addressed.
- Are there radiation issues with this material?

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## There Are Major Engineering Issues That We Need to Understand

- At 20 T we have 1 mega Joule of stored energy.   At 60 T we have 10 mega Joules of stored energy.
- We need to plan how to get the current and stored energy out should there be an incident (i.e., quench).
- Can we use diodes to induce resistance?  Are there diodes massive enough to take 60 T?
- Unlike normal superconductors, heaters to induce a quench may won’t work.
- The overall forces go up with the stored energy.  We need to constrain monstrous forces.

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Lattice Designs and Simulations

- We need to design a lattice for 20, 30, 40, 50, 60 Tesla.
- The lattice must go from high field to a lower field that can encompass the large RF cavities associated with 850-1300 MHz.
- Will need simulations to verify performance.
- Need to match to upstream/downstream cooling
- Upstream HCC parameters
- Downstream PIC parameters

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Conclusion

- This is turning out to be a very exciting proposal.
- Hopefully the referees will think so!

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005

## Proposal Strategy

- There are many magnet experts who understand more about HTS and have not built  a 50 T magnet.
- We need to propose *a high field solenoid* and examine the difficulties at achieving various field levels.
- We need to be careful if we promise 50-60 T and can only deliver say 35 T.
- We need to be able to declare a 35 T solenoid a success to be able to get a Phase II proposal!

- S. Kahn -- Solenoid Proposal

- Nov 9, 2005