A Proposal for a 50 T HTS Solenoid

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Nov 29, 2013 (3 years and 8 months ago)

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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


Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

2

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

Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

3

Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

4

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 Nb
3
Sn or NbTi conductors cannot.


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

Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

5

Comparison of J
E

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
Nb
3
Sn can not.

Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

6

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

J
e
amp/mm
2

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

Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

7

Cross Sections of AMSC HTS Tape

High Strength Tape

High Compression Tape

High Current Tape

React and Wind

Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

8

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

Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

9

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 Scale Factor
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).

Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

10

Current Carrying Capacity for HTS Tape in a Magnetic Field

Scale Factor is relative to 77
ºK 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 factor
4.2K par
4.2K perp
Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

11

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 J
eff

associated to 50 Tesla.


We operate at 85% of the critical current.


All parameters used come from American Superconductor’s Spec
Sheets.



Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

12


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)

Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

13

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.



Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

14

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.

Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

15

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.

Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

16

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

B
0
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

B
0,
tesla

40

40

50


B

dl, 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 newton
s

-
16.5

-
11.9

-
30.5


Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

17

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.

Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

18

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.


Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

19

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=J

B
r

t 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%.


Aug 29, 2006

S. Kahn
--

50 T HTS Solenoid

20

Formulate R&D Plan


Initial measurements of material properties.


J
C

measurements under tensile and compressive strain.


Modulus measurements of conductor.


Thermal cycling to 4

K.


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 J

B 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.