a proposal for a 50 t hts solenoid

Sep 26, 2006 S. Kahn -- 50 T HTS Solenoid 1

A Proposal for a 50 T HTS Solenoid

Steve Kahn

Muons Inc.

September 26, 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 15 T alternating solenoid scheme previously studied.


From R. Palmer

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 Field

Scale 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


Fit to High Field to Extrapolate Beyond 27 T

42 K Scale Factor Extrapolator

y = -5.90994E-05x2 - 1.87412E-02x + 2.15326E+00

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30

Field, T

Scal

e Fa

ctor 2.2 2.17 2.11

Poly. (2.2 2.17 2.11 )

• 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

Field Quadratic Linear

30 1.5378 1.5454

40 1.3091 1.3384

50 1.0685 1.1314

60 0.816 0.9244


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.


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)


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.


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• (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

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 perform computer simulations of 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.

– 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.


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 ??


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.

Component Area Fraction

HTS conductor 0.3483 mm2 0.238

Ag matrix/sheath 0.8127 mm2 0.556

SS Insulator 0.301 mm2 0.206


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:

Specific Heat

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 100 200 300 400 500 600 700

T, K

C J

ou

le/K

cm

3

Ag

Cu

SS

Resistivity

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

0 100 200 300 400 500 600 700

Temperature, K

Res

isti

vity

, o

hm

-m

Cu 85

Ag

SS 304

edV

ba

TETDC

TBTA


Critical Current Measurements

• 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:

Chart Titley = -7.3597E-05x3 + 4.6980E-03x2 - 9.9374E-02x +

1.0108E+00

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30

B, T

I/Ic I/Ic

Poly. (I/Ic)

Critical Current vs T

y = -0.0597x + 5.8033

-1

0

1

2

3

4

5

6

0 50 100 150

T, K

I/Ic Series1

Linear (Series1)

59.0

200

2000

1

1

1),(

c

c

c

c B

BT

BB

J

JJBT

Used only high field part of data to determine Bc20


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.

Ts

T0

T1

)(

)()(

max21

0

critS

OpS

S

AveVcondquench

TTT

TT

TL

CA

Iv

Lorentz Number


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.

REXTLRPR

RSW

Power Supply

Solenoid Magnet


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.


Quench Parameters as a Function of External Resistance

Time Constant vs Ext Resistance

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 200 400 600 800 1000 1200

External Resistance, ohm

Tim

e C

on

stan

t, s

ec

tc

Max Temperture vs. Ext Resistance

0

100

200

300

400

500

600

700

800

0 200 400 600 800 1000 1200


Max

Tem

per

ture

, K

External Voltage vs External Resistance

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

0 200 400 600 800 1000 1200


Ext

ern

al V

olt

age,

V

•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.


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.


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.

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