Y. Iwasa (05/08/03) 1

MASSACHUSETTS INSTITUTE OF TECHNOLOGYDEPARTMENT OF MECHANICAL ENGINEERING

DEPARTMENT OF NUCLEAR ENGINEERING2.64J/22.68J Spring Term 2003

May 8, 2003Lecture 10: Protection & HTS Magnets

Key magnet issues vs. Top; Areas of failure in superconducting magnetsØ Key problems: overheating; high voltage; overstressing; over pressureØ Protection against overheating: self-protecting magnets; normal zone propagation; active protection; detection of quenchØ High voltage — driven mode & persistent mode; overstressingØ Over pressure—bath cooled & CICCØ HTS Magnets & IssuesØ Bi-2223/Ag DataØ YBCO compositeØ Jc ( B )data @ 4.2, 10, and 20 K of superconductorsØ 1-D NZP of YBCO: Energy margin & NZP velocity (FSU/NHMFL)Ø Stability experiment & simulation of YBCO at 77 K (MIT)Ø 1-D NZP of YBCO: Energy margin & NZP velocity (ORNL)

Y. Iwasa (05/08/03) 2

Key Magnet Issues vs Top

ProtectionConductor

Mechanical

StabilityCryogenics

0 ~100Top [K]

Cost or Difficulty

LTS HTS

Y. Iwasa (05/08/03) 3

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) 4

Key Quench-Induced Problems

Ø Overheating

Ø High voltage

Ø Overstressing

Ø Over pressure

Y. Iwasa (05/08/03) 5

Overheating

Ø For a uniform energy conversion over the entire winding, aquench-induced Tmax will remains <100 K, an upper limit tokeep the differential thermal expansion stresses negligible.

Bo2

2 o

hcu (Tm t) - hcu (Top ) = 5.2 109 J/m3

Bo 115 T

1356 K 4.2 K

Energy Conversion

Y. Iwasa (05/08/03) 6

Protection Against Overheating

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 self- protecting magnet must satisfy:

1. Self-Protecting MagnetsBo

2a1

2a2

decay ~

a2 a1

Unzp

Ø “Large” magnets are not self-protecting.

Ø [Unzp]HTS << [Unzp]LTS : HTS magnets not self-protecting.

Y. Iwasa (05/08/03) 7

An Example

Ø Bo=8 T

Ø Emg=106 J

Ø Winding volume=0.06 m3 (~2 ft3 )

Bo

0.6 m

0.4 m

0.2 m

Unacceptable5801

Barely acceptable13010

< 100 K7050

Well below 100 K55100

RemarksTf [K]Winding %

Absorbing Emg

Y. Iwasa (05/08/03) 8

Normal Zone Propagation Velocity

Along Wire Axis--No Matrix

Normal Superconducting z

Cn

Tn

t zkn

Tn

z nJ 2 (normal state)

Cs

Ts

t zks

Ts

z (Superconducting state)

T

t

T

z

z

tUl

T

z (Ul: longitudinal velocity)

Y. Iwasa (05/08/03) 9

CnUldTn

d z

d

d zkn

dTn

d znJ 2

CsUldTs

d zd

d zks

dTs

d z

Assume kn , ks , and d 2Tn / d z2 0 near z 0

CnUld Tn

d t nJ 2 0 (z 0 )

ks

d 2Ts

d z2CsU l

dTs

d t0 (z 0)

Ts (z) = Ae cz Top CC sUl

ks

Y. Iwasa (05/08/03) 10

At z 0 Ts (0) = Tc

Ts (z) = (Tc Top )e (Cs Ul / ks )z Top

At z 0 kn (dTn /dz) = ks (dTs /dz)

kn nJ 2

CnUl

CsUl (Tc Top )

Ul J nkn

CnCs (Tc Top )

Y. Iwasa (05/08/03) 11

Cs Cn C0

Ul

J

C0

n kn

(Tc Top )

Ø Ul JØ Ul 1/C0 [Ul ]hts << [Ul]lts

In the presence of normal metal matrix:

UlJm

Ccdm km

(Tcs Top )

Note that Tcs Tt

Y. Iwasa (05/08/03) 12

With Cn( T ), Cs( T ), kn( T ):

Note that Tcs Tt

Ul J n(Tcs )kn (Tcs )

