MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF MECHANICAL ENGINEERING
DEPARTMENT OF NUCLEAR ENGINEERING
2.64J/22.68J Spring Term 2003
May 8, 2003
Lecture 10: Protection & HTS Magnets
Ø
Ø
Ø
Ø
Ø
Ø
Ø
Ø
Ø
Ø
Ø
Key magnet issues vs. Top; Areas of failure in superconducting magnets
Key problems: overheating; high voltage; overstressing; over pressure
Protection against overheating: self-protecting magnets; normal
zone propagation; active protection; detection of quench
High voltage — driven mode & persistent mode; overstressing
Over pressure—bath cooled & CICC
HTS Magnets & Issues
Bi-2223/Ag Data
YBCO composite
Jc ( B )data @ 4.2, 10, and 20 K of superconductors
1-D NZP of YBCO: Energy margin & NZP velocity (FSU/NHMFL)
Stability experiment & simulation of YBCO at 77 K (MIT)
1-D NZP of YBCO: Energy margin & NZP velocity (ORNL)
Y. Iwasa (05/08/03)
1
Key Magnet Issues vs Top
Cost or Difficulty
Protection
Conductor
Mechanical
Stability
Cryogenics
~100
0
LTS
Y. Iwasa (05/08/03)
Top [K]
HTS
2
Areas of Failure in Superconducting Magnets
In the order of decreasing reported incidents.
Ø Insulation
Ø Mechanical
Ø System performance
Ø Conductor
Ø External system
Ø Coolant
Y. Iwasa (05/08/03)
3
Key Quench-Induced Problems
Ø Overheating
Ø High voltage
Ø Overstressing
Ø Over pressure
Y. Iwasa (05/08/03)
4
Overheating
Energy Conversion
Bo2
2 o
9
1356 K
Bo
3
hcu (Tm t) - hcu (Top ) = 5.2 10 J/m
4.2 K
115 T
Ø For a uniform energy conversion over the entire winding, a
quench-induced Tmax will remains <100 K, an upper limit to
keep the differential thermal expansion stresses negligible.
Y. Iwasa (05/08/03)
5
Protection Against Overheating
1. Self-Protecting Magnets
Ø Normal zone propagation speed, Unzp , fast
enough to spread normal zone over most of
the winding volume from a localized “hot
spot” initially created. Specifically, a selfprotecting magnet must satisfy:
decay
a a1
~ 2
Unzp
Bo
2a1
2a2
Ø “Large” magnets are not self-protecting.
Ø [Unzp]HTS << [Unzp]LTS : HTS magnets not self-protecting.
Y. Iwasa (05/08/03)
6
An Example
Ø Bo=8 T
Bo
Ø Emg=106 J
0.6 m
Ø Winding volume=0.06 m3 (~2 ft3 )
Winding %
Absorbing Emg
Tf [K]
100
55
Well below 100 K
50
70
< 100 K
10
130
Barely acceptable
1
580
Unacceptable
Y. Iwasa (05/08/03)
Remarks
0.2 m
0.4 m
7
Normal Zone Propagation Velocity
Along Wire Axis--No Matrix
Cn
Tn
t
Cs
Ts
t
T
t
z
z
T z
z t
kn
Tn
z
ks
Ts
z
Ul
2
J
n
(Superconducting state)
T
z
Normal
Y. Iwasa (05/08/03)
(normal state)
(Ul : longitudinal velocity)
Superconducting
z
8
Cn U l
dTn
dz
d
dT
kn n
dz
dz
Cs U l
dTs
dz
d
dT
ks s
dz
dz
n
2
J2
2
Assume kn , ks , andd Tn / d z 0 nearz
d Tn
2
Cn U l
0
(z 0 )
J
n
dt
d 2Ts
ks
d z2
