IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Invited presentation 4LE-01 given at ASC 2012.
Quench Analysis
Of High Field REBCO Coils
W. Denis Markiewicz1
Jan Jaroszynski1, Aixia Xu1, Dmytro Abraimov1, Hongyu Bai1,
Heath Hartley1, and Michael S. Walker2
1. National High Magnetic Field Laboratory
Florida State University
2. Intermagnetics General Corporation
Applied Superconductivity Conference
October 7-12, 2012
Portland, Oregon
[Annotations added after the presentation was delivered are in (small) blue font.]
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IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Quench Analysis
Of High Field REBCO Coils
Contents
YQUENCH Code
Ramping loss heating
Power and Temperature relations
Examples of unprotected quench
Example of heater protection
High copper current density
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IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
YQUENCH Analysis Code
YQUENCH analysis code for REBCO (YBCO) coils.
Finite difference thermal analysis,
analytic electrical and magnetic analysis.
Conductor properties and thermal conductivity
as function of field and temperature.
No explicit quench propagation velocity.
The name YQUENCH is in recognition of the early code QUENCH by Martin Wilson.
Pronounced why-quench, the name invokes with humor the serious question as to the
reasons that a YBCO coil might quench, given the high stability of the conductor.
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IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Conductor Properties
SP26
Jc
100
10
0
20
40
Ic scaled to 4mm tape, A
1200
16
14 T
13 T
12 T
11 T
10 T
9T
8T
7T
6T
5T
4T
3T
2T
1.5 T
1T
1000
20 K
30 K
40 K
1000
800
600
400
200
0
-30
60
0
30
60
90
120
150
180
, degree
T (K)
Ic perp(B,T)
Ic (T,θ)
Extensive characterization of temperature dependence of REBCO
critical current as input to quench analysis.
Analytic expressions, to be presented elsewhere, fit extensive data on the temperature
and field orientation dependence of the critical current.
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IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Thermal Conductivity
Analysis Kθ and Kz
Themal Conductivity of Winding Composite
in Angular, Axial, and Radial Direction
Measurement Kr
thermal conductivity (W/m-K)
1000
100
Kθ > Kz > Kr
10
Angular θ
Radial R
Axial Z
1
0
100
200
300
0
0
temperature (K)
Thermal conductivity of windings determined by
analysis and measurement.
H. Bai 2LPQ-01
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IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Quench Protection Coil
Pancake wound
Dry wind
QPC
REBCO coil
Steel co-wind reinforcement
Outer LTS coil
Un-insulated conductor
Insulated co-wind turn insulation
Field total
Field increment QPC
Inner winding diameter
Outer winding diameter
Winding length
Operating Current
Current density average
Current density copper
32 T
17 T
52 mm
212 mm
214 mm
180 A
200 A/mm2
440 A/mm2
The Quench Protection Coil is a representative high field REBCO coil chosen to
illustrate aspects of protection analysis.
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Quench Protection Coil
Conductor Copper Thickness Variations
Coil 1
Coil 2
Coil 3
Current (A)
180
180
180
Copper thickness (µm)
100
80
60
Copper current density (A/mm2)
440
549
732
Average current density (A/mm2)
200
222
250
Versions of the Quench Protection Coil have decreasing amounts of copper in the
conductor with corresponding increase in current density.
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Quench Initiation by Low Critical Current
In this presentation, the source of quench is limited to the case of
low critical current in a turn or arc segment of a turn.
Analysis of quench initiated by
significantly reduced critical current
in single and multiple turns of conductor,
and in a short arc segment of a turn.
Single Turn Ring
Multiple Turn Ring
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Single Turn Arc
IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Coil Critical Current
Critical current
Ic/Io
Operating current
The REBCO coil is assumed to contain conductor
with uniform critical current specification.
The variation of field and field angle gives a large
distribution of local critical current in the coil.
Disk or pancake number
Critical current/Operating current
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1
1.34
5
1.91
24
4.52
IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Ramping Loss Heating
With no surface cooling, the QPC quenches during ramp to field. The
temperature profile just prior to quench is shown.
No surface
cooling.
Quench during
ramping.
Ramping loss heating is calculated for REBCO coil under various
conditions of coil surface cooling.
A. V. Gavrilin 1LPS-05
J. Lu 2MPA-05
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Ramping Loss Heating
The efficiency of cooling on various surfaces depends on the directional
thermal conductivity. Radial thermal conductivity is least effective, and
cooling on the outer surface alone leaves a large temperature increase.
Cooling on
radial outer
surface only.
Significant
temperature
increase.
Ramping loss heating is calculated for REBCO coil under various
conditions of coil surface cooling.
