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### A Proposal for a 50 T HTS Solenoid

Steve Kahn

Muons Inc.

September 26, 2006

S. Kahn -- 50 T HTS Solenoid

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 -- 50 T HTS Solenoid

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 -- 50 T HTS Solenoid

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.

S. Kahn -- 50 T HTS Solenoid

High Strength Tape used for calculations

New and Improved High Strength Plus Tape

Properties of American Superconductor’s High Temperature Superconductor Wire- 6% more current per turn
- 10 % more turns per radial space

S. Kahn -- 50 T HTS Solenoid

Cross Sections of AMSC HTS Tape

High Current Tape

High Compression Tape

High Strength Tape

React and Wind

S. Kahn -- 50 T HTS Solenoid

Some Mechanical Properties of Oxford BSSCO-2212

Strain Degradation at 0.4%

Wind and React

Ultimate Strength~130 MPa

Young’s Modulus

E~51-63 GPa

S. Kahn -- 50 T HTS Solenoid

Why Do We Want to Go to Liquid Helium?

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).

S. Kahn -- 50 T HTS Solenoid

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

S. Kahn -- 50 T HTS Solenoid

Quadratic

Linear

30

1.5378

1.5454

40

1.3091

1.3384

50

1.0685

1.1314

60

0.816

0.9244

Fit to High Field to Extrapolate Beyond 27 T- We are using BSSCO 2223 which has been measured only to 27 T in the perpendicular configuration. We are using it in the parallel configuration.
- We have to extrapolate to high field.
- We know that BSSCO 2212 has been tested to 45 T, so we think that the AMSC tape will work.
- The high field measurements of BSSCO 2212 has a different falloff from BSSCO 2223.
- We certainly will need measurements of the AMSC tape at high field

S. Kahn -- 50 T HTS Solenoid

A Vision of a Very High Field Solenoid

- Design for 50 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 50 Tesla.
- We operate at 85% of the critical current.
- All parameters used come from American Superconductor’s Spec Sheets.

S. Kahn -- 50 T HTS Solenoid

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 -- 50 T HTS Solenoid

A Slightly More Aggressive Approach

- We can vary the amount of stainless steel interleafing as a function of radius to achieve 0.4% strain.
- 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.
- 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.

S. Kahn -- 50 T HTS Solenoid

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.

S. Kahn -- 50 T HTS Solenoid

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
- (We are now using a 1 m length.)
- 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

S. Kahn -- 50 T HTS Solenoid

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 perform computer simulations of quench protection for the HTS system to determine how to protect the magnet in case of an incident.

S. Kahn -- 50 T HTS Solenoid

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.

S. Kahn -- 50 T HTS Solenoid

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%.

S. Kahn -- 50 T HTS Solenoid

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.
- Program for conductor tests at 45 Tesla.
- 45 Tesla magnet has limited aperture (3.1 cm).
- It has a warm aperture.
- There is a 38 Tesla facility in Japan that could be used if the 45 Tesla facility is not available.

S. Kahn -- 50 T HTS Solenoid

Preliminary Calculations for Quench Protection

- I am presenting some preliminary calculations using the quench calculation program QUENCH.
- This program was written by Martin Wilson at Rutherford Lab in the 1970’s. The current version of the program is marketed by B. Hassenzahl of Advanced Energy Analysis. BNL has a license to use it.
- There are other codes available:
- QUENCHPRO at FNAL Technical Division.
- SPQR from CERN.
- Vector Fields is developing a quench propagation code ??

S. Kahn -- 50 T HTS Solenoid

Conductor and Insulator Description

- The conductor is BSCCO 2223 which is 30% HTS filaments and 70% Ag matrix and Ag-Mg sheath (for strength). We assume the matrix/sheath is all Ag for the calculation.
- The insulator is assumed to be the Stainless Steel interleaving. A minimum thickness (0.07 mm) is used since we are describing the inner layers.
- In practice we will likely add a ceramic coating or kapton wrap as insulator. This will inhibit the transverse quench propagation.

S. Kahn -- 50 T HTS Solenoid

Conductor Material Properties Necessary for Quench Protection

- We need the material properties of all the components of the conductor and insulation.
- The important properties are
- Heat capacitance (Specific Heat)
- Resistivity
- Thermal conductance
- Obtained from resistivity with Wiedemann-Frantz law.
- CV and are parameterized as in up to four temperature ranges:

S. Kahn -- 50 T HTS Solenoid

Critical Current Measurements

Used only high field part of data to determine Bc20

- Measurements of critical current as a function of B and temperature are from EHTS (another provider of BSSCO 2223).
- The measured data is used to determine parameters of the following equation:

S. Kahn -- 50 T HTS Solenoid

Ts

T0

Lorentz Number

Quench Propagation Velocity- Quench protection calculations depend on the quench propagation velocity.
- The quench propagation velocity can be calculated from the formula below.
- This is what I did.
- Experience for NbTi shows that the formula does not reproduce the measurements.
- Typically the experimentally determined value is used.
- We need to measure this for HTS.
- One of the weaknesses of the velocity calculation is that the specific heat (CV) varies as T3 and is rapidly varying at the quench front.

S. Kahn -- 50 T HTS Solenoid

Circuit for Quench Energy Extraction

- Quench circuit components:
- Solenoid represented by inductance L. Also there is an internal resistance (not shown) which is about 10 ohm.
- RPR represents the energy extraction resistance. This will take the large share of quench energy.
- Switch will be activated by quench detection system.
- Could even be a diode system.
- REXT represents the resistance associated to leads, power supply, etc.

Power Supply

RSW

RPR

L

REXT

Solenoid Magnet

S. Kahn -- 50 T HTS Solenoid

Circuit Parameters

- QUENCH treats the whole magnet. It does not provide for segmenting the magnet into separate coupled systems.
- The total inductance can be calculated from the stored energy:
- U=½LI2 where U=20 Mega-Joules and I is the total amp-turns(=2.97107).
- There are 444 layers 175 turns/layer = 77625 turns.
- This gives 280 henrys (big!)
- The resistance associated with 61 km of Ag is 8 ohms.
- We certainly will need to trigger an external resistance into the circuit with a quench is detected.

S. Kahn -- 50 T HTS Solenoid

Quench Parameters as a Function of External Resistance

- The figures show the following parameters
- as a function of an external resistance for
- energy extraction.
- Maximum temperature on conductor
- Time constant for decay
- External voltage on external resistance
- Note that as one increases the external
- resistance one decreases temperature, but
- increases the external voltage.

S. Kahn -- 50 T HTS Solenoid

A Better Approach

- It may be a better approach to divide the magnet radial into separate thermally and electrically isolated systems on separate power supplies. These systems would be coupled through mutual inductance.
- Each system would contain less stored energy and could have different time constants and different start times.
- Different sub-systems would have different critical currents since they are at different magnetic fields. Some may not quench at all.
- QUNECH can not simply handle this complex system.
- Do the other codes handle this or do we have to write our own?
- Fermilab people may have thought about this.

S. Kahn -- 50 T HTS Solenoid

What Do We Need to Measure?

- It is clear from this initial calculation that some parameters are not well known. We should try to measure them.
- Electrical resistivity and heat capacity of HTS conductor as a function of temperature. This should be done above critical current.
- Same measurements of Silver as a control.
- Determine Ic(B) at high field. Verify that the critical current relation that we used (which was developed for NbTi, Nb3Sn) works for HTS.
- Measure the quench propagation velocity. This is important.

S. Kahn -- 50 T HTS Solenoid

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