CsU l
Ts (z) = Ae
Y. Iwasa (05/08/03)
cz
dTs
dt
Top
0
z(
C
0
0)
C sU l
ks
9
At z
0 Ts (0) = Tc
Ts (z) = (Tc Top )e
At z
(C s Ul / ks )z
Top
0 kn (dTn /dz) = ks (dTs /dz)
kn n J 2
C nUl
Cs Ul (Tc Top )
Ul
Y. Iwasa (05/08/03)
kn
J
Cn Cs (Tc Top )
n
10
Cs
Cn
C0
J
C0
Ul
Ø Ul
Ø Ul
J
1/C0
kn
(Tc Top )
n
[Ul ]hts << [Ul]lts
In the presence of normal metal matrix:
Jm
Ul
Ccd
Y. Iwasa (05/08/03)
m
(Tcs
km
Top )
Note that Tcs Tt
11
With Cn( T ), Cs( T ), kn( T ):
Ul
n
J
C n (Tcs ) -
(Tcs )kn (Tcs )
1 d kn (T )
kn (Tcs ) d T Tcs
Tcs
Top
Cs (T )d T
Tcs
Top
Cs (T )d T
Note that Tcs Tt
Y. Iwasa (05/08/03)
12
1-D “Adiabatic” NZP—Experimental & Simulation Results
~10 cm
Slides 13-15: from R.H. Bellis and Y. Iwasa (Cryogenics, Vol. 34 1994)
Y. Iwasa (05/08/03)
13
Experimental
Nb3Sn Tape @ 12 K & 225 A
V4
Ul =50 cm/s
V2
V1
Temperature Simulation
V3
Simulation
150 ms
V4
100 ms
25 ms
Tc=16.5 K
Tcs=13.7 K
Y. Iwasa (05/08/03)
V1
V2
V3
14
Bi-2223/Ag Tape @ 14 K & 100 A
Experimental
[Ul ]hts =1 cm/s << [Ul ]lts
Simulation
Temperature Simulation
60 s
10 s
Y. Iwasa (05/08/03)
Tc=93 K
Tcs=44.4 K
15
2. Active Protection
“Detect-and-Dump”
Ø Widely used in large magnets.
Ø Dissipates most of the stored magnet energy into a
“dump resistor” connected across the magnet terminals.
Ø A “hot spot” heated only over a “brief” period of current decay.
Ø Leads to another criterion for operating current density.
Lmg
~
VD
RD
Y. Iwasa (05/08/03)
r(t)
16
Lmg
dI (t )
dt
[r (t ) + RD ]I (t ) = 0
For r(t ) << RD :
Lmg
dI (t )
dt
RD I (t ) = 0
With g k
gd
Acd C cd (T )
dT
dt
Ccd (T )
dT
m (T )
Tf
Ti
Z (Ti , T f )
(T ) 2
I (t )
Am
m
Am
[J op ]2m exp
Acd
Z (Ti , T f )
L
Am
[J op ]2m mg
2RD
Acd
Y. Iwasa (05/08/03)
Jm (t ) = [Jop ]m exp
RD t
Lmg
0:
gq
C cd (T )
dT
m (T )
RD t
Lmg
I (t ) = I op exp
Cc d(T )
dT
dt
m (T )
Am 2
J m (t )
Acd
2RD t
dt
Lmg
Am
[J op ]2m
Acd
0
exp
2Rd t
dt
Lm g
2
Am
2 2Em g I op
[J op ]m
Ac d
2VD I op
L
Am
[J op ]2m mg
Acd
2RD
E
Am
[J op ]2m m g
VD I op
Acd
17
Z (Ti , T f )
Tf
Ti
Ccd (T )
dT
m (T )
Ccd (T )
m
Ccd (T )
m (T )
(T )
Z(Ti , T f )
~constant
~1/T
~T
0
0
Y. Iwasa (05/08/03)
T
0
0
T
0
0 Ti
Tf
T
18
Z(T ) Functions:
1: Ag (99.99%)
2: Cu (RRR 200)
4: Cu (RRR 50)
5: Al (99.99%)
Z [1016 A2 s/ m4]
3: Cu (RRR 100)
T [K]
Y. Iwasa (05/08/03)
19
“Protection” Criterion
[J op ]m
Ac d VD Iop Z (Ti , T f )
Emg
Am
“Cryostable” Criterion
[J op ]cd
Y. Iwasa (05/08/03)
f p Pcd Am q fm
2
(
A
+
A
)
m
s
m
21
Detect-and Dump : Options to improve [Jop]m
1. Increase Iop
y Larger conductor; more expensive for given kA-m
y Larger current leads--greater heat input
y Larger ( I B ) force
y For a given power rating VI, higher I more expensive
2. Increase VD