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Ramping Loss Heating
Axial thermal conductivity is greater and with 50% heat transfer area to liquid
helium at the coil ends, the entire length of the coil is effectively cooled.
Cooling on axial
end surfaces
only.
Limited
temperature
increase.
Ramping loss heating is calculated for REBCO coil under various
conditions of coil surface cooling.
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Ramping Loss Heating
Given the effectiveness of surface cooling, the temperature increase of
ramping loss is ignored in the subsequent quench analysis.
Cooling on end
and outer
surfaces.
Lowest
temperature
increase.
Ramping loss heating is calculated for REBCO coil under various
conditions of coil surface cooling.
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Cooling Capacity of Windings
Temperature rise calculated from local steady state heat load.
20
18
18
18
16
16
16
14
14
14
12
10
Disk 2 - 1 Turn
Disk 2 - 4 Turn
8
Disk 2 - 40 Turns
12
10
Disk 5 - 1 Turn
Disk 5 - 4 Turns
8
Disk 5 - 40 Turns
Temperature (K)
20
Temperature (K)
Temperature (K)
Temperature versus Power for Disk 24
Temperature versus Power for Disk 5
Temperature versus Power for Disk 2
20
12
10
Disk 24 - 1 Turn
Disk 24 - 4 Turns
8
6
6
6
4
4
4
2
2
2
Disk 24 - 40 Turns
0
0.00E+00 1.00E+05 2.00E+05 3.00E+05 4.00E+05 5.00E+05
0
0.00E+00 1.00E+05 2.00E+05 3.00E+05 4.00E+05 5.00E+05
0
0.00E+00 1.00E+05 2.00E+05 3.00E+05 4.00E+05 5.00E+05
Power/Volume (W/m³)
Power/Volume (W/m³)
Power/Volume (W/m³)
Temperature depends on location and extent of source.
Coil ends are cooler, larger sources warmer
on per unit volume basis.
In order to select the initial conductions for a quench in
a realistic manner, the stability of turns was examined.
For a single turn, a reasonable correlation between a
heat balance stability condition and calculated thermal
runaway was observed.
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Cooling and Heating
Cooling of windings to helium
Power dissipation in conductor
Power versus Temperature
8.00E+05
7.00E+05
7.00E+05
6.00E+05
6.00E+05
single turn
5.00E+05
4.00E+05
Disk 5 - 1 Turn
Disk 5 - 40 Turns
3.00E+05
multiple turns
2.00E+05
Power/volume (w/m3)
Power/volume (w/m3)
Power versus Temperature
8.00E+05
5.00E+05
Ic/Io 0.928
Ic/Io 0.945
4.00E+05
Ic/Io 0.967
Ic/Io 1.0
3.00E+05
Ic/Io 1.04
2.00E+05
1.00E+05
decreasing critical
current
1.00E+05
0.00E+00
0.00E+00
4.2
6.2
8.2
Temperature (K)
10.2
Cooling power/volume for rings of
conductor at selected location
as function of temperature.
4.2
5.2
6.2
7.2
8.2
Temperature (K)
9.2
10.2
Power/volume in conductor at
constant operating current of 180 A,
as function of temperature
for decreasing critical current.
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Stability Criterion
unstable
stability limit
Power versus Temperature
8.00E+05
7.00E+05
6.00E+05
Power/volume (w/m3)
Stability is a balance
between heating and
cooling, as described by
Rakhmanov. As the local
critical current is reduced
further below the
operating current, the
increased conductor
heating results in thermal
runaway.
Ic/Io 0.928
5.00E+05
Ic/Io 0.945
Ic/Io 0.967
4.00E+05
Ic/Io 1.0
Ic/Io 1.04
3.00E+05
Disk 5 - 1 Turn
Disk 5 - 40 Turns
2.00E+05
1.00E+05
stable
0.00E+00
4.2
5.2
6.2
7.2
8.2
Temperature (K)
A. L. Rakhmanov et al, Cryogenics 40 (2000) 19-27
V. S. Vysotsky et al, IEEE Trans. Appl. Supercond. 11, 1824 (2001)
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9.2
10.2
IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Quench of Single Turn
Quench of the QPC is examined
for quench initiated by a single turn.
As the critical current of the single turn ring is reduced,
the power dissipation increases.
As thermal stability is exceeded, rapid thermal runaway
occurs and quench is initiated.
Single Turn Ring
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Quench Initiation of Single Turn
Temperature versus Time
10.0
temperature (K)
9.0
8.0
f Ic 0.935
7.0
f Ic 0.938
f Ic 0.942
6.0
5.0
4.0
0.0
1.0
2.0
3.0
4.0
5.0
time (sec )
Thermal runaway and quench onset
at the limit of stability for a single turn.
