U.S. patent application number 15/624237 was filed with the patent office on 2019-01-10 for hypersonic aircraft having homopolar motor with graded resistance.
The applicant listed for this patent is North Carolina State University. Invention is credited to Wan-Kan Chan, Justin Schwartz, Honghai Song, Yawei Wang.
Application Number | 20190009902 15/624237 |
Document ID | / |
Family ID | 60663843 |
Filed Date | 2019-01-10 |
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United States Patent
Application |
20190009902 |
Kind Code |
A1 |
Chan; Wan-Kan ; et
al. |
January 10, 2019 |
HYPERSONIC AIRCRAFT HAVING HOMOPOLAR MOTOR WITH GRADED
RESISTANCE
Abstract
A hypersonic aircraft having a homopolar motor with high
temperature superconducting (HTS) non-insulated (NI) coil magnets
is described. In some implementations, the HTS NI coil magnets can
have a graded resistance design. In some implementations, the HTS
NI coil magnets can include a series of stacked coils, each of the
series of coils comprising multiple turns having turn-to-turn
resistance, where the turn-to-turn resistance of the series of
coils is graded coil-to-coil across the magnet. In some
implementations, the HTS NI coil magnets can include an NI coil
comprising multiple turns and two or more thermal barriers each
disposed between two adjacent turns of the coil, where an
electrically conductive portion of one of the thermal barriers does
not overlap with an electrically conductive portion of a different
adjacent one of the thermal barriers. Some implementations can
include a disk-type homopolar motor/generator including one or more
HTS NI coil magnets.
Inventors: |
Chan; Wan-Kan; (Raleigh,
NC) ; Wang; Yawei; (Raleigh, NC) ; Song;
Honghai; (Okemos, MI) ; Schwartz; Justin;
(Raleigh, NC) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
North Carolina State University |
Raleigh |
NC |
US |
|
|
Family ID: |
60663843 |
Appl. No.: |
15/624237 |
Filed: |
June 15, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62350485 |
Jun 15, 2016 |
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
Y02T 50/60 20130101;
B64C 30/00 20130101; H01F 6/02 20130101; H01F 41/048 20130101; B64D
27/24 20130101; H01F 6/06 20130101; B64C 23/005 20130101; H01L
39/02 20130101 |
International
Class: |
B64C 30/00 20060101
B64C030/00; H01F 6/02 20060101 H01F006/02; H01F 6/06 20060101
H01F006/06; H01L 39/02 20060101 H01L039/02 |
Claims
1. A hypersonic aircraft having a disk-type homopolar
motor/generator, the disk-type homopolar motor/generator
comprising: an electrically conductive metal disk; an electrically
conductive shaft coupled, mechanically and electrically, to the
electrically conductive metal disk; a first electrical contact
configured to be in electrical contact with an edge of the
electrically conductive metal disk; a second electrical contact
configured to be in electrical contact with the electrically
conductive shaft; and a high temperature superconducting (HTS)
non-insulated (NI) coil magnet, comprising: a series of coils that
are stacked, each of the series of coils comprising multiple turns
having turn-to-turn resistance, where the turn-to-turn resistance
of the series of coils is graded coil-to-coil across the HTS NI
coil magnet, wherein the HTS NI coil magnet is arranged so that a
normal component of a magnetic field generated by the HTS NI coil
magnet is substantially perpendicular to a face of the metal
disk.
2. The hypersonic aircraft of claim 1, wherein the series of coils
of the HTS NI coil magnet are axially stacked and graded
coil-to-coil along an axial length of the HTS NI coil maanet.
3. The hypersonic aircraft of claim 1, wherein the series of coils
of the HTS NI coil magnet are radially stacked and graded
coil-to-coil along a radius of the HTS NI coil magnet.
4. The hypersonic aircraft of claim 1, wherein the turn-to-turn
resistance of a first coil of the series of coils is different than
the turn-to-turn resistance of a second coil of the series of
coils, wherein the second coil is stacked adjacent to the first
coil.
5. The hypersonic aircraft of claim 1, wherein the turn-to-turn
resistance of each of the series of coils has a constant
turn-to-turn resistance.
6. The hypersonic aircraft of claim 1, wherein the turn-to-turn
resistance of each of the series of coils is graded turn-to-turn
with respect to the multiple turns of that coil.
7. The hypersonic aircraft of claim 6, wherein the turn-to-turn
resistance is radially graded from a first innermost turn to a last
outermost turn of the multiple turns.
8. The hypersonic aircraft of claim 6, wherein turn-to-turn
resistance varies as a step function of turn number.
9. The hypersonic aircraft of claim 8, wherein the turn-to-turn
resistance of each turn of the multiple turns increases from a
first innermost turn to a last outermost turn of the multiple
turns.
10. The hypersonic aircraft of claim 6, wherein turn-to-turn
resistance varies piecewise continuously from a first innermost
turn to a last outermost turn of the multiple turns.
11. The hypersonic aircraft of claim 10, wherein the turn-to-turn
resistance varies piecewise linearly or piecewise nonlinearly.
12. The hypersonic aircraft of claim 1, wherein turn-to-turn
resistance is an electrical resistance or a thermal resistance.
13. The hypersonic aircraft of claim 1, wherein the turn-to-turn
resistance of the series of coils is graded coil-to-coil across the
HTS NI coil magnet using a layer selected from the group consisting
of: a co-wound layer having thermal resistive and electrical
conductive segments; a layer soldered or bonded to a winding
conductor, the soldered or bonded layer having thermal resistive
and electrical conductive segments; a printed layer on a co-wound
layer, the printed layer on the co-wound layer having thermal
resistive and electrical conductive segments; and a printed layer
on a surface of a winding conductor, the printed layer on the
surface of the winding conductor having thermal resistive and
electrical conductive segments.
14. The hypersonic aircraft of claim 1, wherein the NI coil
comprises a winding conductor selected from a group consisting of:
non-insulated YBCO superconductor tape; non-insulated REBCO
superconductor tape; and non-insulated Bi-2223 multi-filamentary
superconductor tape.
15. A high temperature superconducting (HTS) non-insulated (NI)
coil magnet, comprising: a series of coils that are stacked, each
of the series of coils comprising multiple turns; and coil-to-coil
interfacial materials disposed between adjacent coils of the series
of coils, where the coil-to-coil interfacial materials comprise
thin conductive materials with low coil-to-coil interfacial
resistances that are graded coil-to-coil across the HTS NI coil
magnet.
16. The HTS NI coil magnet of claim 15, wherein the series of coils
are axially stacked and graded coil-to-coil along an axial length
of the HTS NI coil magnet or are radially stacked and graded
coil-to-coil along a radius of the HTS NI coil magnet.
17. The HTS NI coil magnet of claim 16, wherein the coil-to-coil
interfacial resistance varies piecewise linearly or piecewise
nonlinearly along the radius of the coil-to-coil interfacial
materials of axially stacked coils or along an axial width of the
coil-to-coil interfacial materials of the radially stacked
coils.
18. The HTS NI coil magnet of claim 15, wherein the coil-to-coil
interfacial resistance is an electrical resistance or a thermal
resistance.
19. The HTS NI coil magnet of claim 15, wherein the coil-to-coil
interfacial resistance of the multiple turns varies dynamically
based upon local magnetic field strength.
20. The HTS NI coil magnet of claim 15, wherein the coil-to-coil
interfacial resistance of the multiple turns varies dynamically
based upon temperature.
21. The HTS NI coil magnet of claim 15, wherein the coil-to-coil
interfacial materials are formed as a layer selected from the group
consisting of: a layer having thermal resistive and electrical
conductive segments; a layer soldered or bonded to a conductive
layer, the soldered or bonded layer having thermal resistive and
electrical conductive segments; a printed layer on a conductive
layer, the printed layer having thermal resistive and electrical
conductive segments.
22. A homopolar motor/generator including the HTS NI coil magnet of
claim 15.
23. An aircraft including the homopolar motor/generator of claim
22.
24. The aircraft of claim 23, wherein the aircraft is a hypersonic
aircraft.
25. A high temperature superconducting (HTS) non-insulated (NB)
coil magnet, comprising: a coil including multiple turns having
turn-to-turn resistance, where the turn-to-turn resistance of the
coil is graded turn-to-turn with respect to the multiple turns.
26. The HTS NI coil magnet of claim 25, wherein the coil is axially
stacked or radially stacked with a second coil including multiple
turns having turn-to-turn resistance, where the turn-to-turn
resistance of the second coil is graded turn-to-turn with respect
to the multiple turns.
27. The HTS NI coil magnet of claim 25, wherein turn-to-turn
resistance varies as a step function of conductor length.
28. The HTS NI coil magnet of claim 25, wherein turn-to-turn
resistance increases as a step function of turn number from a first
innermost turn to a last outermost turn of the multiple turns.
29. The HTS NI coil magnet of claim 25. wherein the turn-to-turn
resistance varies as a piecewise linear or piecewise nonlinear
function of conductor length.
30. The HTS NI coil magnet of claim 25, wherein the turn-to-turn
resistance is an electrical resistance or a thermal resistance.
31. The HTS NI coil magnet of claim 25, wherein the turn-to-turn
resistance of the multiple turns varies dynamically based upon
local magnetic field strength.
32. The HTS NI coil magnet of claim 25, wherein the turn-to-turn
resistance of the multiple turns varies dynamically based upon
temperature.
33. The HTS NI coil magnet of claim 25, wherein the turn-to-turn
resistance of the coil is graded turn-to-turn with respect to the
multiple turns using a layer selected from the group consisting of:
a co-wound layer having thermal resistive and electrical conductive
segments; a layer soldered or bonded to a winding conductor, the
soldered or bonded layer having thermal resistive and electrical
conductive segments; a printed layer on a co-wound layer, the
printed layer on the co-wound layer having thermal resistive and
electrical conductive segments; and a printed layer on a surface of
a winding conductor, the printed layer on the surface of the
winding conductor having thermal resistive and electrical
conductive segments.
34. The HTS NI coil magnet of claim 25, wherein the NI coil
comprises a winding conductor selected from a group consisting of:
non-insulated YBCO superconductor tape; non-insulated REBCO
superconductor tape; and non-insulated Bi-2223 multi-filamentary
superconductor tape.
35. A homopolar motor/generator including the HTS NI coil magnet of
claim 25.
36. An aircraft including the homopolar motor/generator of claim
35.
37. The aircraft of claim 36, wherein the aircraft is a hypersonic
aircraft.
Description
[0001] This application claims the benefit of U.S. Provisional
Application No. 62/350,485, entitled "Mechanisms Improving
Performance of Superconducting Magnets" and filed on Jun. 15,
2016.
[0002] Embodiments relate generally to aircraft, and more
particularly to hypersonic aircraft having a homopolar motor with a
superconducting magnet.
[0003] Some implementations (first implementations) include a
hypersonic aircraft having a disk-type homopolar motor/generator,
the disk-type homopolar motor/generator comprising an electrically
conductive metal disk, an electrically conductive shaft, a first
electrical contact, a second electrical contact, and a high
temperature superconducting (HTS) non-insulated (NI) coil magnet.
The electrically conductive shaft can be coupled, mechanically and
electrically, to the electrically conductive metal disk. The first
electrical contact can be configured to be in electrical contact
with an edge of the electrically conductive metal disk. The second
electrical contact can be configured to be in electrical contact
with the electrically conductive shaft. The HTS NI coil magnet
comprising a series of coils that are stacked, each of the series
of coils comprising multiple turns having turn-to-turn resistance,
where the turn-to-turn resistance of the series of coils is graded
coil-to-coil across the HTS NI coil magnet. The HTS NI coil magnet
can be arranged so that a normal component of a magnetic field
generated by the HTS NI coil magnet is substantially perpendicular
to a face of the metal disk.
[0004] In some first implementations, the series of coils of the
HTS NI coil magnet are axially stacked and graded coil-to-coil
along an axial length of the HTS NI coil magnet. In some first
implementations, the series of coils of the HTS NI coil magnet are
radially stacked and graded coil-to-coil along a radius of the HTS
NI coil magnet. In some first implementations, the turn-to-turn
resistance of a first coil of the series of coils is different than
the turn-to-turn resistance of a second coil of the series of
coils, wherein the second coil is stacked adjacent to the first
coil. In some first implementations, the turn-to-turn resistance of
each of the series of coils has a constant turn-to-turn resistance.
In some first implementations, the turn-to-turn resistance of each
of the series of coils is graded turn-to-turn with respect to the
multiple turns of that coil. In some first implementations, the
turn-to-turn resistance is radially graded from a first innermost
turn to a last outermost turn of the multiple turns. In some first
implementations, turn-to-turn resistance varies as a step function
of turn number. In some first implementations, the turn-to-turn
resistance of each turn of the multiple turns increases from a
first innermost turn to a last outermost turn of the multiple
turns.
[0005] In some first implementations, turn-to-turn resistance
varies piecewise continuously from a first innermost turn to a last
outermost turn of the multiple turns. In some first
implementations, the turn-to-turn resistance varies piecewise
linearly or piecewise nonlinearly. In some first implementations,
turn-to-turn resistance is an electrical resistance or a thermal
resistance. In some first implementations, the turn-to-turn
resistance of the series of coils is graded coil-to-coil across the
HTS NI coil magnet using a layer selected from the group consisting
of: a co-wound layer having thermal resistive and electrical
conductive segments; a layer soldered or bonded to a winding
conductor, the soldered or bonded layer having thermal resistive
and electrical conductive segments; a printed layer on a co-wound
layer, the printed layer on the co-wound layer having thermal
resistive and electrical conductive segments; and a printed layer
on a surface of a winding conductor, the printed layer on the
surface of the winding conductor having thermal resistive and
electrical conductive segments. In some first implementations, the
NI coil includes a winding conductor that can be non-insulated YBCO
superconductor tape, non-insulated REBCO superconductor tape, or
non-insulated Bi-2223 multi-filamentary superconductor tape.
[0006] Some implementations (second implementations) include a high
temperature superconducting (HTS) non-insulated (NI) coil magnet,
comprising a series of coils that are stacked and coil-to-coil
interfacial materials disposed between adjacent coils of the series
of coils. Each of the series of coils that are stacked comprising
multiple turns. The coil-to-coil interfacial materials comprising
thin conductive materials with low coil-to-coil interfacial
resistances that are graded coil-to-coil across the HTS NI coil
magnet.
[0007] In some second implementations, the series of coils are
axially stacked and graded coil-to-coil along an axial length of
the HTS NI coil magnet or are radially stacked and graded
coil-to-coil along a radius of the HTS NI coil magnet.
[0008] In some second implementations, the coil-to-coil interfacial
resistance varies piecewise linearly or piecewise nonlinearly along
the radius of the coil-to-coil interfacial materials of axially
stacked coils or along an axial width of the coil-to-coil
interfacial materials of the radially stacked coils. In some second
implementations, the coil-to-coil interfacial resistance is an
electrical resistance or a thermal resistance. In some second
implementations, the coil-to-coil interfacial resistance of the
multiple turns varies dynamically based upon local magnetic field
strength. In some second implementations, the coil-to-coil
interfacial resistance of the multiple turns varies dynamically
based upon temperature.
[0009] In some second implementations, the coil-to-coil interfacial
materials are formed as a layer having thermal resistive and
electrical conductive segments, a layer soldered or bonded to a
conductive layer, the soldered or bonded layer having thermal
resistive and electrical conductive segments, or a printed layer on
a conductive layer, the printed layer having thermal resistive and
electrical conductive segments.
[0010] Some implementations (third implementations) include a
homopolar motor/generator including an HTS NI coil magnet of the
second implementations. Some implementations (fourth
implementations) include an aircraft including the homopolar
motor/generator of the third implementations. In some fourth
implementations, the aircraft is a hypersonic aircraft.
[0011] Some implementations (fifth implementations) include an HTS
NI coil magnet comprising a coil including multiple turns having
turn-to-turn resistance, where the turn-to-turn resistance of the
coil is graded turn-to-turn with respect to the multiple turns.