y Increased danger of voltage breakdown, particularly > 800 V
in helium environment
3. Increase Z( Tf )
y Better to keep Tf below ~100 K-150 K
y Cu better than Al
4. Reduce Emg
y Subdivision—common practice with HEP & Fusion magnets
Y. Iwasa (05/08/03)
22
Detection of Non-Recovering Quench
dI(t )
V1(t ) L1
r(t )I(t )
dt
Vout (t ) =V2(t ) -V1 (t )
R2 L1
V2 (t )
Vout (t ) = -
R1 L2
I( t )
R2
R1
R2
r (t )I(t )
L1
V1( t )
r( t )
~
o
I( t )
V2( t )
Y. Iwasa (05/08/03)
dI(t )
L2
dt
Vout( t )
o
R1
R2
L2
23
High Voltage
Ø Driven mode magnet, i.e., operated with its power supply
generally connected, except during a dump.
• High voltage, i.e., VD , appears across the magnet terminals.
Ø Persistent mode magnet, i.e., operated with its power supply
removed, except when the magnet is being charged.
• Terminal voltage is zero; high internal voltage may be induced.
Y. Iwasa (05/08/03)
24
Persistent Mode Operation
Operation Steps
1. With persistent switch (PS) resistive (heater on), energize the magnet.
2. Turn off the heater; PS becomes superconducting; slowly bring the
supply current back to zero.
3. Disconnect the current leads from the magnet terminals.
4. Magnet now operates in “persistent mode.”
Disconnectable joint
>>
Persistent Switch
Lmg
~
Heater
r(t)
>>
Y. Iwasa (05/08/03)
25
Persistent Mode Operation (Continued)
r ( t ) represents:
1. quench-induced variable resistance; may lead to a high internal
voltage OR
2. “small” constant resistance by imperfect splices; causes a “slow”
field decay (time constant=Lmg / r ) in NMR & MRI magnets:
B(t )
B0 e
Y. Iwasa (05/08/03)
( r / mgL)t
B0 1
r
t
Lm g
(for Lm g/ r
1 hr)
26
Internal Voltage In Persistent Mode Magnet
Ø No internal voltage in a uniformly (100%) resistive magnet.
Ø Internal voltage in a partially resistive magnet.
Ø Large voltages can occur when a resistive zone
confined to a small section.
VL
~
r(t )
100%
VR
100%
No internal voltage
Y. Iwasa (05/08/03)
27
Internal Voltage in Persistent Mode
Extent of r ( t )
10%
50%
~
Top 10%
10%
50%
10%
Middle 10%
Top 50%
Bottom 50%
Bottom 10%
Y. Iwasa (05/08/03)
28
Internal Voltage In Driven Mode Magnet
Ø For RD >> r ( t ), internal voltage is essentially due to the
inductive voltage. The maximum inductive occurs at t =0
and it is equal VD .
VL VD (RD >> r )
Lmg
~
VD
RD
r(t)
Effect of r ( t ) is neglected.
Y. Iwasa (05/08/03)
29
Overstressing
Ø Overstressing generally occurs in a multi-coil system.
• A quench in one coil increases the current in the
rest of the coils—this is good for PROTECTION,
because this increased current accelerates spreading
of normal zones in the rest of the coils by inducing
quenches in these coils.