Cn(Tcs ) -1

kn (Tcs )d kn (T )

d TTcs

Cs (T )d TTop

Tcs Cs (T )d TTop

Tcs

Y. Iwasa (05/08/03) 13

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) 14

Nb3Sn Tape @ 12 K & 225 A

Ul =50 cm/s

Experimental

SimulationTemperature Simulation

Tcs=13.7 K

Tc=16.5 K25 ms

150 ms

V1

V2

V3

V4

V1 V2 V3

V4

100 ms

Y. Iwasa (05/08/03) 15

Bi-2223/Ag Tape @ 14 K & 100 A Experimental

SimulationTemperature Simulation

10 s

60 s

[Ul ]hts =1 cm/s << [Ul ]lts

Tcs=44.4 K

Tc=93 K

Y. Iwasa (05/08/03) 16

2. Active Protection

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.

“Detect-and-Dump”

~RD

Lmg

r ( t )

VD

Y. Iwasa (05/08/03) 17

Lmg

dI (t )

d t[r (t ) + RD]I ( t ) = 0

For r( t ) << RD :

Lmg

dI (t )

d tRDI (t ) = 0 I (t ) = I op exp

RDt

Lmg

Jm (t ) = [Jop ]m expRD t

Lmg

With gk gd gq 0 :

AcdC cd (T )dT

d tm (T )

Am

I 2( t ) Cc d(T )dT

d tm (T )

Am

Acd

Jm2 (t )

Ccd (T )

m (T )dT

Am

Acd

[Jop ]m2 exp

2RDt

Lmg

dt

C cd (T )

m (T )T i

T f dT Z (Ti , Tf )Am

Acd

[Jop ]m2 exp

2Rd t

Lm g

dt0

Am

Acd

[Jop ]m2 Lmg

2RD

Z (Ti , Tf )Am

Acd

[Jop ]m2 Lmg

2RD

Am

Ac d

[Jop ]m2 2Em g I op

2

2VD I op

Am

Acd

[Jop ]m2 Em g

VDI op

Y. Iwasa (05/08/03) 18

0 0 00 0 0

Ccd (T ) m (T )

Ccd (T )

m (T )

T T T

Z(Ti , Tf )

Ti Tf

~T~1/T

~constant

Z (Ti , Tf )

Ccd (T )

m (T )Ti

T f

dT

Y. Iwasa (05/08/03) 19

T [K]

Z [1

016 A

2 s/

m4 ]

Z(T ) Functions:

1: Ag (99.99%)

2: Cu (RRR 200)

3: Cu (RRR 100)

4: Cu (RRR 50)

5: Al (99.99%)

Y. Iwasa (05/08/03) 21

[Jop ]m

Ac d

Am

VDIopZ (Ti , Tf )

Emg

[J op ]cd

f p Pcd Amq fm

m ( As + Am )2

“Protection” Criterion

“Cryostable” Criterion

Y. Iwasa (05/08/03) 22

Detect-and Dump : Options to improve [Jop]m

y Larger conductor; more expensive for given kA-my Larger current leads--greater heat inputy Larger ( I B ) forcey For a given power rating VI, higher I more expensive

1. Increase Iop

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) 23

Detection of Non-Recovering Quench

Vout( t )

V1( t )

V2( t )

ooR1

R2

L1

L2

r( t )

~

I( t )

I( t )

V1( t ) L1

dI( t )

dtr( t )I( t ) V2( t ) L2

dI( t )

dtVout ( t ) =V2( t ) -V1( t )

R2 L1 R1 L2 Vout ( t ) = -R2

R1 R2

r ( t )I(t )

Y. Iwasa (05/08/03) 24

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) 25

Persistent Mode Operation

~

Lmg

r ( t )

>

>

>

>

Heater

Persistent Switch

Disconnectable joint

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.”

Y. Iwasa (05/08/03) 26

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:

Persistent Mode Operation (Continued)

B( t ) B0e

(r / Lmg) tB0 1

r

Lm g

t (for Lm g/ r 1 hr)

Y. Iwasa (05/08/03) 27

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.

Internal Voltage In Persistent Mode Magnet

~ 100%r ( t )

100%VL VR

No internal voltage

Y. Iwasa (05/08/03) 28

Internal Voltage in Persistent Mode

~50%

50% 10%

10%

10%

Top 50%

Top 10%Extent of r ( t )

Bottom 50%

Middle 10%

Bottom 10%

Y. Iwasa (05/08/03) 29

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 .