[0012] In some fifth implementations, the coil is axially stacked
or radially stacked with a second coil including multiple turns
having turn-to-turn resistance, where the turn-to-turn resistance
of the second coil is graded turn-to-turn with respect to the
multiple turns. In some fifth implementations, turn-to-turn
resistance varies as a step function of conductor length. In some
fifth implementations, turn-to-turn resistance increases as a step
function of turn number from a first innermost turn to a last
outermost turn of the multiple turns. In some fifth
implementations, the turn-to-turn resistance varies as a piecewise
linear or piecewise nonlinear function of conductor length. In some
fifth implementations, the turn-to-turn resistance is an electrical
resistance or a thermal resistance. In some fifth implementations,
the turn-to-turn resistance of the multiple turns varies
dynamically based upon local magnetic field strength. In some fifth
implementations, the turn-to-turn resistance of the multiple turns
varies dynamically based upon temperature.
[0013] In some fifth implementations, the turn-to-turn resistance
of the coil is graded turn-to-turn with respect to the multiple
turns using a layer selected from the group consisting of: a
co-wound layer having thermal resistive and electrical conductive
segments; a layer soldered or bonded to a winding conductor, the
soldered or bonded layer having thermal resistive and electrical
conductive segments; a printed layer on a co-wound layer, the
printed layer on the co-wound layer having thermal resistive and
electrical conductive segments; and a printed layer on a surface of
a winding conductor, the printed layer on the surface of the
winding conductor having thermal resistive and electrical
conductive segments.
[0014] In some fifth implementations, the NI coil includes a
winding conductor that can be non-insulated YBCO superconductor
tape, non-insulated REBCO superconductor tape, or non-insulated
Bi-2223 multi-filamentary superconductor tape.
[0015] Some implementations (sixth implementations) include a
homopolar motor/generator including an HTS NI coil magnet of the
fifth implementations. Some implementations (seventh
implementations) include an aircraft including a homopolar
motor/generator of the sixth implementations. In some seventh
implementations, the aircraft is a hypersonic aircraft.
[0016] Some implementations (eighth implementations) include a
hypersonic aircraft having a disk-type homopolar motor/generator
comprising an electrically conductive metal disk, an electrically
conductive shaft, a first electrical contact, a second electrical
contact, and an HTS NI multi-coil magnet. The electrically
conductive shaft can be coupled, mechanically and electrically, to
the electrically conductive metal disk. The first electrical
contact can be configured to be in electrical contact with an edge
of the electrically conductive metal disk. The second electrical
contact can be configured to be in electrical contact with the
electrically conductive shaft. The HTS multi-coil magnet can
comprise a plurality of NI coils and two or more thermal barriers.
The plurality of NI coils can each comprise multiple turns. The two
or more thermal barriers can each be disposed between a different
two adjacent turns of the NI coil, where an electrically conductive
portion of one of the thermal barriers does not overlap with an
electrically conductive portion of a different adjacent one of the
thermal barriers. The HTS NI coil magnet can be arranged so that a
normal component of a magnetic field generated by the HTS NI coil
magnet is substantially perpendicular to a face of the metal
disk.
[0017] In some eighth implementations, the electrically conductive
portion of the one of the thermal barriers is covered by a thermal
resistive portion of the different adjacent one of the thermal
barriers. In some eighth implementations, a thermal resistive
portion of the one of the thermal barriers overlaps with a thermal
resistive portion of the different adjacent one of the thermal
barriers. In some eighth implementations, the NI multi-coil
includes a winding conductor that can be YBCO superconductor tape,
non-insulated REBCO superconductor tape, or non-insulated Bi-2223
multi-filamentary superconductor tape. In some eighth
implementations, each of the two or more segmented barriers is
formed as: a co-wound layer having thermal resistive and electrical
conductive segments; a layer soldered or bonded to a winding
conductor, the soldered or bonded layer having thermal resistive
and electrical conductive segments; a printed layer on a co-wound
layer, the printed layer on the co-wound layer having thermal
resistive and electrical conductive segments; or a printed layer on
a surface of a winding conductor, the printed layer on the surface
of the winding conductor having thermal resistive and electrical
conductive segments. In some eighth implementations, the coil is a
circular pancake coil or a racetrack coil.
[0018] Some implementations (ninth implementations) include as HTS
NI coil magnet comprising an NI coil, a first thermal barrier, and
a second thermal barrier. The NI coil can comprise multiple turns.
The first thermal barrier can be disposed between a first two
adjacent turns of the coil, the first barrier comprising a first
electrical conductive portion. The second thermal barrier can be
disposed between a second two adjacent turns of the coil, the
second barrier comprising a second electrical conductive portion.
The first electrical conductive portion of the first thermal
barrier not overlapping any portion of the second electrical
conductive portion of the second thermal barrier.
[0019] In some ninth implementations, the first and second
electrical conductive portions are gaps in the respective first and
second thermal barriers. In some ninth implementations, the first
electrical conductive portion of the first thermal barrier is
covered by a thermal resistive portion of the second thermal
barrier. In some ninth implementations, the first thermal barrier
further comprises a first thermal resistive portion, the second
thermal barrier further comprises a second thermal resistive
portion, and the first thermal resistive portion of the first
thermal barrier overlaps with the second thermal resistive portion
of the second thermal barrier. In some ninth implementations, an
overlapping length of the first thermal resistive portion of the
first thermal barrier and the second thermal resistive portion of
the second thermal barrier is confined in 45.degree..
[0020] In some ninth implementations, the HTS NI coil magnet of
further comprises a current input lead and a current output lead.
The current input lead can be disposed at an innermost turn or an
outermost turn of the coil and at a first half portion of the coil.
The current output lead can be disposed at a different one of the
innermost and outermost turns than the current input lead and at a
second half portion of the coil opposite the first half
portion.
[0021] In some ninth implementations, the first thermal barrier is
an innermost barrier or an outermost barrier, and the first
electrical conductive portion of the first thermal barrier is
covered by a thermal resistive portion of the second thermal
barrier. In some ninth implementations, the first thermal resistive
portion of the first thermal barrier overlaps with the thermal
resistive portion of the second thermal barrier. In some ninth
implementations, the HTS NI coil magnet further comprises a third
thermal barrier disposed between a third two adjacent turns of the
coil. The third barrier can comprise a third electrical conductive
portion. The third thermal barrier can be between the first and
second thermal barriers, the third electrical conductive portion
not overlapping any portion of the first electrical conductive
portion of the first thermal barrier and not overlapping any
portion of the second electrical conductive portion of the second
thermal barrier. The third electrical conductive portion can be
covered by a thermal resistive portion of the first thermal
barrier, and covered by a thermal resistive portion of the second
thermal barrier. In some ninth implementations, the third thermal
barrier further includes a third thermal resistive portion. The
third thermal resistive portion can be overlapped by the first
thermal resistive portion of the first thermal barrier, and
overlapped by the second thermal resistive portion of the second
thermal barrier.
[0022] In some ninth implementations, an overlapping length of the
first thermal resistive portion of the first thermal barrier, the
second thermal resistive portion of the second resistive portion,
and the third thermal resistive portion of the third resistive
portion is confined in 45.degree..
[0023] In some ninth implementations, the coil is a circular
pancake coil or a racetrack coil. In some ninth implementations,
the HTS NI coil magnet further comprises one or more additional NI
coils. The one or more additional coils and the coil can be
connected. Each of the one or more additional coils can have two or
more thermal barriers each disposed between a different two
adjacent turns of the respective one of the one or more additional
coils.
[0024] In some ninth implementations, the two or more thermal
barriers of at least one of the one or more additional barriers has
a different arrangement than that of the first and second thermal
barriers of the coil. In some ninth implementations, the first
thermal barrier is a co-wound layer having thermal resistive and
electrical conductive segments. In some ninth implementations, the
first thermal barrier is a layer soldered or bonded to a winding
conductor, the soldered or bonded layer having thermal resistive
and electrical conductive segments. In some ninth implementations,
the first thermal barrier is a printed layer on a co-wound layer,
the printed layer having thermal resistive and electrical
conductive segments. In some ninth implementations, the first
thermal barrier is a printed layer on a surface of a winding
conductor, the printed layer having thermal resistive and
electrical conductive segments.
[0025] Some implementations (tenth implementations) include a
homopolar motor/generator including an HTS NI coil magnet of the
ninth implementations. Some implementations (eleventh
implementations) include aircraft including a homopolar
motor/generator of the tenth implementations. In some eleventh
implementations, the aircraft is a hypersonic aircraft.
[0026] Some implementations (twelfth implementations) include an
HTS NI coil magnet comprising an NI coil including multiple turns,
and two or more segmented barriers. Each of the segmented barriers
can be disposed between a different two adjacent turns of the NI
coil. Each of the two or more segmented barriers can include one or
more electrical conductive segments and one or more thermal
resistive segments.
[0027] In some twelfth implementations, each of the one or more
electrical conductive segments of a first barrier of the two or
more segmented barriers is covered by a thermal resistive segment
of a second barrier of the two or more segmented barriers, the
second barrier being adjacent to the first barrier. In some twelfth
implementations, each of the one or more electrical conductive
segments of the first barrier is covered by a thermal resistive
segment of a third barrier of the two or more segmented barriers,
the third barrier being adjacent to the first barrier. In some
twelfth implementations, each of the one or more thermal resistive
segments of a first barrier of the two or more segmented barriers
overlaps with a thermal resistive segment of a second barrier of
the two or more segmented barriers, the second barrier being
adjacent to the first barrier.
[0028] In some twelfth implementations, each of the one or more
thermal resistive segments of the first barrier overlaps with a
thermal resistive segment of a third barrier of the two or more
segmented barriers, the third barrier being adjacent to the first
barrier. In some twelfth implementations, an overlapping length of
the thermal resistive segments of a first barrier of the two or
more segmented barriers and the thermal resistive segments of a
second barrier of the two or more segmented barriers are confined
in 45.degree., the second barrier being adjacent to the first
barrier. In some twelfth implementations, an overlapping length of
the thermal resistive segments of a first barrier of the two or
more segmented barriers, the thermal resistive segments of a second
barrier of the two or more segmented barriers, and the thermal
resistive segments of a third barrier of the two or more segmented
barriers are confined in 45.degree., the second barrier being
adjacent to the first barrier, the third barrier being adjacent to
the first barrier. In some twelfth implementations, each of the one
or more electrical conductive segments of a first barrier of the
two or more segmented barriers does not overlap with an electrical
conductive segment of a second barrier of the two or more segmented
barriers, the second barrier being adjacent to the first barrier.
In some twelfth implementations, each of the one or more electrical
conductive segments of the first barrier does not overlap with an
electrical conductive segment of a third barrier of the two or more
segmented barriers, the third barrier being adjacent to the first
barrier.
[0029] In some twelfth implementations, each of the two or more
segmented barriers is: a co-wound layer having thermal resistive
and electrical conductive segments; a layer soldered or bonded to a
winding conductor, the soldered or bonded layer having thermal
resistive and electrical conductive segments; a printed layer on a
co-wound layer, the printed layer on the co-wound layer having
thermal resistive and electrical conductive segments; or a printed
layer on a surface of a winding conductor, the printed layer on the
surface of the winding conductor having thermal resistive and
electrical conductive segments. In some twelfth implementations,
the NI coil includes a winding conductor that can be non-insulated
YBCO superconductor tape, non-insulated REBCO superconductor tape,
or non-insulated Bi-2223 multi-filamentary superconductor tape. In
some twelfth implementations, the coil is a circular pancake coil
or a racetrack coil.
[0030] Some implementations (thirteenth implementations) include a
homopolar motor/generator including an HTS NI coil magnet of the
twelfth implementations. Some implementations (fourteenth
implementations) include an aircraft that includes a homopolar
motor/generator of the thirteenth implementations. In some
fourteenth implementations, the aircraft is a hypersonic
aircraft.
[0031] Some implementations (fifteenth implementations) include an
HTS NI coil magnet comprising a coil including multiple turns and
one or more thermal barriers each disposed between a different two
adjacent turns of the coil. The one or more thermal barriers can
include a material that is thermal resistive and electrical
conductive to block heat propagation while permitting substantially
full capacity turn-wise current sharing between the adjacent turns.
In some fifteenth implementations, the NI coil includes a winding
conductor that can be non-insulated YBCO superconductor tape,
non-insulated REBCO superconductor tape, or non-insulated Bi-2223
multi-filamentary superconductor tape. In some fifteenth
implementations, the coil is a circular pancake coil or a racetrack
coil.
[0032] Some implementations (sixteenth implementations) include a
homopolar motor/generator including an HTS NI coil magnet of the
fifteenth implementations. Some implementations (seventeenth
implementations) include an aircraft that includes a homopolar
motor/generator of the sixteenth implementations. In some
seventeenth implementations, the aircraft is a hypersonic
aircraft.
BRIEF DESCRIPTION OF THE DRAWINGS
[0033] The patent or application file contains at least one drawing
executed in color. Copies of this patent or patent application
publication with color drawing(s) will be provided by the Office
upon request and payment of the necessary fee.
[0034] Many aspects of the present disclosure can be better
understood with reference to the following drawings. The components
in the drawings are not necessarily to scale, emphasis instead
being placed upon clearly illustrating the principles of the
present disclosure. Moreover, in the drawings, like reference
numerals designate corresponding parts throughout the several
views.
[0035] FIGS. 1A and 1B illustrate examples of high temperature
superconducting (HTS) magnets including multiple coils, in
accordance with various embodiments of the present disclosure.
[0036] FIGS. 2A through 2E illustrate examples of intra-coil,
inter-coil and/or coil-to-coil grading of HTS non-insulated (NI)
coil magnets of FIGS. 1A and 1B, in accordance with various
embodiments of the present disclosure.
[0037] FIGS. 3A and 3B is a perspective view illustrating an
example of a multiple turn HTS NI coil magnet system including
double pancake coils (DPCs), in accordance with various embodiments
of the present disclosure.
[0038] FIG. 4 is a schematic diagram illustrating an example of a
circuit network model of the multi-turn HTS NI coil of FIG. 3A, in
accordance with various embodiments of the present disclosure.
[0039] FIGS. 5A, 5B and 5C illustrate examples of azimuthal current
distributions (top plots) and radial current distributions (bottom
plots) on an unmodified, inter-coil graded and intra+inter-coil
graded NI-coil magnets during ramping, in accordance with various
embodiments of the present disclosure.
[0040] FIGS. 6A and 6B illustrate examples of azimuthal current
distributions (top plots) and radial current distributions (bottom
plots) on the unmodified and inter-coil graded multi-NI-coil
magnets of FIGS. 5A and 5B during fast discharging, in accordance
with various embodiments of the present disclosure.
[0041] FIGS. 7A through 7D illustrate simulation results of the
unmodified NI-coil magnet of FIG. 5A during ramping, in accordance
with various embodiments of the present disclosure.
[0042] FIGS. 8A through 8C illustrate simulation results of the
unmodified NI-coil magnet of FIG. 5A during fast discharging, in
accordance with various embodiments of the present disclosure.
[0043] FIG. 9 illustrates a comparison of ramping times of the
unmodified NI-coil magnet of FIGS. 5A and 6A, the inter-coil graded
magnet of FIGS. 5B and 6B, and the intra+inter-coil graded magnet
of FIG. 5C, in accordance with various embodiments of the present
disclosure.
[0044] FIGS. 10A through 10C illustrate examples of grading types,
in accordance with various embodiments of the present
disclosure.
[0045] FIG. 11 is an illustration of a homopolar motor including an
NI multi-coil superconducting magnet with grading stability
enhancements, in accordance with various embodiments of the present
disclosure.
[0046] FIG. 12 is a diagram of an example hypersonic aircraft
having a homopolar motor/generator with an HTS NI coil magnet, in
accordance with various embodiments of the present disclosure.
[0047] FIG. 13 is a block diagram of a hybrid coupled multiphysics
NI coil model, in accordance with various embodiments of the
present disclosure.
[0048] FIG. 14 is a schematic of a spirally-wound equivalent
circuit network model for NI coils, in accordance with various
embodiments of the present disclosure.
[0049] FIG. 15 illustrates geometry for coupled 3D spirally-wound
thermal and electromagnetic multi-coil models, in accordance with
various embodiments of the present disclosure.
[0050] FIG. 16 illustrates an example GRNI implementation that
involves both intra-coil grading and inter-coil grading, in
accordance with various embodiments of the present disclosure.
[0051] FIG. 17 illustrates distributions of temperature, azimuthal
and radial currents during a quench-recovery process in a 20-turn
NI pancake coil at 77 K, in accordance with various embodiments of
the present disclosure.