• This increased current may also cause overstressing
in these coils.
Y. Iwasa (05/08/03)
30
Overstressing (& Protection)
Example: 2-Coil System
A quench in Coil 1 induces an extra current in Coil 2.
1.
2.
Io
Helps spreading out normal zone
faster and over a large volume.
May overstress Coil 2
I1
Io
L1
R1
I1
I(t)
I1
M
I2
R2
I2
Io
t
Y. Iwasa (05/08/03)
I1
~
Overstress limit
r (t )
Io
L2
I2
I1
I2
31
Protection Circuit for an NMR Magnet
+
–
Y. Iwasa (05/08/03)
Within Cryostat
32
Over Pressure
Ø In every superconducting magnet system, driven, persistent, in
which coolant is cryogen (helium, nitrogen), a quench generally
causes generation of vapor within the cryostat, raising the
cryostat pressure above a safe limit (no greater than ~ 1/3 atm).
• Cryostat must be equipped with a relief valve or a “burst”
disk to permits a rapid release of the vapor from the cryostat.
Ø For CICC there is another problem of having to estimate the
internal pressure generated in CICC.
• Conduit thickness and vent line diameter must be sized
according to the maximum quench-induced internal pressure.
Y. Iwasa (05/08/03)
33
HTS Magnets & Issues
˚Hc2 [ T ]
150
HTS: YBCO; BSCCO; MgB2
LTS: Nb-Ti; Nb3Sn
YBCO
BSCCO 2223
100
Magnet Grade Conductors:
NbTi; Nb3Sn; BSCCO 2223
BSCCO 2212
50
Nb3Sn
0
MgB2
NbTi
0
Y. Iwasa (05/08/03)
20
40
60
80
100
T [K]
34
HTS
BSCCO 2223 currently available as “magnet grade
conductor.”
Powder in Ag tube
Ø BSCCO 2212 being developed but not easily available.
Ø YBCO, compared with BSCCO, regarded more promising for
electric power devices.
Ø MgB2 also regarded promising, because of its low cost.
Y. Iwasa (05/08/03)
35
Bi-2223 High Current Density Wire: Non-Reinforced
Thickness (avg): 0.21 (+/-0.02mm)
Width (avg):
4.1 (+/- 0.2mm)
Min. Critical Stress: 75 MPa
Min. Critical Strain: 0.15%
Min. Bend Dia:
100 mm
Variable Specifications:
Min. Ic:
Piece Length:
115 A—135 A
100 m —200 m
Strain
Ic/Ic(o)
0.002
0.8
0.0016
0.6
0.0012
0.4
0.0008
0.2
0.0004
0
Strain
Ic/Ic(o)
1
0
0
20
40
60
80
100
Stress at 77K (MPa)
Slides 35-39: Based on American Superconductor Corp. Data Sheets
Y. Iwasa (05/08/03)
36
Bi-2223 High Strength Reinforced Tape
Stainless Steel Strips
Thickness (avg): 0.31 (+/-0.02mm)
Width (avg):
4.1 (+/- 0.2mm)
Min. Critical Stress: 265 MPa
Min. Critical Strain: 0.4%
Min. Bend Dia:
70 mm
Variable Specifications:
Min. Ic:
115 A—135 A
Piece Length: 100 m —300 m
Ic/Ic(o)
Strain
1
0.7
0.6
0.8
0.6
0.4
0.3
0.4
Strain (%)
Ic/Ic(o)
0.5
0.2
0.2