Stability critical current ~0.92 x operating current.
Stable temperature limit ~ 5.1 K.
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It is interesting to
observe that a faction of
an ampere of critical
current separates a
stable state from one
that experiences thermal
runaway in a matter of
seconds.
IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Evolution of quench in single turn without protection.
The temperature evolution of a single turn quench in disk 5 of QPC.
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Evolution of quench in single turn without protection.
Unprotected quench of single turn,
temperature continues to rise without significant
radial or axial quench propagation.
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Quench of Single Turn Arc
Quench of the QPC is examined
for quench initiated by a single turn arc
of 80 mm length.
As the critical current of the single turn ring is reduced,
the power dissipation increases.
As thermal stability is exceeded, rapid thermal runaway
occurs and quench is initiated.
Single Turn Arc
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Evolution of quench in single turn arc without protection.
Thermal runaway
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IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Evolution of quench in single turn arc without protection.
Unprotected quench of single turn arc,
temperature continues to rise without significant
radial or axial quench propagation,
but with full angular spread.
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Prior to Thermal Runaway
Prior to thermal runaway, the temperature increase is slow and the
constant spread reflects the lack of quench propagation.
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Thermal Runaway
Thermal runaway is characterized by a rapid increase in temperature.
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After Thermal Runaway
Following thermal runaway, increased temperature spreads by
thermal diffusion along the direction of the conductor.
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Classic Protection Schemes
SelfProtection
External
Discharge
Heaters
Shunts
Self-protection methods rely on quench propagation which is limited for REBCO
conductor. External discharge of low current coils is typically associated with high
voltage. Distributed heater protection is examined here. Shunts have been used
historically on tape magnets and may find application to REBCO coils.
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Distributed Heater Quench Protection
test coil heater spacer
distributed heater concept
Active protection system.
Heater elements embedded in spacers
between modules.
Design considerations:
number of heaters in coil,
heater element distribution in spacer,
heater operation power.
32 T magnet heater spacer
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Heater Performance Test
Quench time vs Heater Current
Coil Current 200
1.80
Module 5
Time to Quench [s]
1.60
Module 2
1.40
Module 3
1.20
1.00
0.80
0.60
0.40
0.20
0.00
10.0
12.0
14.0
16.0
18.0
Heater Current [A]
Test coil O.D. 124 mm, tested in 20 T background field,
heater tests at 200 A operating current over range of currents, power.
Data establishes value of heater rise time parameter in YQUENCH.
P.D. Noyes et al, IEEE Trans. Appl. Superconduct., 22, 3, 4704204 (2012)
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IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Discharge of Quench Protection Coil
with Heaters
Heater performance and design considerations
associated with the heaters are demonstrated
through the forced quench of the QPC by activation
of the heaters.
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Heater Design Aspects
Heater power requirements
are large n x 10 kW.
Motivation to limit heater distribution.
Heaters placed
heaters
every double pancake
or every other double pancake.
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IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Heater Design Aspects
Heater power requirements
are large n x 10 kW.
Motivation to limit heater distribution.
Heaters placed
heaters
50 % disk coverage
or 25 % disk coverage.
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Module Temperature Rise with Heaters
In this and subsequent
examples, it is seen that
the heaters are relatively
inefficient, quenching
only the ends of the coil.
This is largely the result
of large critical currents
in the center of the coil.
One strategy for
protection is reduced
critical currents where
the radial field is limited.
Every other
module (DP)
50 % coverage
coil axis
Heating is largely limited to disks adjacent
to the protection heaters.
The heaters primarily quench the end modules of the coil,
leaving central modules superconducting.
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IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Module Temperature Rise with Heaters
In this set of examples,
the coil is quenched by
the action of the heaters
and as a result, the
maximum temperature is
relatively low. In an
actual quench situation,
the temperature at the
origin of quench has
already increased
significantly by the time
the heaters are
activated.
Every
module (DP)
50 % coverage
coil axis
Heaters every double pancake eliminates axial gradients
at expense of heater power.
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Module Temperature Rise with Heaters
Heater disk coverage of 50 % and four fold symmetry
gives relatively uniform temperature in pancake.
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Module Temperature Rise with Heaters
Heater disk coverage of 25 % and two fold symmetry
reduces heater power requirements accordingly, but gives
larger temperature distribution in pancake.
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Module Temperature Rise with Heaters
The rather limited
quench temperature rise
is partly the result of the
limited stored energy in
the example coil, but it is
also the result of a
relatively rapid increase
in coil resistance and
consequent rapid
current decay, as will be
seen subsequently.
Every
module (DP)
25 % coverage
coil axis
Reduction of heater coverage reduces overall heater
power requirements at expense of reduced heater
efficiency at center of coil.