[0052] FIG. 18A is a graph showing normalized center magnetic field
versus time profiles during quench-recovery at 77 K, taken from an
NI coil and a modified counterpart with a single-turn of Kapton
strip added, and FIG. 18B is a graph showing the corresponding
temperature versus time profiles, in accordance with various
embodiments of the present disclosure.
[0053] FIGS. 19A and 19B are graphs showing partial thermal-cutoff
(FIG. 19A) and overcurrent (FIG. 19B) at 77 K on a NI coil modified
by adding a single turn of Kapton thermal barrier to the center
turn of the winding pack, in accordance with various embodiments of
the present disclosure.
[0054] FIG. 20 illustrates local heating created by current
"squeezing" through the turn gap of the full-turn Kapton thermal
barrier, in accordance with various embodiments of the present
disclosure.
[0055] FIG. 21 illustrates a GRNI magnet with an 8-turn barrier
design, in accordance with various embodiments of the present
disclosure.
[0056] FIG. 22A is a graph showing normalized center magnetic field
versus time profiles during quench-recovery at 77 K, taken from two
graded NI coils installed with the 8-turn or 16-turn barrier design
and from a non-graded counterpart, and FIG. 22B is a graph showing
normalized the corresponding temperature versus time profiles, in
accordance with various embodiments of the present disclosure.
[0057] FIG. 23A is a graph showing a snapshot of the temperature
distribution during a quench initiated by Heater1 in the coil with
the 8-turn design at 77 K, and FIG. 23B is a graph showing the
corresponding azimuthal current distribution, in accordance with
various embodiments of the present disclosure.
[0058] FIG. 24A is a graph showing a snapshot of the temperature
distribution during a quench initiated by Heater1 in the coil with
the 16-turn design at 77 K, and FIG. 24B is a graph showing the
corresponding azimuthal current distribution, in accordance with
various embodiments of the present disclosure.
[0059] FIG. 25A is a graph showing normalized center magnetic field
versus time profiles during quench-recovery at 4.2 K, taken from
two NI coils installed with the 8-turn or 16-turn barrier design
and from a non-graded counterpart, and FIG. 25B is a graph showing
the corresponding temperature versus time profiles, in accordance
with various embodiments of the present disclosure.
[0060] FIG. 26 illustrates a GRNI magnet with a 2.times.8-turn
barrier design, in accordance with various embodiments of the
present disclosure.
[0061] FIG. 27A is a graph showing normalized center magnetic field
versus time profiles during quench-recovery at 4.2 K, taken from a
NI coil installed with the 2.times.8-turn design and from a
non-graded counterpart, and FIG. 27B is a graph showing the
corresponding temperature versus time profiles, in accordance with
various embodiments of the present disclosure.
[0062] FIG. 28A is a graph showing normalized center magnetic field
versus time profiles during quench-recovery at 77 K, taken from a
NI coil installed with the 2.times.8-turn design and from a
non-graded counterpart, and FIG. 28B is a graph showing the
corresponding temperature versus time profiles, in accordance with
various embodiments of the present disclosure.
[0063] FIG. 29 is a graph showing comparison of the rates of change
in preserved magnetic fields generated by the "Heater1, 8-turn",
"Heater2, 8-turn" and "Heater1, no barrier" cases shown in FIG.
22A, in accordance with various embodiments of the present
disclosure.
[0064] FIG. 30A shows normalized center magnetic field versus time
profiles during quench-recovery at 77 K on a graded coil and
non-graded counterpart, both with 4 mH inductance, in accordance
with various embodiments of the present disclosure.
[0065] FIG. 30B is a graph showing the temperature versus time
profiles corresponding to FIG. 30A.
[0066] FIG. 30C shows normalized center magnetic field versus time
profiles during quench-recovery at 77 K on the same graded and
non-graded coils as in FIG. 30A, but both with 0.4 mH inductance,
in accordance with various embodiments of the present
disclosure.
[0067] FIG. 30D is a graph showing the temperature versus time
profiles corresponding to FIG. 30C, in accordance with various
embodiments of the present disclosure.
[0068] FIG. 31 illustrates arc lengths or arc angles as design
parameters of a modified NI coil design, in accordance with various
embodiments of the present disclosure.
[0069] FIG. 32 illustrates turn numbers as design parameters of a
modified NI coil design, in accordance with various embodiments of
the present disclosure.
[0070] FIG. 33 illustrates a modified NI coil having arc lengths
and numbers of the conductive and resistive segments varied from
barrier to barrier, in accordance with various embodiments of the
present disclosure.
[0071] FIG. 34 illustrates a modified NI coil having a single-turn
barrier, in accordance with various embodiments of the present
disclosure.
[0072] FIG. 35 is a table listing parameters common to 77 K and 4.2
K simulations, in accordance with various embodiments of the
present disclosure.
[0073] FIG. 36 is a table listing parameters used 77 K simulations,
in accordance with various embodiments of the present
disclosure.
[0074] FIG. 37 is a table listing parameters used 4.2 K
simulations, in accordance with various embodiments of the present
disclosure.
DETAILED DESCRIPTION
[0075] In a high temperature superconducting (HTS) magnet, the
operating current, or more specifically the operating current
density, is limited not only by the in-field performance of the HTS
conductor but also by the protection requirement. If a quench, by
definition when a superconducting magnet accidently loses its
superconductivity, occurs in an insulated HTS magnet operated at a
very high current density, for example, above 30 kA/cm.sup.2, the
magnet will burn even with a protection scheme.
[0076] A quench can be induced in a high temperature
superconducting (HTS) magnet by a large enough local heat
disturbance. The heat disturbance can come from many sources, for
example, the AC losses during current ramping (charging and/or
discharging) and local fluctuations in cooling of the coils. If a
quench is not stopped soon enough, the rising temperature created
by the quench will eventually destroy the magnet. Some methods to
prevent such a scenario from happening include initially detecting
an onset of a quench by monitoring the temperature, voltage or
other measurable quantities of the coils and, once detected,
cutting of the power source from the coils and allowing the stored
magnetic energy to dissipate at a fast but controlled speed to
prevent damaging the coils by limiting the peak temperature and the
discharge-induced inductive voltage. However, it is a great
challenge to detect a quench reliably and fast enough to activate
the quench protection mechanism. This is mainly because the quench
propagation speed in a HTS magnet is very slow. It is also
challenging to implement an effective quench protection
mechanism.
[0077] Disclosed herein are various examples related to mechanisms
for improving the performance of superconducting magnets. These
mechanisms can enhance the thermal stability and reduce the risk of
quenching in existing superconducting magnets composed of multiple
superconducting coils with low turn-to-turn thermal and/or
electrical resistances, while maintaining or improving the
advantage of the fast ramping rates of these magnets, as compared
to their counterparts composed of no-insulation or non-insulated
(NI) coils, and partially-insulated (PI) coils. While NI coils are
used in the discussions presented herein and as examples for
comparison to the disclosed mechanisms for improving the
performance of superconducting magnets, the disclosed mechanisms
can also be applied to other types of magnet coils such as PI
coils. These benefits can make a superconducting magnet modified by
the disclosed mechanisms more stable and reliable, and can provide
a practical superconducting coil with a reasonable ramping time and
a longer mean time between failures. The disclosed mechanisms not
only provide benefits to NI coils or coils with low turn-to-turn
resistances that already have high thermal stability, but also to
self-protecting superconducting NI coils. When applied to
self-protecting magnets, these mechanisms can greatly reduce the
risk of quenching, improve the recovery time after a recovered
quench and thus improve the operational stability, availability and
reliability of the coils.
[0078] Self-protecting NI coil magnets fabricated in accordance
with the present disclosure are well-suited for mission critical
applications such as aviation propulsion motors. This is because
such magnets have low risk of quenching; had a quench happened,
they need no external protection mechanism and thus have
smallerform factor and are easier to maintain. Other applications
for these enhanced superconducting magnets include, but are not
limited to, high field magnets for accelerators, wind power
superconducting generators, superconducting motors for general uses
and mission critical applications such as aviation propulsion,
superconducting magnetic energy storage, MRI and high field magnets
for scientific research. Reference will now be made in detail to
the description of the embodiments as illustrated in the drawings,
wherein like reference numbers indicate like parts throughout the
several views.
[0079] HTS magnets can be composed of a single or multiple
superconducting coils, each coil is further composed of multiple
turns. Examples of HTS magnets including multiple coils (1-3) are
provided in FIGS. 1A and 1B. In the case of multi-coil magnets, the
coils (1-3) can be connected radially to increase the diameter as
illustrated in FIG. 1A or stacked axially to increase the axial
length of the coil as shown in FIG. 1B, or configured in a mixture
of both radial and axial connections. Some HTS coils are fabricated
by co-winding the conductor with a layer of electrically and
thermally insulated material. These kinds of insulated coils can
have low to moderate thermal stability in the sense that any finite
heat disturbance energy that is large enough can induce a
sustainable quench (as opposed to a recoverable quench, which
eventually subsided). In a new type of HTS coils, the co-winding
insulation layer is either removed completely or replaced by a
co-winding layer of very low resistance, either electrically or
thermally, or both, to improve the thermal stability of HTS coils.
The co-winding layer can be either co-wound with the conductor
during fabrication of the coil or pre-soldered to the conductor
before winding. These kinds of coils with very low turn-to-turn
resistances are called no-insulation or non-insulated or simply NI
coils. Extensive studies have shown that NI coils intrinsically
possess much higher thermal stability than insulated coils. Some
coils are even shown to be self-protecting, in the sense that
during a quench, its magnetic energy stored in a coil is dissipated
within the coil itself safely without external quench protection
mechanism. The main reason that NI coils are highly stable is that
the low turn-to-turn thermal and electrical resistances allow heat
and current to diverge both in the azimuthal and radial directions
away from the hot-spot, which is generated first by a heat
disturbance and later by induced Joule heating, to the neighboring
turns. This results in reduced heat buildup and Joule heating, a
sustainable quench is therefore difficult to be initiated. For any
highly stable NI coil, even if it is self-protected, if a quench
happens in the NI coil, the consequences are operationally
disruptive, expensive and even catastrophic. For example, the
operation of a quenched magnet is degraded or even stopped when the
stored energy has been dissipated; and the magnet's current has to
be recharged again through a ramping process that can be very slow.
Thus, it is advantageous to minimize the risk of quenching.
[0080] A major drawback associated with these NI coils is that
their current ramping times during charging and discharging are
much longer than those of their insulated counterparts. The ramping
times in a large magnet composed of NI coils (i.e., a NI-coil
magnet) with a large inductance can be in tens of hours, which is
excessive for practical operation in some or most application
cases. The reason that NI coils have slow ramping rates is that the
inductive impedance induced by the time-varying current increases
the current flow resistance along the length of the conductor,
meanwhile, a low turn-to-turn electrical resistance between the
turns allows some of the current to "leak" through a diverged,
lower resistance path across the turns directly to the current
output lead, thus reducing the azimuthal current, which flows along
the length of the conductor, that is needed to charge the
superconductor in the coil.
[0081] Few methods are available to solve or improve the slow
ramping rate issue in NI-coil magnets. Some methods are based on
the same principle, that of limiting the amount of diverging
current that bypasses the longitudinal path along the turns and
flows across the turns to the current output lead. These methods
are realized either by reducing the inductance of the magnet or by
increasing the turn-turn electrical resistance in the NI coils. The
former method is impractical and the later may be implemented
either by co-winding a layer of low electrical resistance, which is
higher than the intrinsic turn-to-turn electrical resistance of the
un-modified NI coil, or by laminating a thin metallic layer on the
conductor. The commonly used laminated metallic layers are copper,
brass and steel thin sheets. Many of these methods uniformly
increase the turn-to-turn electrical resistance between all the
turns of the entire magnet by a single, fixed electrical resistance
value. It has been shown through experimental and computational
analyses that the higher the turn-to-turn electrical resistance,
the faster the ramping rates are for both charging and discharging
in single and multi-coil magnets.
[0082] There is also a partially-insulated coil fabrication method
which is similar to the co-wound NI coil method. This method can be
implemented by co-winding an insulated material at selected places
within the coil, for example, one or more turns of Kapton layer for
every 10 turns. A coil fabricated by this method is called a
partially-insulated (PI) coil. Such coils possess improved thermal
stability when compared to their insulated counterparts and
improved ramping rates when compared to their NI counterparts. The
improvement in ramping rates, however, are in general much less
effective than in the co-wound and laminated NI-coil counterparts
mentioned above. As a result, PI coils are less commonly studied
and used. Herein, only the NI coils will be referred in discussions
and comparisons, but the same concepts also apply to PI coils.
[0083] Some methods that increase the turn-to-turn electrical
resistance with a fixed value across the entire magnet, however,
also reduce the thermal stability of the modified NI-coil magnet.
The higher the turn-to-turn electrical resistance, the larger the
reduction in thermal stability. When the resistance of a modified
NI coil is larger than a certain value, the coil behaves
essentially like an insulated coil counterpart, in particular, the
coil's thermal stability becomes the same as that of an insulated
counterpart. In general, even with added low turn-to-turn
resistance, the thermal stability of the NI coil is still much
higher than that of its insulated counterpart. Another problem
associated with NI-coil magnet with or without added (low)
resistances is that localized current concentrations form within
the magnet during ramping and fast discharging.
[0084] Embodiments disclosed herein include single-coil or
multi-coil magnets composed of NI coils that can mitigate all the
drawbacks discussed above. Some such embodiments include adding
graded turn-to-turn electrical resistances and/or graded
coil-to-coil electrical resistances in the case of multi-coil
magnets, to control the current flow within the NI coils, such that
the current leak and local current concentration phenomenon can be
greatly reduced during ramping and quenching. In contrast, some NI
magnets use only a single fixed constant turn-to-turn electrical
resistance value (normally with coil-to-coil insulation material,
including air gap, placed between every two adjacent coils) across
the entire magnet to improve the ramping times. The same concepts
of grading turn-to-turn and coil-to-coil electrical resistances on
NI coils also apply to turn-to-turn and coil-to-coil thermal
resistance. Graded turn-to-turn and/or coil-to-coil thermal
resistances can be used to control the heat flow in a modified NI
coil or NI-coil magnet to direct the heat propagation of a hot spot
in a designed, beneficial way, for example, away from a less stable
region. Hereafter, unless otherwise stated, resistance can refer to
either an electrical resistance or a thermal resistance or both.
Also, graded values refer to a set of generally distinct values
that can be carefully selected to meet some functional purposes by
means of analytical equations, computational simulations or
experiments; and the values can have the same repeated values.
Graded NI coils can enhance the thermal stability (especially in
non-self-protecting NI coils), reduce the risk of quenching
(especially in self-protecting NI coils), and maintain or improve
the charging and discharging ramping rates of NI-coil magnets,
including those with added turn-to-turn resistance.
[0085] There are two ways to apply graded turn-to-turn resistances
to a NI-coil magnet: intra-coil grading and inter-coil grading.
With intra-coil grading, the turn-to-turn resistances are graded
with respect to all the turns within the same coil. Under
intra-coil grading, the turn-to-turn resistance between two
adjacent turns can be different from those of other turns within
the same coil. FIGS. 2A and 2B graphically illustrate examples of
intra-coil grading on a radially wound coil and on each individual
radially wound coil of an axially stacked NI-coil magnet,
respectively. With inter-coil grading, the turn-to-turn resistances
are graded with respect to all the coils within the same magnet.
Under inter-coil grading, every coil among the magnet has its own
fixed turn-to-turn resistance, but the resistance can be different
from those of other coils within the same magnet. FIG. 2C
graphically illustrates an example of inter-coil grading on an
axially stacked NI-coil magnet. Combinations of intra+inter-coil
grading are also possible. For example, the intra-coil grading can
be varied differently between some or all of the coils of the
magnet, which results in inter-coil grading of the magnet. FIG. 2B
illustrates an example of an intra+inter-coil graded NI-coil magnet
with axially stacked coils. While shown with axially stacked coils,
the inter-coil grading of FIG. 2C and the intra+inter-coil grading
of FIG. 2B are equally applicable to radially stacked coils. In
other embodiments, a combination of radial intra-coil grading and
axial inter-coil grading can be implemented.