0.1
0
0
50
100
150
200
250
300
0
350
Stress at 77K (MPa)
Y. Iwasa (05/08/03)
37
Scaling Ratio to 77K (self-field) in // External Field
6
20
Scaling Ratio, Ic(T,B)/Ic(77K,0)
5
35
50
4
3
2
1
0
0
1
2
3
4
5
6
7
8
Parallel Magnetic Field (Tesla)
Y. Iwasa (05/08/03)
38
Scaling Ratio to 77K (self-field) in
External Field
6
20K
35K
50K
Scaling Ratio, Ic(T,B)/Ic(77K,0)
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
Perpendicular Magnetic Field (Tesla)
Y. Iwasa (05/08/03)
39
Scaling Ratio, 77K to 4.2K
6.00
Bpar, 4.2K
Bperp, 4.2K
5.00
4.00
3.00
2.00
1.00
0.00
0
2
4
6
8
10
12
MagneticField,Tesla
Y. Iwasa (05/08/03)
40
1-D NZP in YBCO Composite—Energy Margin & NZP Velocity
Keithley
2001 DMM*
Keithley
2001 DMM*
Keithley
2001 DMM*
V3
V2
V1
HTS sample
Keithley
2000 DMM
Vcernox1
Keithley
2000 DMM
Vcernox2
Keithley
2000 DMM
Vcernox3
NiCr heater
HP 6286A
DC-P/S
Vtot
Keithley
2000 DMM*
HP 8112A
pulse generator
500 A / 100 mV
V(I)
HP 6681A
DC-P/S
Keithley
2000 DMM
Keithley
2001 DMM*
GPIB
*set on buffer read for increased speed/resolution
Slides 45-51: Based on Justin Schwartz ( DOE Meeting July 2002)
Y. Iwasa (05/08/03)
45
Bi2223 tape: Recovery
0.008
Voltage (V)
0.006
V1
0.004
V2
0.002
V3
0.000
6
7
8
9
10
11
12
13
14
15
Time (s)
Temperature (K)
110
100
C1
C2
90
80
0
Y. Iwasa (05/08/03)
10
20
30
Time (s)
40
50
46
Bi-2223 High Current Density Wire: Non-Reinforced
Thickness (avg): 0.21 (+/-0.02mm)
Width (avg):
4.1 (+/- 0.2mm)
Min. Critical Stress: 75 MPa
Min. Critical Strain: 0.15%
Min. Bend Dia:
100 mm
Variable Specifications:
Min. Ic:
Piece Length:
115 A—135 A
100 m —200 m
Strain
Ic/Ic(o)
0.002
0.8
0.0016
0.6
0.0012
0.4
0.0008
0.2
0.0004
0
Strain
Ic/Ic(o)
1
0
0
20
40
60
80
100
Stress at 77K (MPa)
Slides 36-40: Based on American Superconductor Corp. Data Sheets
Y. Iwasa (05/08/03)
36
Iop=19 A; Ic=22 A
Temperature (K)
81.1
81.0
C1 (closest)
80.9
80.8
C2
80.7
C3 (closest)
80.6
0
10
20
30
40
50
Time (s)
Y. Iwasa (05/08/03)
48
NZP @ 19 A & 80.6 K
3.00E-02
2.50E-02
Voltage (V)
2.00E-02
1.50E-02
V1
1.00E-02
V2
V3
Primary
Heater pulse
5.00E-03
V4
100
0.00E+00
0
1
2
3
4
5
6
7
8
Time (s)
Y. Iwasa (05/08/03)
49
Minimum Quench Energy (mJ)
Energy Margin vs. I/Ic (Ic =22 A @ 80.6 K )
90
80
70
60
50
40
30
20
10
0
50
60
70
80
90
100
Fraction I/Ic (%)
Y. Iwasa (05/08/03)
50
Quench Propagation
Velocity (cm/s)
NZP Velocity vs. I/Ic
1.00
0.80
0.60
0.40
0.20
0.00
50
60
70
80
90
100
I/Ic (%)
Y. Iwasa (05/08/03)
51
Quench/Recovery
Experiment & Simulation