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Quench Protection Coil
with Arc Quench
and Protection Heaters
The action of the protection heaters is shown for a quench
in disk (pancake) 5 of the QPC initiated by low critical
current in an arc segment. The temperature rise in the
disk is given in a sequence of slides, showing the local
hotspot and more general temperature increase resulting
from the heaters. Then the effect on the critical current is
shown, starting with the local low critical current of the
segment that initiates the quench and showing the general
collapse of the critical current as a result of the
temperature increase caused by the heaters.
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Temperature of Quench Initiation Disk
Quench
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Temperature of Quench Initiation Disk
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Temperature of Quench Initiation Disk
Heater
activation.
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Temperature of Quench Initiation Disk
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Temperature of Quench Initiation Disk
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Temperature of Quench Initiation Disk
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Temperature of Quench Initiation Disk
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Temperature of Quench Initiation Disk
After this time, the
maximum
temperature begins
to decrease due to
thermal conductivity
out of the hotspot.
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Temperature of Quench Initiation Disk
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Temperature of Quench Initiation Disk
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Temperature of Quench Initiation Disk
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Critical Current of Quench Initiation Disk
Reduced critical
current initiates
quench.
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Critical Current of Quench Initiation Disk
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Critical Current of Quench Initiation Disk
Heater
activation.
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Critical Current of Quench Initiation Disk
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Critical Current of Quench Initiation Disk
Collapse of critical
current as a result
of heating.
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IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Protection of Short Arc Quench
Arc of 4 mm length found
to be fully stable
independent of critical
current.
Hotspot Temperature
for Quench of Arc - or Not
250
200
Temperature (K)
Analysis of short arc
quench gives uniform
hotspot temperature with
decreasing length, down
to 32 mm.
150
100
stable ?
50
0
0
Stability of intermediate
lengths uncertain.
20
40
60
Arc Length (mm)
80
100
Can a short length of conductor go normal, fail to be
detected and result in a high hotspot temperature?
Apparently not. In fact, very short lengths may be
fully stable.
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Protection of Short Arc Quench
Stable critical current distribution of normal 4 mm arc.
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Protection of Short Arc Quench
Stable temperature distribution of normal 4 mm arc.
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Quench Evolution
Magnet Current, Hotspot Temperature, Field Decay
200
180
160
140
Value
120
REBCO Current
100
Outer Current
80
Field
60
Temperature
40
20
0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Time (s)
Characteristicly,
the current decay of the REBCO coil is rapid
with distributed heater protection.
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Quench Evolution
Protection Heater Energy , Dissipated Magnetic Energy
and Sum Total
1.2E+05
Total dissipated
energy
1.0E+05
Energy (J)
8.0E+04
Dissipated stored energy
ENHTOT
6.0E+04
ENRTOT
4.0E+04
ENTHTOT
Heater energy
2.0E+04
0.0E+00
0
1
2
3
4
5
6
7
Time (s)
Heater power requirement for this example is 10 kW for 1 sec.
The heater energy dissipated in the coil is a small fraction of
the dissipated stored energy.
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Decreasing Copper Thickness
Takeoff Temperature vs. Conductor Copper Thickness
300
Temperature (K)
250
200
100 μm Cu
90 μm Cu
150
80 μm Cu
70 μm Cu
100
60 μm Cu
50
0
0.5
1.5
2.5
3.5
4.5
Relative Time (s)
Decreased conductor copper thickness results in
faster temperature rise and reduced time for quench protection,
as seen here for the initial temperature rise
at constant operating current.
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Hotspot Temperature versus
Quench Detection Voltage
350
300
Temperature (K)
The hotspot
temperature of the
example QPC is
recalculated for
various copper
thicknesses. As the
quench detection
sensitivity increases,
the hotspot
temperature is
reduced.
250
200
100 µ Cu
150
80 µ Cu
100
60 µ Cu
50
0
0.0
0.5
1.0
1.5
2.0
Quench Detection Voltage (V)
2.5
Copper thickness (µm)
100
80
60
Copper current density (A/mm2)
440
549
732
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IEEE/CSC & ESAS European Superconductivity News Forum (ESNF) No. 23 January 2013
Discussion and Summary
Quench in REBCO high field coil examined for case of locally
reduced critical current.
Quench current depends on size and location of reduced
critical current region.
Rate of temperature increase after thermal runaway
depends on the copper content of the conductor,
independent of the initial conditions of quench.
Significant quench velocity along conductor is observed after
thermal runaway.
Protection heater effectiveness depends on local critical
current.
Copper current density of 400 – 500 A/mm2 appears
feasible with heater protection.
[Annotations added after the presentation was delivered are in (small) blue font.]
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