[0086] Coil-to-coil grading can be applied to the material inserted
between any two adjacent coils (coil-to-coil interfacial material)
of a radially stacked or axially stacked NI multi-coil magnet, as
graphically illustrated in FIG. 2D. In the case of a some
multi-coil magnets, the material inserted between every two
adjacent coils is an insulation material having the same resistance
between all coils, including air gap. In the proposed method, the
coil-to-coil interfacial material can be replaced by thin
conductive materials with low resistances, which are graded with
respect to all the interfacial layers (between every two adjacent
coils) within the magnet. In addition, the coil-to-coil interfacial
material can also be graded with respect to the axial length within
the same coil-to-coil interfacial material in the case of a
radially stacked multi-coil magnet, or with respect to the radius
within the same coil-to-coil interfacial material in the case of an
axially stacked multi-coil magnet, or in a mixture of both ways in
a radially and axially stacked multi-coil magnet. This kind of
grading is called coil-coil grading. FIG. 2E graphically
illustrates an example of coil-to-coil grading on an axially
stacked multi-coil magnet with a distinct constant value across the
radius on each individual coil-to-coil interfacial material. The
basic working principle behind the intra-coil grading lies in the
fact that the larger the turn-to-turn electrical resistance, the
smaller is the radial current flowing across the turn-to-turn
interfacial contact area and thus per the conservation of current,
the larger is the azimuthal current flowing along the turn that
"pushes out" the radial current. So, higher turn-to-turn electrical
resistances can be applied to an area with higher radial current
concentration (and lower azimuthal current concentration) to lower
the concentration. Similarly, lower turn-to-turn resistances can be
applied to areas with higher azimuthal current concentrations. This
principle also works on inter-coil grading. Thus, grading of
turn-to-turn resistances in NI-coil magnets mitigates localized
current concentration issue while improving the ramping rates.
[0087] Hereafter, a NI-coil magnet fabricated with the proposed
method by applying an intra-coil grading, an inter-coil grading, a
coil-coil grading, or a mixture of all types of grading is called a
graded-resistance NI-coil magnet. In contrast, a NI-coil magnet
having a single fixed turn-to-turn resistance across the entire
magnet is called a uniform-resistance NI-coil magnet. The
beneficial consequences of applying the proposed method include an
improved thermal stability and risk of quenching than the
uniform-resistance coil counterpart with the same ramping rates.
Recall that a uniform-resistance NI-coil magnet has better ramping
rates but slightly lower thermal stability than an unmodified
NI-coil counterpart, and that an unmodified NI-coil magnet has much
higher thermal stability than an insulated counterpart. Overall, a
graded-resistance NI-coil magnet can be operationally more
efficient, stable and reliable than its insulated, NI and
uniform-resistance counterparts.
[0088] Both NI coils and metallic insulation (MI) coils, which are
those with co-wound low-electrical-resistance metallic strips,
including the co-wound coils described above, have been
investigated for high temperature superconducting (HTS) coils
employing (RE)Ba2Cu3O7-x conductors. Due to the direct metal
contact between turns, the overall thermal stability and quench
protection can be improved. In the case of a quench initiated by a
local heat disturbance, heat and electrical current can be spilled
off into neighboring turns, so that quench is harder to sustain and
hot areas can be protected from overheating or mechanical damage.
However, delay between field and current ramping has been found
during a charging process and it may limit the maximum ramping
rate. This may be attributed to the electrical current flowing in
both in the azimuthal direction and in radial direction, when an
induced voltage occurs at coil terminals. The higher the end-to-end
voltage is, the higher the ratio between the radial and azimuthal
component, and the less the current directly contributes to the
magnet center field.
[0089] However, a majority of large superconducting system such as
MRI or NMR magnets consist of quite a few coils in series. Owing to
mutual inductance between coils, the current distributions may be
much more complex than in a single coil. This is a very practical
problem in NI and MI coil development. Most experimental or
simulated results apply to a single NI and/or MI coil, where
non-uniform current distributions in the multiple coils may not be
able to be discovered. Both the voltage and current in multiple
coils stacked on the same axis can be studied during both charging
and discharging processes. Current distributions will be compared
in coils at various locations along with the voltage and magnetic
field dynamic changes, to illustrate a non-uniform current
distribution during the dynamic processes.
[0090] Multiple Coil Model of HTS Magnet System. Simulations of
charging and discharging characteristics were carried out on a
magnet system which comprises 7 double pancake coils that are on
the same axis and are made by employing (RE)Ba2Cu3O7-x conductors
using a no-insulation winding approach. A numerical circuit network
model was developed to take turn-to-turn contact resistivity into
account and to determine the azimuthal and radial current
components during charging and discharging. It was found that the
current distribution is not uniform from the upper coil to the
middle and from the coil inner diameter to the outer diameter. In
addition, the current distribution tendency is opposite to each
other in the charging and discharging processes. The voltage and
magnetic field were calculated and correlated to the current
distribution analysis to understand uneven electromagnetic
phenomena in the multiple coils system.
[0091] Referring to FIG. 3A, shown is a schematic diagram
illustrating an example of a multiple turn HTS NI coil magnet
system. The HTS NI coil magnet of FIG. 3A comprises a stack of
seven double pancake (DP) coils on the same axis and in series
(DPC1-DPC7), with HTS referring to (RE)Ba2Cu3O7-x conductors. HTS
NI coil magnets can include one or more turns. The turns can be
identical NI DP coils stacked in series. The table in FIG. 3B
provides details about the multi-turn HTS NI coil magnet used in
various simulations. Each DP coil was wound employing REBCO tapes
with 130*2 turns. The width and thickness of the tape was 4 mm and
0.125 mm, respectively. The inner diameter of the coil was 100 mm.
The distance between upper and lower coil inside the DP was 1 mm
and the distance between two adjacent DP coils was 2 mm. The
operating temperature of the magnet was designed at 40 K where its
critical current of the tape was 390 A and the critical current of
the magnet was about 100 A at 40 K.
[0092] Network Model for the Multiple Coil System. To analyze the
current distribution inside the NI coil, an equivalent circuit
network model was developed. FIG. 4 shows a schematic illustration
of the analysis model for NI pancake coils. In this model, the
transport current inside the NI coil is decomposed into that along
the azimuthal direction and radial direction. The anticlockwise
direction is defined as the positive direction of the azimuthal
current. The centrifugal direction is defined as the positive
direction of the radial current. Each turn of the coil is
subdivided into n.sub.e fine arc elements (n.sub.e=24 in this
simulation), with each arc element represented by circuit
parameters. In the example shown in FIG. 4, n.sub.e=4 and in the
simulation, n.sub.e=24. The whole coil is equivalent to the network
circuit. The magnet of FIG. 3A with 7 DPCs is equivalent to 14
circuit networks in series.
[0093] In each independent circuit mesh, the governing equations
can be derived from the Kirchhoff's voltage law. At each circuit
node, the governing equations can be derived from Kirchhoff's
current law as:
{ i k - i k + 1 + j k - n e - j k = 0 u k - u k + n e - j k - 1 R r
, k - 1 + j k R r , k = 0 ; ( 1 ) ##EQU00001##
where i and j represent the azimuthal and radial currents,
respectively. The term R.sub.r,k is the equivalent radial
resistance (equivalent to turn-to-turn resistance) of the k-th arc
element including that of turn-to-turn contact, substrate and
laminations. The intrinsic equivalent radial resistivity of the NI
coils can range from 10 .mu.Ocm.sup.2 to 100 .mu.Ocm.sup.2. In this
study, the intrinsic turn-to-turn resistivity is set to be 70
.mu.Ocm.sup.2. The term u.sub.k represents the voltage on the k-th
arc element, which is induced by the azimuthal inductance and
resistance.
[0094] The azimuthal resistance R.sub.s,k can be neglected when the
transport current is below the critical current. Therefore, the
voltage of the k-th arc element can be calculated by:
u k = L k di k dt + M k , I di l dt ( 2 ) ##EQU00002##
where L.sub.k represents the self-inductance of k-th arc element.
The term M.sub.k,I is the mutual inductance with all the other arc
elements, which includes that of the same pancake coil and all the
other pancake coils.
[0095] FIGS. 5A, 5B and 5C illustrate examples of azimuthal current
distributions (top plots) and radial current distributions (bottom
plots) on an unmodified, inter-coil graded and intra+inter-coil
multi-NI-coil magnets during ramping and FIGS. 6A and 6B illustrate
examples of azimuthal current distributions (top plots) and radial
current distributions (bottom plots) on the unmodified and
inter-coil graded multi-NI-coil magnets of FIGS. 5A and 5B during
fast discharging. Referring to FIGS. 5A and 6A, shown are the
distributions of the azimuthal (top plots) and radial (bottom
plots) currents in a multi-coil magnet comprising original,
regular, unmodified NI coils with intrinsic turn-to-turn resistance
during a ramping up and fast discharging, respectively. It can be
seen in FIG. 5A that during the ramping up, a large concentration
of azimuthal current occurs near the inner turns of the top few and
bottom few coils, and a large concentration of radial current
occurs near the outer turns of the coils clustered around the
center of the magnet. During the fast discharge of FIG. 6A, large
concentrations of azimuthal current and negative (radially inward)
radial current occur near the outer turns of the coils clustered
around the center of the magnet. These high current concentration
areas are the locations that have lower thermal stability and
higher risk of quenching.
[0096] Ramping Behavior. Ramping simulations were performed on the
magnet with the 7 DP coils of FIGS. 3A and 3B using the circuit
network model of FIG. 4. FIG. 7A shows the ramping transport
current from the power supply applied to the magnet, the magnet
voltage and the magnetic field induced at the coil magnet center
during a ramping operation with a ramping rate of 1 A/s. The magnet
voltage is the sum of all the DP coil voltages. Some current flows
through the turn-to-turn contact in the ramping process, due to the
voltage on each turn induced by the inductance as shown in FIG. 7A.
Therefore, the magnetic field does not increase proportionately
with the operating current and a significant delay is observed.
[0097] The table in FIG. 7B summarizes the inductance and mutual
inductances between the 7 DP coils (DPC1-DPC7), upon which the
ramping voltages were simulated. FIG. 7C plots voltages on the 1st
and 2nd DP coils (DPC1 and DPC2) from the upper end of the NI coil
magnet, and the 4th (middle) DP coil (DPC4) during the ramping
process. As seen in FIG. 7C, the middle coil (DPC4) has a larger
voltage than the upper end coils (DPC1 and DPC2). Their peak
voltages are about 0.032 V, 0.038 V and 0.042 V, respectively.
Before the current arrives at the steady target value 80 A, both
the azimuthal and radial current component increases, but the
middle coil (DPC4) has a higher radial current, so that it has
higher voltage. When the current is kept constant at 80 A, the
radial current component starts to merge into the azimuthal
component, so the voltage starts to decrease.
[0098] In each NI coil, the azimuthal and radial current shows an
approximately homogenous distribution along the angular direction
in most regions during the time-varying process. To describe the
distribution of the azimuthal and radial current in different
coils, two variables were defined as follows:
{ I sav = k = 1 n e i k / n e I rsum = k = 1 n e j k ( 3 )
##EQU00003##
where I.sub.sav is the average azimuthal transport current on each
turn, and I.sub.rsum is the total radial current flowing through
each turn.
[0099] FIG. 5A shows the distributions of I.sub.sav and I.sub.rsum
during a ramping process with the same ramping rate of 1 A/s. When
the operating current from power supply increases to 80 A at t=80
s, the azimuthal transport currents (top plot) of most turns are
still much lower than that. The NI coils at different locations are
not charged at the same rate. The coils at the upper and lower end
of the magnet are charged faster than others. The coils in the
middle of the magnet show a more significant charging delay. In
each coil, the turns near the inner diameter is charged faster than
those near the outer diameter. This may be attributed to a
different electromagnetic field for the different turns. In
contrast, more radial current (bottom plot) is generated in the
middle coils and the radial current near the outer diameter is much
higher than that near the inner diameter. Larger radial currents
will generate more Joule heat, and as a result the thermal
non-equilibrium may hurt the charging process.
[0100] FIG. 7D quantitatively plots the amount of azimuthal and
radial current components in the 1st, 2nd, and 4th coils (DPC1,
DPC2, and DPC4 from the upper end to the middle of the NI coil
magnet) during the entire ramping process at the rate of 1 A/s. As
indicated by their voltage, the 1st coil (upper most DPC1) has the
largest azimuthal current but the smallest radial current, which is
desired from the magnet charging point of view. At the same time,
the 4th coil (middle DPC4) has less current in azimuthal direction
but more in radial direction. As the result, the middle coil DPC4
has a higher ramping voltage. Furthermore, when the current levels
off, the radial component starts to decrease, merging into the
azimuthal component, until the 80 A transport current begins
flowing in the azimuthal direction.
[0101] Fast-discharging Behavior. In contrast with the ramping
process, the discharging process may exhibit contrary phenomena in
terms of the current distributions and induced voltages. FIG. 8A
shows a plot of a typical voltage and magnetic field versus time
during the fast-discharge process. The voltage dramatically
increases (negatively) to a value due to sudden change in the
external circuit and then gradually decreases back to zero based on
the internal contact resistance RL circuit. Meanwhile the magnetic
field decreases in an approximately exponential curve. For each of
the coil, the 4th coil (DPC4) has a slightly higher voltage than
the 1st coil (DPC1), which is balanced by both the azimuthal and
radial current. FIG. 8B shows the voltages of the coils at
different locations during the fast discharge process.
[0102] FIG. 6A in the fast discharging process has a strong
contrast with FIG. 5A in the ramping process in terms of the
current, voltage and magnetic field. At 40 s after the external
circuit is switched open, the upper coil (DPC1) not only has less
azimuthal current but also has less radial current though most
concentrate around the outer diameter, while the middle coil (DPC4)
has both more azimuthal component and more radial component which
concentrates on the outer diameter. In another word, regions near
the middle & outer turns in the magnet are under high current
density and dynamic changes. FIG. 8C provides the quantitative
current flowing in the azimuthal and radial directions. FIG. 8C
shows the average azimuthal transport current and radial current in
the 1st (upper DPC1), 2nd (DPC2) and 4th (middle DPC4) coil during
the fast discharging process. As the currents are decreasing, they
are equal to each other but their signs are opposite due to the
existing circuit being only inside the coil. Note that the radial
current is negative which indicates the radial current direction is
reversed, flowing from outer diameter to inner diameter. Also note
that changing the distance between adjacent DPCs will change the
mutual inductance, which will affect the current distributions in
the multiple coils, but the main trend will be very similar.
[0103] Referring next to FIGS. 5B and 6B, shown are the
distributions of the azimuthal (top plots) and radial (bottom
plots) currents in a multi-NI-coil magnet modified with inter-coil
grading during a ramping and discharging, respectively, which is
the counterpart of the unmodified multi-NI-coil magnet shown in
FIGS. 5A and 6A. In this simulation example, the same constant
turn-to-turn resistance was added between all the turns within the
same coil. The constant resistances are graded from coil to coil,
depending on their locations in the magnet. In the example of FIGS.
5B and 6B, the constant turn-to-turn resistivity in each coil,
which is not optimized, counting from the top to the bottom coil,
is 70, 80, 90, 100, 90, 80, 70 Om.sup.2, respectively. Here, 70
Om.sup.2 was assumed to be the intrinsic turn-to-turn
resistivity.
[0104] In practice, the intrinsic turn-to-turn resistivity depends
on the winding tension, the roughness of the surface of the
conductor and the uniformity of the turn-to-turn contact surface.
It can be seen from FIGS. 5B and 6B that when the turn-to-turn
resistances are graded from coil to coil (but kept constant within
each coil), the current distributions of both the azimuthal and
radial currents are much more uniform axially across the entire
magnet as compared to those in the unmodified magnet shown in FIGS.
5A and 6A. Note that in comparison to the original NI-coil magnet,
the peaks and ranges of the currents become smaller and narrower
upon the application of grading. However, the currents are still
not uniformly distributed within the same coil in the radial
direction. This intra-coil non-uniformity can be reduced by
applying intra-coil grading to each coil by grading the
turn-to-turn resistances within the same coil.