Bath cooling @77K
Forced-flow cooling @ 2-3 atm 80-81K
Y. Iwasa (05/08/03)
52
Forced Flow Experimental Setup
Pressure
Gauge
Pressure
Regulator
Needle Shut/Open Volume
Valve
Meter
Valve
Liquid
Nitrogen
Water
77K Hx
Sample
Holder
RT Hx
N2 Gas Tank
77K (Styrofoam Bath)
High-Pressure (3-atm) Section
Y. Iwasa (05/08/03)
53
Y. Iwasa (05/08/03)
54
New Forced-Flow Sample Holder
Y. Iwasa (05/08/03)
55
Y. Iwasa (05/08/03)
56
Y. Iwasa (05/08/03)
57
Y. Iwasa (05/08/03)
58
Y. Iwasa (05/08/03)
59
Sample 2: V( I ) Plot @77K [ Ic=105A ]
[ Source-Measured Ic > 100A ]
20
V [uV]
15
10
5
0
-5
0
20
40
60
80
100
120
I [A]
Y. Iwasa (05/08/03)
60
Sample 2: Forced-Flow (~81K; 5cm/s)
200
170A
I [A]
150
100
65A
71A
45A
50
24A
0
1000
71A
V [mV]
750
500
65A
250
24A
45A
0
0
1
2
3
4
5
6
Time [s]
Y. Iwasa (05/08/03)
61
Sample 2: Forced-Flow (~81K; 3cm/s)
200
I [A]
150
100
65A
45A
50
24A
0
1000
V [mV]
800
600
65A
400
45A
200
24A
0
0
1
2
3
4
5
6
Time [s]
Y. Iwasa (05/08/03)
62
Sample 2: Forced-Flow (@81K)
1000
800
V [mV]
170A/65A (3cm/s)
600
400
170A/65A (5cm/s)
200
0
0
1
2
3
4
5
Time [s]
Y. Iwasa (05/08/03)
63
Sample 2: Forced-Flow (5cm/s) & Bath
1000
V [mV]
800
170A/71A (5cm/s)
600
400
200
170A/75A (Bath)
0
0
1
2
3
4
5
6
Time [s]
Y. Iwasa (05/08/03)
64
Simulation
Q = h Tw =hAs(Tw-Tf)
h=kNu/D
Re ≥ 3000 , turbulent flow
Nu = 0.023 Re 0.8 Pr 0.3
Re < 3000 , laminar flow
Nu = 3.66 +
0.0668(D / L )Re Pr
2/3
1 + 0.04[(D / L )Re Pr ]
Nitrogen Properties at 2 bar
( From Handbook of Cryogenic Engineering, I. G. WeisendΙΙ, 1998)
T(K)
ρ(kg/m3)
Cp(j/kg K)
µ(Pa s)
κ(W/m K)
83.0
779.9
2079
0.1228°10-3
0.1247
84.0
8.628
1376
0.5791°10-5
0.849°10-2
Y. Iwasa (05/08/03)
65
Sample 2: Bath @77 K & Simulation
350
75A
300
60A
T [K]
250
40A
200
150
100
20A
50
0
0
1
2
3
4
5
Time [s]
1200
Measurement
Simulation
1000
65A
V [mV]
800
65A
600
45A
400
45A
200
24A
24A
0
Y. Iwasa (05/08/03)
66
Sample 2: Forced-Flow (3 cm/s) & Simulation
1200
Measurement
Simulation
1000
65A
V [mV]
800
65A
600
45A
400
45A
200
24A
24A
0
350
Entrance
Middle
Exit
65A
300
250
T [K]
45A
200
150
24A
100
50
0
0
1
2
3
4
5
Time [s]
Y. Iwasa (05/08/03)
67
Sample 2: Forced-Flow (5 cm/s) & Simulation
1200
1000
Measurement
Simulation
71A
65A
71A
V [mV]
800
600
400
45A
65A
200
45A
24A
24A
0
350
71A
300
Entrance
Middle
Exit
65A
T [K]
250
200
45A
150
24A
100
50
0
0
1
2
3
4
5
Time [s]
Y. Iwasa (05/08/03)
68
YBCO Samples in a Conduction Cooling Setup
• The sample was mounted
between a Kapton-tapeinsulated Cu-block and a G-10
block.
• It was affixed to the first- stage
cold-head of a Cryomech GB-37
cryocooler for conduction
cooling to about 40 K.
• A copper shield was added
around the G-10 block to ensure
a better uniform temperature of
the tape.
• A heater was affixed to the
copper base,and three PRT
Thermometers are placed on
the YBCO top surface.
Slides 69-78: Based on Winston Lue ( ASC2002, August 2002 )
Y. Iwasa (05/08/03)
69
Over-Current Pulse Induced NZP
180
150
150
V
75
V
]
K
[
65
T
]
120
A
[
I
85
V
V
55
45
90
V
0
4
8
12
t [s]
16
20
V
24
V
Ip = 117.4 A
60
V
1
2
3
4
100
5
6
7
8
50
U
[
m
V
]
30
0
0
4
8
12
16
0
24
20
t [s]
200
100
V
54
53
150
]
A
[
I
V
52
]
51
K
[ 50
V
T 49
V
48
47
V
46
45
0
3
6
9
t [s]
12
15
18
V
100
V
Ip = 116.5 A
50
0
V
0
3
6
9
12
15
1
2
80
3
4
5
6
7
8
60 U
[
40 m
V
]
20
0
18
• At each operating current, Iop an
initial over-current pulse was
applied. The transient pulse energy
was varied by changing the
magnitude, Ip or the duration of the
pulse.
• The figures show at T= 45 K, and at
an Iop of 33.7-A and 2-s over-current
pulse duration, an Ip of 117.4 A
caused a quench while 116.5 A did
not.
• Distinctive normal zone propagation
was observed when there was a
quench.
• The inserts show the temperatures
measured by a PRT at the center of
the sample.
t [s]
Y. Iwasa (05/08/03)
70
Stability Margins in the Range 45—80 K
g
r 120
a
m
100
]
3y
t 80
i
l
i 60
b
a
40
t
S
20
0
45
Measured
50
55
60
65
70
75
80
85
T [K]
Tcs = Top + (Tc − Top )(1 − I t I cop )
Y. Iwasa (05/08/03)
• To measure the stability margin, the
operating current was set near the lowest
zone Ic at a particular temperature.
• At the highest recovery pulse current, the
V-I product integrated over the initial pulse
divided by the zone volume is used to
estimate the stability margin.
• The measured stability margins ranged
from 16 to 120 J/cm3 as temperature lowers
from 80 to 45 K.
• Comparison with the specific heat integrals
indicated better fit to Tc than to Tcs for the
HTS tapes.
• The higher margins measured at lower
temperatures are attributed to the higher
conduction cooling.
71
Minimum Propagation Currents
200
200
V1
70
V2
]
K65
[
60
T
150
]
A
[
V3
V5
50
45
0
10
20
30
t [s]
40
50
V6
60
V7
6
14
22
100
•
]
V
m
[
U
V8
Iop = 27.4 A
50
150
V4
55
100
I
0
-2
75
•
50
30
38
46
54
0
62
t [s]
180
200
100
150
V2
90
]
K
[ 80
]
120
A
[
90
I
V3
60
V5
50
0
10
20
30
40
50
V6
60
V7
t [s]
100
]
V
m
[
U
V8
Iop = 28.4 A
60
150
V4
T70
40
•
V1
110
At 45.4 K, the sample was
subjected to an initial overcurrent pulse of 118 A for 2 s
while increasing the operating
propagation in 1 A steps.
The figures show recovery at
an operating current of 27.4 A
and propagation at 28.4 A - a
minimum propagation current.
The initial heat input to zone 4
was about 4.6 J or 350.4 J/cm3
- about 3 times the stability
margin.