[0105] Referring now to FIG. 5C, shown is the distributions of the
azimuthal (top plot) and radial (bottom plot) currents in the
multi-NI-coil magnet of FIGS. 5B and 6B, but now modified with
intra-coil grading in addition to the inter-coil grading, during a
ramping. In the example of FIG. 5C, the turn-to-turn resistivities
(not optimized) in coil 1 (the top coil), 2, 13 and 14 (the bottom
coil) are graded from 70 Om.sup.2 on the innermost turn to 91
Om.sup.2 on the outermost turn; 75-97.5 Om.sup.2 in the coil 3, 4,
11 and 12; 80-104 Om.sup.2 in coil 5, 6, 9 and 10; and 85-110.5
Om.sup.2 in coil 7 and 8. In comparison to the original NI-coil
magnet of FIG. 5A, the peaks and ranges of the currents become
smaller and narrower upon each application of grading. When
compared to FIG. 5B, the current distributions are now much more
uniform in the radial direction within all the individual coils,
and in the axial direction across the entire magnet.
[0106] In some embodiments, an optimal set of turn-to-turn
resistances graded by both the intra-coil grading and inter-coil
grading may be determined to distribute the currents uniformly
across the entire magnet, both radially and axially. It is
important to notice that the differences between the maximum and
minimum values of the azimuthal and radial currents are smaller
after applying the grading, indicating that the currents are more
uniform. Also, the peak value of the radial current is smaller
after applying grading, indicating that more current is directed
back to the conductor as azimuthal current to charge the magnet. By
increasing the turn-to-turn resistances via grading, the ramping
rates in graded-resistance NI-coil magnets can be improved over the
unmodified NI counterparts.
[0107] FIG. 9 illustrates the improvements of ramping time in
graded-resistance multi-coil magnets, by applying the inter-coil
grading of FIGS. 5B and 6B, and by applying both the intra- and
inter-coil grading of FIG. 5C, as compared to the unmodified
NI-coil magnet of FIGS. 5A and 6A. Curve 903 shows the ramping time
for the original unmodified NI-coil magnet of FIGS. 5A and 6A,
curve 906 shows the ramping time for the inter-coil graded magnet
of FIGS. 5B and 6B, and curve 909 shows the ramping time for the
inter+intra-coil graded magnet of FIG. 5C. The simulations stopped
when the center field reached 99% of the steady field. When
compared to uniform-resistance NI-coil magnet during ramping, the
uniformly distributed currents in a graded-resistance NI-coil
magnet counterpart with the same ramping performance results in
better thermal stability and lower risk of quenching.
[0108] The charging and discharging characteristics of the HTS NI
coils stacked on the same axis has been examined. As discussed with
respect to the unmodified NI coil magnet, the electromagnetic
behaviors in the charging and discharging are opposite and the
azimuthal and radial current component are not uniform in the coils
from the upper to the middle. This may be attributed to not only
the turn-to-turn metal contacts but also the difference in the
self-inductance and mutual inductance at different locations. Note
that only the azimuthal component of current contributes to the
desired magnetic field, but both the azimuthal and radial
components of current may result in Joule heating. During the
ramping process, the unmodified coil magnet has more azimuthal
current in the upper and lower coils near the inner diameter, but
has more radial component in the middle coils near the outer
diameter. On the contrast, during the fast discharging process, the
unmodified NI coil magnet has both higher radial and azimuthal
currents in the middle coils near the outer diameter.
[0109] Graded turn-to-turn resistances (thermal, electrical or
both) can be realized by controlling the winding tension, by
changing the roughness of the contact surfaces of the conductor, or
more practically, by co-winding (including pre-soldered) a thin
plate with controlled resistance variation along the length of the
conductor. The transverse (not sheet) resistivity of a co-winding
thin plate can be adjusted in several ways, including but not
limited to control the thickness and material properties of the
co-wound layer, deposit a resistive thick film on a conductive thin
substrate by sputtering or screen printing process as used in
manufacture of thin/thick film resistors. One such example is to
co-wind the conductor with segments of thin plates of the same
thickness but of different material properties at different
sections of the length of the conductor. For example, for the first
10 turns, the conductor can be co-wound with a layer of thin copper
plate, for the next 10 turns with brass plate and for the third 10
turns with steel, and so on. Yet another way is to manufacture the
thin plate as a thin-plate composite composed of two strips of
distinctly different resistivities bounded side by side along their
thin edges or wide surfaces. The effective transverse resistivity
is controlled by adjusting the ratio of the widths or thicknesses
of the two strips. And yet another way is to manufacture the thin
plate with a functional pattern along the length, including but not
limited to a pattern formed by alternating low resistance and high
resistance segments. By controlling the length ratio of the
alternating high and low resistance segments, the effective
transverse resistance of the patterned layer can be controlled.
[0110] The grading of resistances can be implemented in many ways,
including but not limited to using a step function (as shown in
FIG. 10A), a piecewise linear function (as shown in FIG. 10B), or a
piecewise nonlinear function (as shown in FIG. 10C) of the
conductor length, or a step function (FIG. 10A) of turn or coil
number. The patterning example in the co-winding layer described
above is one example of using step function of the conductor
length. A piecewise continuous function (FIG. 10B and FIG. 10C) of
length produces a graded-resistance NI-coil magnet in which the
turn-to-turn resistance within a single coil varies (linearly as in
FIG. 10B or nonlinearly as in FIG. 10C) as a continuous function 1
in the first length segment of the total length of the winding
conductor, then as a continuous function 2 in the second connected
length segment (connected from the first segment), and so on up to
the last connected length segment as another continuous function. A
step function of turn number produces a graded-resistance NI-coil
magnet in which the turn-to-turn resistance is a constant between
every two adjacent turns (or fraction of turn) but differs from
those in other turns. The grading of resistance can even be
controlled dynamically depending on the strength of the local
magnetic field by using, for example, magnetoresistance materials.
In some implementations, materials where their resistances depend
strongly on temperature over the range above the operating
temperature can be used. This allows the turn-to-turn resistance to
be adjusted dynamically during a quench.
[0111] The graded coil-to-coil interfacial resistance (FIG. 2E) can
be implemented in a similar way as a thin layer of material
sandwiched between every two adjacent coils. For each coil-to-coil
interfacial resistance, it can be a constant value, can be
patterned or can even be controlled dynamically by local magnetic
field or local temperature as in the control of turn-to-turn
resistances. In addition, each coil-to-coil interfacial resistance
can also be graded axially across the width of the interfacial
material in a radially stacked NI-coil magnet and radially across
the radius of the interfacial material in an axially stacked
NI-coil magnet in a piecewise linear or piecewise nonlinear
fashion.
[0112] FIG. 11 is an illustration of a disk-type homopolar
motor/generator 1100 including an HTS NI coil or multi-coil
superconducting magnet 1102 with grading stability enhancements, in
accordance with various embodiments of the present disclosure. The
motor 1100 includes an electrically conductive metal disk 1104 (as
a rotating conductor), an electrically conductive shaft 1106
mechanically and electrically coupled to the electrically
conductive metal disk 1104, and liquid metal brushes (1108 and
1110) electrically contacting an edge of the electrically
conductive metal disk 1104 and the electrically conductive shaft
1106, respectively. The disk-type homopolar motor/generator 1100
can be DC operated with no AC losses or ripple fields.
[0113] In operation, a normal component (B) of the magnetic field
generated by the HTS NI coil or multi-coil superconducting magnet
1102 is substantially or generally perpendicular to a face of the
electrically conductive metal disk 1104 and acts on the metal disk
1104, which rotates when DC power is applied to first and second
electrical contacts (e.g., liquid metal brushes 1108 and 110) or
generates DC power from the first and second electrical contacts
(e.g., liquid metal brushes 1108 and 1110) when the electrically
conductive metal disk 1104 is rotated. It will be appreciated that
liquid metal brushes are shown and described as examples and that
other types of contacts suitable for rotational contact can be
used, such as slip rings.
[0114] A disk-type homopolar motor/generator as described above can
have application in numerous devices and systems including aircraft
such as hypersonic aircraft, among many others. FIG. 12 shows a
diagram of an example hypersonic aircraft 1200 having one or more
homopolar motor/generators 1202 in accordance with the present
disclosure. The homopolar motor/generator(s) 1202 can include an
HTS NI coil or multi-coil magnet as described herein. In some
embodiments, homopolar motor/generator(s) 1202 can include one or
more HTS NI coil or multi-coil magnets such as those shown in FIGS.
1A, 1B, 2A, 2B, 2C, 2D, 2E, 3A, 15, 16, 21, 26, and 31-34, and/or
combinations thereof.
[0115] In some applications in which an HTS NI coil or multi-coil
magnet is used to generate power, such as, for example, in
homopolar motor/generator 1202 of a vehicle/aircraft as shown in
FIG. 12, it may be desirable for the magnet to be configured to
contain the propagation of a hot spot such that at least a fraction
of the transport current is preserved in the winding pack (e.g.,
homopolar motor/generator 1202 does not lose power during/after a
quench occurs and can provide continuous power) and provide a
faster recharge time during self-protecting recovery and a reduced
magnetic field transient. For example, in some embodiments,
homopolar motor/generator(s) 1202 can include an HTS NI multi-coil
magnet comprising two or more coils connected in series, in
parallel, or in a mixed combination, the coils having the same or
different thermal barrier designs configured to contain the
propagation of a hot spot while still permitting turn wise current
sharing such as, for example, those barrier designs shown in FIGS.
26, 26, and 31-34, and described below.
[0116] The no-insulation (NI) approach to winding
(RE)Ba.sub.2Cu.sub.3O.sub.x (REBCO) high temperature superconductor
(HTS) solenoids has shown significant promise for maximizing the
efficient usage of conductor while providing self-protecting
operation. Self-protection in a NI coil, however, does not diminish
the likelihood that a recoverable quench occurs. During a
disturbance resulting in a recoverable quench, owing to the low
turn-to-turn contact resistance, transport current bypasses the
normal zone by flowing directly from the current input lead to the
output lead, leading to a near total loss of the azimuthal current
responsible for magnetic field generation. The consequences are
twofold. First, a long recovery process is needed to recharge the
coil to full operational functionality. Second, a fast magnetic
field transient is created due to the sudden drop in magnetic field
in the quenching coil. The latter could induce a global inductive
quench propagation in other coils of a multi-coil NI magnet,
increasing the likelihood of quenching and accelerating the
depletion of useful current in other coils, lengthening the
post-quench recovery process.
[0117] Embodiments include a graded-resistance construction
designed to tackle the mentioned problems while maintaining the
superior thermal stability and self-protecting capability of NI
magnets. Through computational modeling and analysis on a hybrid
multiphysics model, patterned resistive-conductive layers are
inserted between selected turn-to-turn contacts to contain hot-spot
heat propagation while maintaining the turn-wise current sharing
required for self-protection, resulting in faster post-quench
recovery and reduced magnetic field transient. Effectiveness of the
designs have been studied at 4.2 K and 77 K. Embodiments include
REBCO magnets with high current density, high thermal stability,
low likelihood of quenching, and rapid, passive recovery, and also
with high operational reliability and availability.
[0118] The no-insulation (NI) approach to
(RE)Ba.sub.2Cu.sub.3O.sub.x (REBCO) high temperature
superconducting (HTS) magnets is one of the most innovative new
approaches to high field superconducting magnet design, resulting
in higher winding pack density and superior thermal stability, as
compared to some insulated REBCO magnets. NI coils are expected to
be self-protecting, recovering from quenches without external
quench protection mechanisms or other active measures. As a result,
the NI approach reduces the costs of fabrication and operation of
REBCO magnets. For many applications, the NI approach may resolve
many of the long-standing challenges preventing the advancement of
REBCO-based applications. Yet the rapid advancement of the NI coil
concept has also identified a number of important challenges and
issues; these are defined here as Issues 1-4.
[0119] Issue 1: During a current ramping, the inductive impedance
along the conductor increases, causing part of the transport
current to "leak" through the turn-to-turn contact, which has very
low electrical contact resistance, as a radial current. The
consequence is much slower charging/discharging rate as compared to
an insulated counterpart. Results have shown that the higher the
total turn-to-turn electrical resistance, the faster is the
charging/discharging rate. In general, the charge and discharge
times are proportional to the time constant:
.tau. = L R r ( 4 ) ##EQU00004##
where L is the coil inductance and R.sub.r is the characteristic
resistance, which is essentially the sum of the turn-to-turn
contact resistances of the coil.
[0120] Issue 2: During charging or discharging, local current
concentrations form within a large NI magnet composed of one or
multiple NI coils. The regions with high local current
concentration have increased likelihood of quenching in the event
of a heat disturbance.
[0121] Issue 3: During a quench in a NI coil, even if it is a
recoverable one, when the hot-spot creates a large normal zone, the
azimuthal current responsible for the generation of magnetic field
can drop abruptly, even to nearly zero. This has two consequences.
One consequence is that current has to be recharged to fill the
current-depleted turns from a low remaining value during recovery
and thus the coil goes through a lengthy period without generating
significant magnetic field, impacting its operational availability.
The other consequence is a fast magnetic field transient which
leads to a stability issue described below as "Issue 4."
[0122] Issue 4: Experiment and simulation results show that in a
multi-coil NI magnet, the fast decreasing magnetic field transient
caused by a fast discharge in a quenching coil can induce a quench
that propagates to the adjacent coils in the magnet via AC losses
and inductive coupling. This generates a rapid, wide-spread quench
propagation in the multi-coil NI magnet. Fast, global quench
propagation is desirable in insulated HTS magnets, since a quick
but controlled energy dump can prevent destructive overheating. In
the case of a NI magnet composed of individually self-protecting NI
coils, however, the effects of a wide-spread quench propagation are
twofold: i) the recovery process is dramatically lengthened, since
instead of recharging only the initially quenched coil, it is now
necessary to recharge all the coils that quenched, and ii) the
stability and reliability of the NI magnet are reduced.
[0123] Embodiments include Graded-Resistance NI (GRNI) methods that
maintain the advantages of the NI approach while mitigating the
challenges described above. Embodiments include a GRNI construction
method that tackles specifically the slow recovery issue described
in Issue 3 on a single NI coil. The method involves constructing
GRNI magnets by manipulating the turn-to-turn contact resistances
via grading and patterning to contain the propagation of a hot-spot
such that a fraction of the transport current is preserved in the
winding pack. Benefits of this technique and construction can
include much faster recharge time during self-protecting recovery
and reduced magnetic field transient. The method, when applied to
multi-coil NI magnets, also mitigates the problem described in
Issue 4, since the reduction in magnetic field transient reduces
the likelihood of the occurrence of inductive quench propagation,
thus increasing the stability of multi-coil NI magnets. An
additional benefit of this method is improved ramping rate. The
method has been studied computationally via hybrid multiphysics NI
coil models at both the 77 K and 4.2 K operating temperatures.
Embodiments include self-protecting REBCO magnets with high current
density, high thermal stability, low likelihood of quenching, and
rapid, passive recovery that also have high operational reliability
and availability.
[0124] Due to the low turn-to-turn contact resistance, current can
flow in both azimuthal and radial directions throughout the entire
NI coil. As result, every individual turn in a NI coil must be
taken into account in simulation. The most viable way to model the
electrical behavior of the entire NI coil is by using a
spirally-wound equivalent circuit network model. FIG. 13 shows a
block diagram of a hybrid NI magnet model. The equivalent circuit
network model calculates the currents distributions. The calculated
nodal current distributions are input into a finite element (FE)
thermal magnet model (T) as heat sources and into a FE
electromagnetic magnet model (B) to calculate the magnetic field
distribution. Meanwhile, the calculated temperature and magnetic
field are fed back to the equivalent circuit network model for the
calculation of the critical current. The entire coupled hybrid
magnet model is run in COMSOL Multiphysics simulation software.
[0125] FIG. 14 shows a schematic circuit diagram for a
representative spirally-wound equivalent circuit network model for
a single NI coil. Equivalent circuit network model of NI coils is
well-established and experimentally validated. A network model for
the multi-coil NI magnet is built by cascading multiple single-coil
network models in series via connecting the current output lead of
the previous coil to the current input lead of the next coil. For
simplicity, the following description of the network model is based
on a single-coil model. The current calculated by the network model
is decomposed into an azimuthal current and a radial current that
flows through the turn-to-turn contact in the radial direction.
Each turn of the coil is subdivided into .sub.ne (.sub.ne=4 in the
example shown) fine arc elements along the azimuthal direction;
each arc element is represented by an inductance-resistor circuit.
The arc number (.sub.ne) per turn is adjusted adaptively according
to the dynamics of the electrical behavior. For example, turns that
are closer to the hot-spot are modified with larger .sub.ne per
turn, and those further away, with a lower .sub.ne per turn. In
this way, the size of the system of equations representing the
network can be reduced significantly, especially in a multi-coil
magnet model. At each circuit node, the governing equation is
derived from Kirchhoff's current law and in each independent
circuit mesh, from Kirchhoff's voltage law:
{ i k - i k + 1 + j k - n e - j k = 0 u k - u k + n e - j k - 1 R r
, k - 1 + j k R r , k = 0 ; ( 5 ) ##EQU00005##
where i.sub.k and j.sub.k represent the azimuthal current and
radial current of the k.sup.th arc element, respectively, u.sub.k
is the voltage across the k.sup.th arc element circuit and
R.sub.r,k is the radial turn-to-turn resistance of the k.sup.th arc
element. The azimuthal current i includes that in the
superconducting layer and normal layers in a REBCO conductor,
including the substrate, stabilizer and metallic thin-film
laminations. A positive i flows in the anticlockwise direction and
a positive j flows in the radially outward direction. Hereafter,
the subscripted index k of a variable refers to the variable of the
k.sup.th arc element, unless stated otherwise. The equivalent
turn-to-turn resistance, which includes the contact resistance and
transverse resistance of the conductor, is calculated as:
R r , k = .rho. r S k ( 6 ) ##EQU00006##
where S.sub.k is the contact surface area and .rho..sub.r is the
equivalent radial contact resistivity, which is found
experimentally to be typically 70 .mu..OMEGA.cm.sup.2 at 77 K.
[0126] The voltage u.sub.k, across the k.sup.th arc element is the
sum of resistive and inductance voltages calculated as:
u k = L k di k dt + l .noteq. k M k , l di l dt + V R , k ( i k , I
c , k , T k ) ( 7 ) ##EQU00007##
where L.sub.k represents the self-inductance and M.sub.k,l is the
mutual inductance coupled with other arc elements. The inductances
are calculated by Biot-Savart Law via an integration method.
V.sub.R,k is the voltage across the azimuthal resistance of the
k.sup.th arc element, which consists of two parallel resistances:
the resistance of the superconducting layer R.sub.sc,k (inset of
FIG. 14) and that of the normal layers R.sub.n,k (inset of FIG.
14). V.sub.R,k depends on the azimuthal current i.sub.k, critical
current I.sub.c,k and temperature T.sub.k, and is calculated from
the following relationships:
{ E 0 l k ( i sc , k I c , k ) .alpha. - ( i k - i sc , k ) R n , k
= 0 , V R , k = E 0 l k ( i sc , k I c , i ) .alpha. , i n , i = i
k - i sc , k , R n , k = .rho. n ( T k ) l k S c , I c , k = I c 0
I c ( T k ) I c ( B .cndot. , k , B .perp. , k ) , ( 8 )
##EQU00008##
where i.sub.sc,k is the current in the superconducting layer.
l.sub.k and S.sub.c are the length of the arc element and cross
sectional area of the conductor, respectively. p.sub.n is the
temperature-dependent equivalent resistivity of all the normal
layers, including the substrate, stabilizer and metallic thin-film
laminations, and is estimated by using the parallel rule of
mixtures. i.sub.n,k is the normal-layer current flowing through
R.sub.n,k. The voltage V.sub.R,k in equation (8) equals the voltage
across R.sub.sc,k, and is expressed as the E-I power law of HTS
conductors with E.sub.0=1.times.10.sup.-4 V/m and .alpha.=31. The
critical current I.sub.c,k depends on the temperature T.sub.k and
magnetic field B.sub.k. I.sub.c0 is the self-field critical current
of the REBCO conductor.
[0127] The temperature-dependent critical current I.sub.c in (5) is
calculated as:
I c ( T ) = { I c 0 T c - T T c - T o if T < T c , for T
.gtoreq. T 0 0 if T .gtoreq. T c ( 9 ) ##EQU00009##
where T.sub.o=77 K or 4.2 K is the operating temperature,
T.sub.c=92 K is the critical temperature. The field- and
angular-dependent critical current in (5) is calculated as:
I c ( B , .theta. ) = I c ( B .cndot. , B .perp. ) = 1 [ 1 + ( kB
.cndot. ) 2 + B .perp. 2 / B c ] b ( 10 ) ##EQU00010##
where B.sub..quadrature.r and B.sub..perp. represent the magnetic
fields parallel and perpendicular to the wide tape surface,
respectively. Here k, b and B.sub.c are parameters curve-fitted
from experimental data of the conductors used. For 77 K
simulations, the experimental data are generated from in-house
measurements and for 4.2 K simulations, they are taken from Xu A,
Jaroszynski J J, Kametani F, Chen Z, Larbalestier D C, Viouchkov Y
L, Chen Y, Xie Y and Selvamanickam V 2010 Angular dependence of
J(c) for YBCO coated conductors at low temperature and very high
magnetic fields Supercond. Sci. Technol. 23 014003. FIGS. 35-37
show Tables 1-3, respectively, listing the key parameters used in
the 77 K and 4.2 K simulations. Table 1 shown in FIG. 35 lists key
parameters common to both the 77 K and 4.2 K simulations. Tables 1
and 2 shown in FIGS. 35 and 36, respectively, list the key
parameters used in the 77 K simulations. Tables 1 and 3 shown in
FIGS. 35 and 37, respectively, list the key parameters used in the
4.2 K simulations.
[0128] For a single coil with an approximation that temperature is
uniformly distributed across the height of the coil, a 2D FE
thermal model can be used to reduce the degree of freedom. For a
multi-coil magnet, the FE thermal and electromagnetic models are
always 3D and always share the same geometry of the magnet; the
difference is that the electromagnetic model has an air region.
FIG. 15 shows an example of the geometry for 3D FE thermal and
electromagnetic multi-coil magnet models; the air region for the
electromagnetic model is not shown. The FE models are
spirally-wound with the same turn number and dimensions specified
in the network model. The REBCO conductor used is approximated as a
homogenous conductor with the effective homogenous thermal and
electrical material properties estimated using the
rule-of-mixtures.
[0129] The governing equations of the homogenous 2D or 3D thermal
model are expressed as (with the arc element number k ignored):
{ d ( T ) C p ( T ) .differential. T .differential. t + .gradient.
( - k .gradient. T ) = Q n = .rho. n ( T ) ( i nI / S c ) 2 in
.OMEGA. , - n ( - k .gradient. T ) = 0.5 Q r = 0.5 .rho. r ( j I /
S k ) 2 on .differential. .OMEGA. ~ , - n ( - k .gradient. T ) = -
P c ( T - T o ) on .differential. .OMEGA. c , ( 11 )
##EQU00011##
where d and C.sub.p are the temperature-dependent equivalent
density and specific heat capacity. Q.sub.n is the Joule heating on
the normal layers and Q.sub.r is the radial Joule heating on
.differential.{tilde over (.OMEGA.)}, which is the union of all the
internal turn-to-turn contact surfaces. i.sub.nI and j.sub.I are
the interpolated normal-layer and radial currents, and P.sub.c is a
cooling function of temperature difference imposed on the boundary
.differential..OMEGA..sub.c, which is the union of the innermost
and outermost surfaces of the magnet (.differential..OMEGA. is the
union of all the external boundaries). For 77 K simulations,
P.sub.c represents a cooling power similar to the heat load (lift)
curve of a commercial cryocooler. For 4.2 K simulations, P.sub.c
represents the pool boiling heat transfer curve (as heat flux) of
liquid helium (LHe) under 1 atm pressure. The nodal normal-layer
current i.sub.n, azimuthal current i and radial current j obtained
from the network model are populated along the conductor length to
form 3D (or 2D) current distributions i.sub.nI, i.sub.I and j.sub.I
using 3D (or 2D) interpolations for the calculations of Joule
heating in the thermal model and magnetic field in the
electromagnetic model (see FIG. 13). The interpolated currents are
assumed to be uniform across the conductor thickness and width. A
heater located inside the thermal model is used to simulate a local
heat disturbance.
[0130] The 3D FE electromagnetic model is coupled to the network
model to calculate the magnetic field generated by the interpolated
coil current. The inductive voltage term in equation (7), which
calculates the voltage induced by a changing current, implicitly
takes into account the voltage induced by the changing magnetic
field. As a result, static Maxwell equations are used for the
calculation of magnetic field as follows:
{ .gradient. .times. .gradient. .times. A = J e in .OMEGA. B =
.gradient. .times. A in .OMEGA. .gradient. A = 0 in .OMEGA. B n = 0
on .differential. .OMEGA. ( 12 ) ##EQU00012##
where B is the magnetic flux density, A is the vector magnetic
potential and .mu. is the permeability. The current density
J.sub.e=j.sub.I/S.sub.k, i.sub.I/S.sub.c, 0 (, , means 3D vector in
cylindrical coordinates). The third equation is added for gauge
fixing.
[0131] The calculated temperature and magnetic field distributions
(spatially continuous variables) are extracted from the thermal and
electromagnetic models, respectively, at the same set of physical,
discrete point locations (along the conductor length) associated to
the network model's nodes. The extractions are done by using point
probes (as a "domain point probe" data monitoring function in
COMSOL) (see FIG. 13). In each time step, the extracted temperature
and magnetic field are input to the network model to derive the
temperature-dependent material properties and calculate the
critical current I.sub.c in equations (9) and (10).
[0132] Embodiments include GRNI methods based on the idea of
manipulating the turn-to-turn thermal and electrical resistances in
a NI coil to control its electrical and thermal behaviors. In the
hybrid model, turn-to-turn thermal and electrical resistances are
added to the contact between two adjacent turns, namely turn n-1
and turn n, by inserting interfacial equations (as internal
boundary conditions in COMSOL):
{ - n ( - k .gradient. T ) = - k ~ s , n ( .phi. ) T n - 1 - T n d
s on .differential. .OMEGA. ~ n , - n ( - k .gradient. T ) = - k ~
s , n ( .phi. ) T n - T n - 1 d s on .differential. .OMEGA. ~ n - 1
, ( 13 ) ##EQU00013##
where .differential.{tilde over (.OMEGA.)}.sub.n-1 and
.differential.{tilde over (.OMEGA.)}.sub.n are the two adjacent
internal turn-to-turn contact boundaries on turn n-1 and turn n.
{tilde over (k)}.sub.s,n(.PHI.) is the thermal conductivity of the
insertion as a function of the arc length angle (.PHI.). This
function allows a graded or patterned thermal resistance to be
defined for the insertion between turn n-1 and turn n. T.sub.n is
the temperature measured on the boundary .differential.{tilde over
(.OMEGA.)}.sub.n and d.sub.s is the thickness of the insertion.
[0133] Graded or patterned turn-to-turn electrical resistance
insertion is added by two steps. First, by changing the radial
turn-to-turn contact resistance R.sub.r,k (defined in equation (6))
in the same pattern defined by {tilde over (k)}.sub.s,n(.PHI.). For
example, wherever a section {tilde over (k)}.sub.s,n(.PHI.) is
defined as thermal insulation, all the R.sub.r,k that falls within
the same section are changed to electrical insulation too. Second,
by changing the radial Joule heating on the contact between turn
n-1 and turn n to match the changes in R.sub.r,k. The radial Joule
heating term in equation (11) is modified as
-n(-k.gradient.T)=0.5 {tilde over (.rho.)}.sub.r,n(.PHI.)
(j.sub.I/S.sub.k).sup.2 on .differential.{tilde over
(.OMEGA.)}.sub.n-1 and .differential.{tilde over (.OMEGA.)}.sub.n,
(14)
where {tilde over (.rho.)}.sub.r,n (.PHI.) is a function of the arc
length angle for the turn-to-turn electrical resistivity for the
insertion between turn n-1 and turn n. Its value is modified from
R.sub.r,k accordingly to match the pattern defined in {tilde over
(k)}.sub.s,n(.PHI.).
[0134] GRNI designs/methods disclosed herein are developed to
mitigate Issues 1-4 described above. The methods engineer the
thermal and electrical behaviors of NI coils by manipulating the
turn-to-turn contact resistance via grading and patterning. Two
types of grading can be applied to a multi-coil magnet: intra-coil
grading and inter-coil grading. Intra-coil grading involves
manipulating the turn-to-turn resistance with respect to all turns
within a single coil. Inter-coil grading involves manipulating the
turn-to-turn resistance with respect to all coils within the same
magnet. FIG. 16 shows an example of GRNI multi-coil magnet with
both intra- and inter-coil grading using arbitrary values.
Embodiments disclosed herein address Issue 3 andsignificantly
reduce the magnetic field transient which also mitigates Issue
4.
[0135] The GRNI designs/methods disclosed herein are based on a
comprehensive understanding of the underlying mechanisms that give
HTS NI magnets their high thermal stability and self-protecting
capability. FIG. 17 (first row, t=5 ms) shows that during the
formation of a local normal zone in a 20-turn NI pancake coil
operated at 77 K, transport current redistribution occurs
turn-wise, i.e., along the entire turn in which the normal zone is
growing, instead of just bypassing the local normal zone as
commonly believed. A turn in which a local normal zone has formed
is referred thereafter simply as a "normal turn". This turn-wise
current sharing effect causes the azimuthal current (mainly from
the superconducting layer) to be "pushed away" from all the normal
turns and "absorbs" by the neighboring superconducting turns as a
radial current, resulting in an overcurrent in those neighboring
turns. Note that as more turns become normal, the overcurrent in
the neighboring turns becomes higher. A local normal zone that
causes a turn-wise loss of azimuthal current is referred hereafter
as a "thermal-cutoff" region, to highlight that this peculiar
behavior only happens in coils with very low turn-to-turn
resistance, including the NI coils. FIG. 17 (second row, t=100 ms)
shows that once complete thermal-cutoff occurs, i.e., the hot-spot
has propagated to thermally-cutoff an entire radial cross section
of the coil, the azimuthal current is nearly zero across the entire
coil. Much of the transport current flows directly from the input
to the output current lead, bypassing the thermal-cutoff region.
FIG. 17 (third row, t =5 s) shows that the hot-spot eventually
retreats and the coil recovers from the transient quench. In
addition to good heat conduction across the turn-to-turn contact,
the turn-wise current sharing-and-absorption and the
input-to-output-lead current bypass prevents Joule heating at the
hot-spot from creating normal zone growth, resulting in a
self-protecting coil.
[0136] Notice that in FIG. 17, much of the azimuthal current at the
vicinity of the current leads is negative, indicating that the
current bypasses the thermal-cutoff zone by reversing (clockwise)
from the current input lead to the output lead. The consequences of
this current redirection include potential heating around the
current leads and a near total-depletion of "useful" azimuthal
current responsible for magnetic field generation. The "No barrier"
curve in FIG. 18A shows that the normalized center magnetic field
drops abruptly to nearly zero when complete thermal-cutoff begins
in the same NI coil. As a result, even if the coil is
self-protecting and recovers fully, a lengthy recharge process is
required before the magnet returns to full functionality. The "No
barrier" curve in FIG. 18B shows that the hot-spot peak
temperature, which tops at 185 K, caused by a large disturbance in
the same coil decreases steadily after the heat source ends,
indicating that even if a complete thermal cutoff occurs, recovery
still occurs. During the entire quench-recovery process, the power
supply remains connected and the magnetic field returns slowly and
much later to its final operating value.
[0137] To tackle the slow recovery issue (Issue 3), a GRNI approach
is used to limit the depletion of "useful" (azimuthal) current
during a quench. The key idea is demonstrated in FIGS. 19A and 19B.
A straightforward, simple resistance grading composed of a single
full-turn of 60 .mu.m Kapton insulation is inserted as a thermal
barrier between two center turns of the same NI coil shown in FIG.
18. The heater is placed at the middle of the outer half-section of
the coil. The Kapton thermal barrier limits heat propagation from
the hot-spot to the inner half-section of the coil. Thus the
temperature there remains below the critical temperature T.sub.c
and the transport current on the inner half section remains. Notice
that the turns on the cold side of the barrier, i.e., on the
inner-half of the coil, are overcurrent (126
A>I.sub.c(B.sub.max, 77 K)=115.5 A, see Table 2 of FIG. 36). The
curve "60 .mu.m barrier" in FIG. 18A shows that this simple
implementation maintains about half of the center magnetic field
during a quench-recovery process with the power supply constantly
applied. Since the thermal barrier also renders less heat
dissipation, the peak hot-spot temperature also increases, as FIG.