50
30
0
-2
6
14
22
30
38
46
54
0
62
t [s]
Y. Iwasa (05/08/03)
72
Minimum Propagation Current vs. Temperature
30
•
measured
extrapolated
25
fitted average
]
A
[
p20
Im
•
•
15
10
45
50
55
60
65
70
75
80
Minimum propagation
currents were also determined
by extrapolating the velocity
versus current plots to zero
velocity.
Minimum propagation
currents of 12 to 27 A were
observed at 80.8 to 45.4 K.
The existence of minimum
propagation current is thought
to be the result of conduction
cooling.
85
T [K]
Y. Iwasa (05/08/03)
73
NZP Velocity vs. Iop
i
t 10
a
g
a 8
p
o
r 6
p
Ic2=68.8 A
Ic6=64.9 A
I =61.5 A
c7
v2
v6
v7
h 4
c
n
e 2
u
Q
0
20
i
t 30
a
g
25
a
p
o 20
r
p
15
h
c 10
n
e
u 5
Q
0
10
T=45.8 K
25
30
35
I op [A]
I =22.3-A
40
45
50
T=76.4-K
c2
I =20.4-A
c3
I =18.7-A
c7
v2-1
• NPZ always starts from the
middle (zone 4) of this sample.
• NZP velocities were found to be
increasing linearly with the
current.
• No more than 20 mm/s of NZP
velocity was measured when Iop
was set below Ic.
• The outer zones which received
better cooing resulted in lower
NZP velocity and higher
minimum propagation current.
v
3-2
v7-8
15
20
I
op
Y. Iwasa (05/08/03)
25
[A]
30
35
74
NZP Velocity vs. Temperature
i 20
t
a
g
a
15
p
o
r
p 10
2.5
I =30.3 A
op
2
I7
c
/p
Io
•
1.5
h
c
n 5
e
u
Q
0
45
•
v
•
2
v
1
55
0.5
80
7
50
Y. Iwasa (05/08/03)
60 65
T [K]
70
75
NZP velocities were
measured at five
different temperatures.
NZP velocities at an
operating current of 30.3
A were found at the
different temperatures
and plotted in the figure.
NZP velocity vs.
temperature shows a
similar dependence as
the ratio of operating to
critical current.
75
Modified Adiabatic Theories of NZP Velocity
1.
Constant material properties (Dresner)
I
vA
2.
Imp
k
A Cp
Tc Top
Variable material properties (Zhao and Iwasa)
I
vB
Im p
kn
A
Tc
Cs dT Cn
T po
3.
n
1 dkn
kn dT
Tc
Cs dT
Top
Constant material properties with a different transition temperature
(Bellis and Iwasa)
vC
I
Im
A
Y. Iwasa (05/08/03)
p
kn
C nCs Tt
Top
Tt
Tcs
1
Tc
2
Tcs
76
NZP velocities: Experiment & Modified Adiabatic Theories
i
t 20
a
g
a
p 15
o
r
p
10
h
c
n
e 5
u
Q
0
45
vA
•
Iop=30.3 A
vB
v
C
vm (Fig. 9)
•
•
50
55
Y. Iwasa (05/08/03)
60
65
T [K]
70
75
Inclusion of a minimum
propagation current is
necessary to achieve better
agreement with the data.
The agreement of the two
Iwasa’s theories indicated
the validity of a new
transition point for HTS,
Fair agreement is found
between the data the
modified theory of Iwasa.
80
77
ORNL Conclusion
• Stability margins ranged from 16 to 120 J/cm3 as temperature lowers
from 80 to 45 K. Comparison with the specific heat integrals indicated
better fit to Tc than to Tcs for the HTS tapes.
• Distinctive NZP in YBCO was observed at each of the measured
temperatures.
• Minimum propagation current as a function of temperature was
measured. Its existence is thought to be the result of conduction cooling.
• NZP velocities of no more than 20 mm/s were measured. Velocity vs.
temperature data show a similar dependence as the ratio of operating to
critical current and agrees with a modified adiabatic theory.
Y. Iwasa (05/08/03)
78