18B shows. Moreover, since in general, a thermal insulator is also
an electrical insulator, this simple implementation also prevents
turn-wise current sharing from redistributing to the neighboring
turns. As a result, current only flows to the neighboring turns
through the narrow turn gap in the Kapton barrier, shown in FIG.
20, resulting in unwanted local heating which eventually causes a
non-recoverable quench. Thus, a more complex design is needed not
only to prevent complete thermal-cutoff and local heating but also
to maintain the turn-wise current sharing mechanism required for
self-protection.
[0138] FIG. 21 demonstrates an effective GRNI design example
applied to a 39.5-turn NI pancake coil with an inductance of 4 mH.
The grading is composed of one set of two full turns of patterned
thermal barriers, using 60 .mu.m Kapton thin strip, inserted
between turns 16 and 17, and between turns 24 and 25, with 8 turns
between the two barriers. Electrically (and thermally) conductive
arc segments of various lengths are inserted at periodic intervals
along the barriers. Here, in the model, the conductive arc segments
are realized by simply not adding any Kapton strip. The conductive
segments allow turn-wise current sharing to occur to maintain high
thermal stability and to prevent local heating, in particular,
around the current input and output leads and one similar to that
shown in FIG. 20, from occurring during local thermal-cutoff
formation. Note that the current input and output leads of the coil
shown in FIG. 21 are placed at the opposite sides of the coil. This
arrangement allows more paths for the shared current to reach the
current leads from the conductive segments when thermal cutoff
occurs. The conductive segment on one barrier turn is covered by an
insulation segment on the other barrier turn. Here, the overlapping
length of the insulation segments are always confined in 45 degrees
and thus the conductive segments are also confined to 45 degree.
The design shown in FIG. 21 ensures that a hot-spot initiated at
any location of the coil is contained by at least one layer of
barrier and that current always find a path to flow without
generating local heating. Hereafter, the design in FIG. 21 is
referred as the "8-turn" design.
[0139] Simulation Results--77 K Cases
[0140] To study the effectiveness of the 8-turn design, the
39.5-turn single-pancake model is tested with hot-spots initiated
at different places; three of the tested hot-spot locations are
shown in FIG. 21 (at Heater1, Heater2, and Heater3). These
locations are keys to determine the effectiveness of the grading
design in preserving the magnetic field and self-protecting
capability of the coil. Table 1 lists the common key parameters
used in the 77 K and 4.2 K simulations. Table 2 lists the
parameters used in the 77 K simulations. FIG. 22A shows the
normalized center magnetic field versus time profiles generated by
a NI coil graded with the 8-turn design and a non-graded NI
counterpart. All simulations are performed under the same heater
energy (476 W for 40 ms) and cooling conditions with the power
supply always connected. A complete thermal-cutoff similar to the
one seen in FIG. 18A is induced in the non-graded NI coil by
Heater1, causing the center magnetic field to drop abruptly to
nearly zero, as the "Heater1, no barrier" curve in FIG. 22A shows.
In contrast, more than 50% of magnetic field is preserved in all
three heater cases during a quench in the graded coil, as the
"Heaterx, 8-turn" dashed curves in FIG. 22A show, indicating that
the heater-generated hot-spots are successfully contained and no
complete thermal-cutoff results. Note that the fraction of field
preserved in the "Heater1, 8-turn" case is higher than those in the
"Heater2, 8-turn" and "Heater3, 8-turn" cases. This is because for
the Heater1 case, there are a total of 32 turns (16 from each
outer, cool side of the barriers) out of 40 turns (on the upper
half of the coil) available for carrying current, whereas there are
only 16 turns available for the other two heater cases.
[0141] FIG. 22B shows peak temperature at the hot-spot versus time
profiles corresponding to all cases in FIG. 22B. The peak
temperatures generated by Heater2 and Heater3 are slightly lower
than that of the non-graded coil, showing that the cooling on
either the outer or inner radius is sufficient to dissipate the
heat generated by the heaters. The peak temperature of the hot-spot
generated by Heater1 is .about.217 K, about 29 K higher, and
decreases more slowly than the other cases. The reason for this is
seen in FIG. 23A, which shows a snapshot of the thermal-cutoff
generated by Heater1; much of the heat generated by Heater1 is
contained between the overlapped insulation segments. The eight
turns between the thermal barriers form a long, narrow heat mass
channel for the heat to propagate, and as a result the heat builds
up quickly and dissipates inefficiently and slowly along the
contained channel. Nevertheless, a complete thermal cutoff, i.e.,
normal zone across the entire radial cross section of the coil, is
prevented. FIG. 22B reflects the fact that despite the high peak
hot-spot temperature generated by a strong heater energy at
different locations, the peak temperature in each case eventually
returns to the operating temperature, signifying complete recovery.
In all cases, when the temperature drops below T.sub.c=92 K during
recovery, the magnetic field recovers slowly to the original value,
but recovery in the 8-turn GRNI coil is .about.23% faster than that
in the non-graded NI counterpart.
[0142] To demonstrate the option in lowering the peak temperature
around Heater1, here the 8-turn design is modified by doubling the
turn number between the double-barrier to 16 turns, with 12 turns
left on each side outside of the barriers. Hereafter, this new
design is referred as the "16-turn" design. The normalized center
field and temperature profiles generated from the 16-turn design
(labeled as "Heaterx, 16 turns", with the same heater locations as
in the 8-turn cases) are also included in FIGS. 22A and 22B for
easy comparison. Since now there are only 12 turns (versus 16 turns
in the 8-turn design) available for carrying current near Heater2
and Heater3, the fractions of field preserved are lower in the
16-turn design (.about.0.4) than the 8-turn design (.about.0.5) in
both heater cases. Surprisingly, for the Heater1 case, the fraction
of field preserved is higher in the 16-turn design than that in the
8-turn design (.about.0.65 versus 0.63), despite the fewer
current-carrying turns outside the barriers (total 24 turns versus
32 turns) near the Heater1. As expected, by increasing the number
of turns between the barriers, the heat generated between the
barriers by Heater1 is now dissipated more effectively along a
wider heat mass channel, as shown in FIG. 24A, resulting in a lower
peak temperature, which is now .about.190 K, as compared to
.about.217 K in the 8-turn design. The peak temperature also
decreases much faster than in the 8-turn design after the heater is
turned off.
[0143] Simulation Results--4.2 K Cases
[0144] All 4.2 K simulations are performed using the same heater
energy as in the 77 K cases under LHe pool cooling and constantly
connected power supply. Table 3 lists the parameters used in the
4.2 K simulations. FIG. 25 shows the normalized center magnetic
field and peak temperature versus time profiles obtained from the
same non-graded NI coil and NI coils graded with the 8-turn and
16-turn designs used in the 77 K simulations. For the non-graded
coil, the hot-spot created by Heater1 ("Heater1, no barrier"
curves) is quickly amplified into a large "second" quench after the
heater is turned off, leading to a complete thermal cutoff with a
damaging peak temperature reaching 398 K. This second quench
nevertheless recovers later. As a result, the center field first
drops abruptly to zero and then recovers slowly. Similar behaviors
occur for Heater2 (not shown) and Heater3 cases in the graded
coils, as the "Heater3, 8-turn" and "Heater3, 16-turn" curves show,
although the peak temperatures are now smaller than 270 K. In
contrast, when the hot-spots created by Heater1 are contained by
either the 8-turn barrier ("Heater1, 8-turn" curve) or 16-turn
barrier ("Heater1, 16-turn" curve), no "second" quench occurs,
leading to surprisingly large fractions of field preserved.
[0145] These results hint that for the 4.2 K cases, when the turn
number between an insulated segment (of a barrier) and the nearest
insulated segment (on another barrier) or cooling boundary is equal
to or smaller than 16 turns (may be a few turns more), a hot-spot
would be effectively contained and a fraction of the field would be
preserved, as in the Heater1 cases. Otherwise, the hot-spot could
be amplified and the field would be drop to nearly zero, as in the
"no barrier" and Heater3 cases. These observations suggest a
refined GRNI design demonstrated in FIG. 26. The new design,
referred hereafter as the "2.times.8-turn" design, is composed of
two sets of 8-turn barriers, with eight turns in between them. This
design ensures that there is always no more than 16 turns from one
insulated segment to the nearest insulated segment or cooling
boundary. As a result, the conditions that would lead to an
amplified hot-spot are removed.
[0146] The results in FIGS. 27A and 27B show that the
2.times.8-turn design works well at 4.2 K. The fractions of field
preserved in all the 4.2 K graded cases are all >0.84, with peak
temperatures lower than 202 K. Notice that the large, second quench
occurred in the non-graded coil no longer exists with the new
design. FIGS. 28A and 28B shows that the 2.times.8-turn design also
works at 77 K (with the same parameters and cooling used in FIG.
22). The fractions of field preserved in all the 77 K cases are all
>0.55, with peak temperatures lower than 217 K. These 77 K
results are comparable to those for the 77 K, 8-turn design shown
in FIG. 22.
[0147] The conditions for the proposed GRNI method to work properly
are that the NI coil must be self-protecting and it must be able to
recharge itself during recovery. The latter implies that the power
supply must remain connected during the quench-recovery process.
This requirement further simplifies the protection design and
lowers the costs of fabrication and operation of HTS magnets.
[0148] An effective grading design must maintain the
self-protecting capability of the NI coil that the grading applied
to. The turn-wise current sharing self-protection mechanism shown
in FIG. 17 implies that for a given NI coil, there is a minimum
number of turns outside the barriers, as shown in FIG. 21, that
must be present to carry the shared current and heat to maintain
the self-protection capability of the coil. Once the minimum number
of turns for self-protection is found, the remaining task is to
design the barriers such that the benefit in field preservation
balances the increased peak temperature. FIG. 22 demonstrated that
a larger number of turns between the barriers lower the peak
hot-spot temperature, but also reduces turns available to carry
current, resulting in a smaller fraction of field preservation.
Another important design parameter is the overlapping length of the
insulation segments. The overlapping length must be sufficiently
long to avoid the heat from leaking to the current-carrying turns
through the overlapped channel to the nearest conductive opening.
However, it must not be too long to obstruct the cooling and
current sharing capabilities. The 8-turn, 16-turn and
2.times.8-turn designs always overlap the insulation arc segments
in 45 degree arc angle; in this way, the conductive arc segments
are left with also a 45 degree arc angle. Coils with smaller
diameter may need longer overlapped insulation segments and coils
with larger diameter can have shorter overlapped lengths.
[0149] Besides the design parameters shown in FIG. 21, the
thickness and material properties of the barriers also affect the
performance of the grading. The thicker the thermal insulation
layer, the less heat leaks to the cool side of the coil, and thus
the larger fraction of magnetic field preserved. Since a thicker
thermal barrier also renders less heat dissipation on and cooling
from the other side of the barrier, however, the peak hot-spot
temperature increases with thicker barrier. Ideally, the materials
used for the barriers would be thermally insulating to limit
thermal-cutoff but electrically conductive to allow full capacity
in turn-wise current sharing as shown, for example, in FIG. 34. In
general, a material with high thermal resistivity also has high
electrical resistivity. Therefore, in some embodiments disclosed
herein the barrier designs are based on the assumption that the
materials are either an insulator or a conductor, both thermally
and electrically. The design patterns presented in FIG. 21 are not
the only viable solutions; grading design based on other more
efficient material properties and grading patterns and better
manufacturability are possible. In general, the more turns a single
coil has, the more feasibility a design has in selecting grading
patterns, barrier turn placements and parameters to control the
peak temperature under a safe limit and maximize the magnetic field
preservation while maintaining the self-protection capability.
[0150] Since magnetic field strength is proportional to the
magnitude of the field-generating current, the theoretical fraction
of preserved center magnetic field is equal to the total number of
current-carrying turns on the cool side of the barriers divided by
the total number of turns in the coil. So the theoretical fraction
of field preserved for the Heater1 case is 32/40=0.8 for the 8-turn
and 2.times.8-turn designs, and 24/40=0.6 for the 16-turn design.
The actual fractions, however, depend on the effectiveness of the
design. For example, FIG. 23A shows that for the Heater1 case of
the 8-turn design, due to high heat buildup within the narrow heat
mass channel, heat leaks to the cool sides of the barriers, rising
the temperature there above the current-sharing temperature. This
turns parts of the current-carrying turns resistive, causing them
to carry a current <=I.sub.a (=80 A), as shown in FIG. 23B,
resulting in lower actual fraction, at .about.0.63, lower than the
theoretical 0.8. FIG. 24A shows that for the Heater1 case of the
16-turn design, wider heat mass channel allows more efficient heat
dissipation, resulting in less heat leak across the barriers.
Therefore, the temperature outside the barriers remain below the
current-sharing temperature and so the current-carrying turns are
able to support an overcurrent after absorbing additional current
shared from the normal turns, in addition to the transport current,
as shown in FIG. 24B (with a current 86.5 A>I.sub.a). As a
result, the actual fraction in this case is .about.0.65, higher
than the theoretical 0.6. For Heater2 and Heater3 cases, since the
hot-spot is cooled at one side and has more turns than the Heater1
cases act as heat mass, little heat leaks across the insulation
segment. As a result, in all the designs, the actual fractions for
Heater2 and Heater3 cases are higher than the respective
theoretical values.
[0151] Due mainly to the low effective heat capacity at 4.2 K, a NI
coil has much lower thermal stability when bath-cooled by LHe than
when operated at 77 K. A local quench, if not contained, could be
amplified (i.e., more turns become normal quickly) through fast
heat propagation into a large-scale quench with a damaging peak
temperature. Such scenario is seen from the quick "second" quench
observed in the "Heater1, no barrier" case in FIGS. 25B (and 15B).
This second quench is induced by the remnant heat of the heater
before the hot-spot temperature drops below T.sub.c. Even though
the peak temperature reaches 398 K, the coil eventually recovers
from the second quench after much of the transport current has
bypassed the thermal-cutoff region. For the "Heater3, 8-turn" and
"Heater3, 16-turn" cases, the turn numbers between the cooling
boundary and the nearest insulated barrier segment are 24 and 28
turns, respectively. These are greater than 16 turns, which likely
is equal to or close to the threshold for effective heat
containment. As a result, even though heat flow to the
current-carrying turns is blocked by an insulated barrier in these
designs, the hot-spots created by Heater3 are amplified after the
heater is turned off, leading to a recoverable second quench. The
resulted large volume of heat energy eventually causes a complete
thermal-cutoff, leading to total loss of the magnetic field, as
seen in FIG. 25A. FIGS. 27 and 28 show that the 2.times.8-turn
design not only effectively preserves the magnetic field and
self-protecting capability in both the 4.2 K and 77 K cases, more
importantly, it also improves stability by preventing amplified
quenches from happening and reduces substantially quench-induced
field drops in the 4.2 K cases.
[0152] The exceedingly high peak temperature generated by the
recoverable second quench seen in the "Heater1, no barrier" case in
FIG. 25B tells that even a non-graded NI coil operated at 4.2 K is
self-protecting, it may still need a quench protection to limit the
peak temperature in the event of a quench. In a high-field coil
operated at 4.2 K, the energy density can be tens to hundreds of
J/cm.sup.3. An accumulated turn-wise current sharing originating
from multiple normal turns in such coil could create enough Joule
heating along the overcurrent turns to generate a whole-coil
quench. In such case, a NI coil is no longer self-protecting. A
barrier design similar to the 2.times.8-turn design can be used to
limit the number of normal turns in a thermal-cutoff and thus could
potentially prevent such large-scale quench from happening and
render a non-self-protecting NI coil capable of self-protecting.
More detailed study is needed to explore this potential
advantage.
[0153] Notice from Tables 2 and 3 the current ratios
I.sub.a/I.sub.c(sf, 4.2 K)=0.34 and I.sub.a/I.sub.c(B.sub.max, 4.2
K)=0.68 are about the same as I.sub.a/I.sub.c(sf, 77 K)=0.36 and
I.sub.a/I.sub.c(B.sub.max, 77 K)=0.69, respectively. Even so, FIGS.
15 and 16 show that the minimum fraction of field preserved among
the 4.2 K cases, at 0.84, is much higher than that in the 77 K
cases, at 0.55. This is because the self-field critical current
I.sub.c0 is higher and the I.sub.c(B, .theta.) curve (the
lift-factor curve described by equation (10)) has higher and wider
field- and angular-dependent peaks near 4.2 K than near 77 K. The
consequence is that the neighboring superconducting turns are able
to absorb more turn-wise current shared from the normal turns,
causing less overcurrent-induced Joule heating and thus smaller
thermal-cutoff, in the 4.2 K cases than in the 77 K cases.
[0154] For a coil with very large number of turns or very strong
cooling and operated at 77 K, complete thermal-cutoff is less
likely, even for large heat disturbance energy. This is because the
temperature at the turns far from the hot-spot will remain well
below T.sub.c. In such a scenario, multiple sets of barriers
similar to the 2.times.8-turn design can be installed to limit the
size of a thermal-cutoff region. By doing so, more current is
preserved in a quench and thus recovery is faster and the magnetic
field transient is smaller. Therefore, a multiple-barrier design
brings the same beneficial effects discussed previously to such
coils/magnets.
[0155] A quench in a non-graded NI coil can lead to a rapid
decrease, and thus a fast transient in magnetic field. As mentioned
in Issue 4, experimental and computational results show that a fast
magnetic field transient in one of the many coils of a multi-coil
NI magnet with large inductance can inductively induce quenches in
other coils. Such inductive quench propagation, though beneficial
to insulated multi-coil magnets, is undesirable in a multi-coil
magnet composed of self-protecting NI coils, since instead of
recharging just the initially quenched coil during a recovery, all
quenched coils must recover, extending the recovery time
significantly. Using the GRNI approach to preserve a fraction of
magnetic field during quench-recovery, the degree (rate, magnitude
and duration) of magnetic field transient is reduced, lowering the
likelihood of inductive quench propagation. FIG. 29 compares the
rate of change (dB/dt) in the generated magnetic fields
corresponding to the "Heater1, 8-turn", "Heater2, 8-turn" and
"Heater1, no barrier" cases shown in FIG. 22A. As compared to the
degree of transient in the "Heater1, no-barrier" case, the
transient in the "Heater1, 8-turn" case is relatively much smaller
and the transient in the "Heater2, 8-turn" case is slightly smaller
in magnitude but much shorter in duration. A transient with either
a smaller magnitude or a shorter duration reduces the inductive
coupling effects on other coils of a multi-coil magnet in the event
of a quench. Therefore, the GRNI method, when applied to a
multi-coil NI magnet composed of self-protecting NI coils, not only
increases stability but also accelerates recovery, as only the
initially quenched coil needs to recover.
[0156] The beneficial effects of the proposed approach in
accelerating recovery in NI coils/magnets and reducing the
likelihood of quenching in multi-coil NI magnets increases with
coil inductance. As predicted by equation (4), a coil with larger
inductance requires longer time to recharge; so the more current
preserved during a quench, the less current that needs to be
re-redistributed and thus the faster the recovery in such coil. In
a multi-coil magnet, the larger the inductance, the stronger the
inductive coupling effects between coils and therefore inductive
quench propagation becomes more likely. FIG. 30 compares the
effects of the 8-turn design on two identical 39.5-turn NI coils
used previously; the only difference is in their inductances. The
inductance is 4 mH (as before) for the coil that generates the
results shown in FIGS. 30A and 30B, and 0.4 mH for FIGS. 30C and
30D. The actual, calculated inductance for the 39.5-turn NI coil is
0.4 mH; the 4 mH inductance shown in Table 1 is numerically
increased 10.times. to mimic the inductance effects of a
(.about.3.times.) larger coil. For the 4 mH coil, when the 8-turn
design is added to the coil, the quench-recovery process is
accelerated by 23% when compared to the non-graded coil. In
contrast, the improvement is less than 6% in the 0.4 mH coil when
the same grading is added. Moreover, .about.60% of the magnetic
field is preserved in the 4 mH coil, whereas only .about.45% in the
0.4 mH coil. In both coils, the peak temperatures corresponding to
the same grading/non-grading cases are about the same. These
results show that the proposed GRNI method is more effective in
reducing the recovery time and increasing the stability in
multi-coil magnets with larger inductance.
[0157] Any form of increasing the turn-to-turn resistance
accelerates the ramp rate. From equation (4), the larger the
characteristic resistance R.sub.r (i.e., total turn-to-turn
resistance), the greater the improvement in ramp time. Therefore,
another benefit of the proposed GRNI method is the mitigation of
Issue 1, i.e., the ramp rate is improved. In fact, all results
regarding recovery time in the graded coils are affected by
increased R.sub.r (due to the grading), albeit the effect is very
small.
[0158] Implementation of the general GRNI concept in a practical
way requires the ability to control the turn-to-turn resistance,
which depends on a number of parameters, including the
resistivities and thicknesses of all materials present, the surface
roughness, interface quality and pressure. A number of approaches
can be used for achieving resistivity grading, including sputtering
of metallic claddings and printing of conductive inks with varying
properties directly to the conductor surface or the surface of a
co-wound strip, or co-winding various sectional metallic/resistive
strips with different resistivities and/or thicknesses. Sputtering
is likely effective for short samples. Co-winding adds some
complexity to the magnet winding process and is limited to
materials available in thin strip. It also poses mechanical
integrity challenge at the thickness transitions. Conductive ink
printing via inkjet or 3D printing is expected to be the most
accurate and feasible method, and allows control of the resistance
and patterning by varying the material deposited and/or its
thickness continuously in real-time and is well-suited for
long-length reel-to-reel grading fabrication. Conductive ink
printing is a fabrication technique based on well-established
conductive metallic ink printing technologies for printed
electronics. The electrical resistivity of a conductive ink can be
customized, ranging from an electrical conductor to resistor or
insulator. The thermal resistivity of conductive inks, though not
well-documented, should in general increase with electrical
resistivity.
[0159] FIG. 31 illustrates arc lengths (or in arc angles) (.phi.1,
(.phi.2, and (.phi.3 as design parameters of a modified NI coil
design 3100, in accordance with various embodiments of the present
disclosure. Coil 3100 includes electrical conductive segments 3104
and thermal resistive segments 3102, with (.phi.1 representing the
arc length (or in arc angle) of the electrical conductive segments
3104, and (.phi.2 and (.phi.3 representing the minimum arc lengths
(or in arc angles) of the overlapped thermal resistive segments
3102 of two adjacent barriers, which extends from one end of an
electrical conductive segment 3104 located on one of the barriers
to the nearest end of the nearest electrical conductive segment
3102 located on the other barrier.
[0160] Any material with a thermal conductivity smaller than 0.5
W/(mK) at room temperature (300 K) is considered a "thermal
resistive" or "thermally resistive" material (resistivity being the
reciprocal of conductivity). Any material with an electrical
conductivity larger than 5.times.10.sup.5 S/m at room temperature
(300 K) is considered an "electrical conductive" or "electrically
conductive" material. An electrical conductive segment/portion of a
barrier can be composed of electrical conductive material or
represent a gap in the barrier that permits direct turn-wise
current sharing.
[0161] The arc length (or in arc angle) (.phi.1 is selected to be
long enough to let enough current to flow across the barrier (e.g.,
from the normal turns to the neighboring superconducting turns
during a formation of a thermal cutoff). The electrical conductive
segment 3104 is in general also thermal conductive, so it also
allows heat to pass through the barrier turn, which helps to
dissipate heat to keep a lower peak temperature but also increases
the thermal-cutoff size in radial direction since heat now passes
through the barrier turn. The arc lengths (or in arc angles)
(.phi.2 and (.phi.3 are selected to be long enough to minimize heat
from leaking from one electrical conductive segment 3104 (which is
in general also thermal conductive) on one barrier to the nearest
electrical conductive segment 3104 on the other barrier.
[0162] In some embodiments, the arc lengths (or arc angles) (.phi.1
and (.phi.2 can be the same as shown, for example, in FIGS. 21 and
26 which show designs with 45-degree arc lengths. The arc lengths
(or in arc angles) (.phi.1, (.phi.2 and/or (.phi.3 can be different
for different barriers as shown, for example, in FIG. 33.
[0163] In some embodiments, an ideal electrical conductive segment
is also thermally resistive, and an ideal thermal resistive segment
is also electrically conductive. But in general, a material with
high thermal resistivity also has high electrical resistivity
(i.e., low electrical conductivity), and vice versa.
[0164] FIG. 32 illustrates turn numbers as design parameters of a
modified NI coil design 3200, in accordance with various
embodiments of the present disclosure. Coil 3200 includes an
innermost turn 3202, an outermost turn 3204, an innermost barrier
3206, an outermost barrier 3208, and a middle barrier 3210. Coil
3200 can be configured by parameters n1-n6. Each of barriers
3206-3210 is considered to be adjacent to one or two of the other
barriers 3206-3210. For example, middle barrier 3210 is adjacent to
two different barriers: innermost barrier 3206 and outermost
barrier 3208, innermost barrier 3206 is adjacent to middle barrier
3210 (and the innermost turn 3202), and outermost barrier 3208 is
adjacent to middle barrier 3210 (and the outermost turn 3204).
Other embodiments can include coil designs having more barriers
than the three barriers 3206-3210 of coil 3200, as shown, for
example, by the four-barrier coil design of FIG. 26, and each of
the barriers in such a coil design will also be considered to be
adjacent to one or two of the other barriers of the coil
design.
[0165] Parameter n1 represents turns between two barriers (e.g.,
3206 and 3210) and affects the peak temperature--the less turns,
the smaller is the heat mass to dissipate the built-up heat
(between the two barriers) and thus the higher the peak
temperature. In general, the more n1 turns the better in the aspect
of limiting peak temperature. In some embodiments, at very low
cryogenic temperature, e.g., at 4.2 K, as simulations shown, there
is a safe turn tolerance or limit that if not met, a large
(probably recoverable) quench may be accelerated. So, there is a
balance or tradeoff for the n1 turn number.
[0166] Parameter n2 is the number of turns from the outermost
barrier 3208 to the outermost turn 3204 of the coil. Parameter n3
is the number of turns from the innermost barrier 3206 to the
innermost turn 3202 of the coil. Parameters n4 and n5 are the
number of turns from the nearest thermal resistive segment across
an electrical conducting segment to the outermost turn 3204 (n4) or
innermost turn 3202 (n5). Parameter n6 is the number of turns from
the two nearest thermal resistive segments across an electrical
conducting segment of a middle barrier such as 3210.
[0167] Parameters n2 and n3 can define the maximum ratio or
fraction of current preserved, as n2 (or n3) divided by the total
turn number of the coil 3200, when a thermal-cutoff occurs near the
electrical conducting segment of a middle barrier such as 3210,
e.g., in the region of n6, in an ideal case (i.e., when no heat
leaks across the thermal resistive segments to lower the critical
currents of the superconducting current-carrying turns in the
regions outside of the region of n6).
[0168] Parameters n4 and n5 can define the maximum ratio or
fraction of current preserved, as n4 (or n5) divided by the total
turn number of the coil 3200, when a thermal-cutoff occurs in the
region of n5 for the n4 parameter, or in the region of n4 for the
n5 parameter, in an ideal case (i.e., when no heat leaks across the
thermal resistive segment to lower the critical currents of the
superconducting current-carrying turns).
[0169] In some very low cryogenic temperature cases, e.g., at 4.2
K, as simulations show, there is a safe turn tolerance or limit
that must be met. If one of n1 to n6 surpasses this safe limit, a
large, accelerated (probably recoverable) quench may occur. So,
there is a balance or tradeoff for the turn numbers here.
[0170] FIG. 33, illustrates a modified NI coil 3300 having arc
lengths and numbers of the conductive 3304 and resistive 3302
segments varied from barrier to barrier, in accordance with various
embodiments of the present disclosure. The arc lengths and numbers
of the conductive 3304 and resistive 3302 segments can be varied
from barrier to barrier, to match the characteristic of a
superconducting coil/magnet. For example, suppose the coil 3300 has
weaker cooling on the innermost surface 3306, the electrical
conductive (and in general also thermal conductive) segments 3304
on the innermost barrier (composed of segments 3302 and 3304
closest to the innermost surface 3306) are longer to let more heat
to dissipate to the neighboring turns to compensate the weaker
cooling on the innermost surface 3306 of the coil 3300.
[0171] FIG. 34 illustrates a modified NI coil 3400 having a
single-turn barrier 3402, in accordance with various embodiments of
the present disclosure. The single-turn barrier 3402 is composed of
an ideal material that has very high thermal resistivity but very
low electrical resistivity. Heat will be constrained to one side of
barrier 3402 to reduce the size of a thermal-cutoff but current can
still flow to the other side of barrier 3402 to maintain
self-protection capability of the modified NI coil 3400.
[0172] GRNI designs disclosed herein can be applied to magnets with
a winding conductor composed of non-insulated (e.g., in bare form
or in bare, untreated form) superconductor material. For example,
the GRNI designs are disclosed herein as applied to HTS NI coil
magnets with a winding conductor composed of non-insulated (e.g.,
in bare, untreated form) REBCO superconductor tape. The designs can
also be applied to any HTS NI coil magnet wound with other
non-insulated HTS superconductor tapes, such as, for example,
yttrium barium copper oxide (YBCO) superconductor tape and bismuth
strontium calcium copper oxide (BSCCO) (Bi-2223) multi-filamentary
superconductor tape.
[0173] GRNI designs disclosed herein can be applied to HTS NI coil
magnets fabricated in any shape as long as the winding conductor
can be wound to fit that shape. For example, the GRNI designs are
disclosed herein as applied to HTS NI coil magnets in the form of
circular pancake coil. The designs can also be applied to any HTS
NI coil magnet fabricated in other forms, such as, for example, as
a saddle-shaped racetrack coil for dipole magnet, as a twisted
non-planar field coil used in the Wendelstein 7-X stellarator
fusion reactor, or as a toroidal field coil used in ITER's tokamak
fusion reactor.
[0174] Embodiments disclosed herein include a GRNI method designed
specifically to mitigate issues including: slow recovery speed and
potential quench propagation caused by fast magnetic field
transient. The proposed resistance-grading method installs
patterned turn-to-turn thermally (and electrically) resistive
layers on selected turn-to-turn contact locations in a
self-protecting NI coil to prevent the heat generated by a heat
disturbance from propagating to form a large thermal-cutoff region
while maintaining the turn-wise current sharing capability required
for self-protection. This approach prevents the azimuthal current,
and thus the magnetic field, from being reduced to nearly zero in a
recoverable quench, significantly accelerating the post-quench
recovery needed to bring the coil/magnet back to full
functionality. When applied to multi-coil NI magnets, GRNI methods
disclosed herein also reduce the likelihood of quenching, thus
increasing the magnet stability.
[0175] GRNI designs disclosed herein were studied via simulations
performed on a hybrid model that couples a circuit network model
with 2D or 3D thermal and 3D electromagnetic models. As discussed
herein, simulation results show the effects of design parameters
and inductance on quench behavior, field preservation and field
transient rate at 77 K and 4.2 K. Results also demonstrate that
GRNI designs can effectively reduce recovery time and magnetic
field drop and transient, and substantially enhance the thermal
stability of NI coils operated at 4.2 K. Through the proposed
method, self-protecting REBCO magnets with high operational
reliability and availability can be built.
[0176] It should be noted that ratios, concentrations, amounts, and
other numerical data may be expressed herein in a range format. It
is to be understood that such a range format is used for
convenience and brevity, and thus, should be interpreted in a
flexible manner to include not only the numerical values explicitly
recited as the limits of the range, but also to include all the
individual numerical values or sub-ranges encompassed within that
range as if each numerical value and sub-range is explicitly
recited. To illustrate, a concentration range of "about 0.1% to
about 5%" should be interpreted to include not only the explicitly
recited concentration of about 0.1 wt % to about 5 wt %, but also
include individual concentrations (e.g., 1%, 2%, 3%, and 4%) and
the sub-ranges (e.g., 0.5%, 1.1%, 2.2%, 3.3%, and 4.4%) within the
indicated range. The term "about" can include traditional rounding
according to significant figures of numerical values. In addition,
the phrase "about `x` to `y`" includes "about `x` to about
`y`".
[0177] It should be emphasized that the above-described embodiments
of the present disclosure are merely possible examples of
implementations set forth for a clear understanding of the
principles of the disclosure. Many variations and modifications may
be made to the above-described embodiment(s) without departing
substantially from the spirit and principles of the disclosure. All
such modifications and variations are intended to be included
herein within the scope of this disclosure.
* * * * *