Internal Voltage In Driven Mode Magnet

VL VD (RD >> r )

~RD

Lmg

r ( t )

VD

Effect of r ( t ) is neglected.

Y. Iwasa (05/08/03) 30

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.

Overstressing

Y. Iwasa (05/08/03) 31

Io I1 I2

Io I1

I1

I2

R1

R2

L1

L2

I1

I2

r (t )

~ M

Io

Io

A quench in Coil 1 induces an extra current in Coil 2.

I1 I2

Overstress limit

I ( t )

t

Overstressing (& Protection)

Example: 2-Coil System

1. Helps spreading out normal zonefaster and over a large volume.

2. May overstress Coil 2

Y. Iwasa (05/08/03) 32

+–

Within Cryostat

Protection Circuit for an NMR Magnet

Y. Iwasa (05/08/03) 33

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) 34

150YBCO

BSCCO 2223

Nb3Sn

MgB2

BSCCO 2212

NbTi

0 20 40 60 80 1000

50

100

T [K]

˚Hc2 [ T ]

HTS Magnets & Issues

HTS: YBCO; BSCCO; MgB2

LTS: Nb-Ti; Nb3Sn

Magnet Grade Conductors:NbTi; Nb3Sn; BSCCO 2223

Y. Iwasa (05/08/03) 35

BSCCO 2223 currently available as “magnet gradeconductor.”

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.

HTS

Y. Iwasa (05/08/03) 36

Bi-2223 High Current Density Wire: Non-Reinforced

Thickness (avg): 0.21 (+/-0.02mm)Width (avg): 4.1 (+/- 0.2mm)Min. Critical Stress: 75 MPaMin. Critical Strain: 0.15%Min. Bend Dia: 100 mm

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100

Stress at 77K (MPa)

Ic/I

c(o)

0

0.0004

0.0008

0.0012

0.0016

0.002

Str

ain

Ic/Ic(o) Strain

Variable Specifications:Min. Ic: 115 A—135 APiece Length: 100 m —200 m

Slides 35-39: Based on American Superconductor Corp. Data Sheets

Y. Iwasa (05/08/03) 37

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250 300 350

Stress at 77K (MPa)

Ic/Ic(o

)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Str

ain

(%

)

Ic/Ic(o) Strain

Bi-2223 High Strength Reinforced Tape

Thickness (avg): 0.31 (+/-0.02mm)Width (avg): 4.1 (+/- 0.2mm)Min. Critical Stress: 265 MPaMin. Critical Strain: 0.4%Min. Bend Dia: 70 mm

Variable Specifications:Min. Ic: 115 A—135 APiece Length: 100 m —300 m

Stainless Steel Strips

Y. Iwasa (05/08/03) 38

Scaling Ratio to 77K (self-field) in // External Field

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8

Parallel Magnetic Field (Tesla)

Sca

ling

Rat

io, I

c(T

,B)/

Ic(7

7K,0

)

20

35

50

Y. Iwasa (05/08/03) 39

Scaling Ratio to 77K (self-field) in External Field

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8

Perpendicular Magnetic Field (Tesla)

Sca

ling

Rat

io, I

c(T

,B)/

Ic(7

7K,0

)

20K

35K50K

Y. Iwasa (05/08/03) 40

Scaling Ratio, 77K to 4.2K

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0 2 4 6 8 10 12

Magnetic Field, Tesla

Bpar, 4.2K

Bperp, 4.2K

Y. Iwasa (05/08/03) 45

1-D NZP in YBCO Composite—Energy Margin & NZP Velocity

Keithley2001 DMM*

Keithley2001 DMM*

Keithley2001 DMM*

Keithley2000 DMM

Keithley2000 DMM

Keithley2000 DMM

Keithley2000 DMM*

HP 6286ADC-P/S

HP 8112Apulse generator

HP 6681ADC-P/S

Keithley2000 DMM

Keithley2001 DMM*

500 A / 100 mV

V3 V2 V1 Vcernox1 Vcernox2

Vtot

V(I)

GPIB

HTS sample NiCr heater

Vcernox3

*set on buffer read for increased speed/resolution

Slides 45-51: Based on Justin Schwartz ( DOE Meeting July 2002)

Y. Iwasa (05/08/03) 46

Bi2223 tape: Recovery

0.000

0.002

0.004

0.006

0.008

6 7 8 9 10 11 12 13 14 15

Time (s)

Vo

ltag

e (V

) V1

80

90

100

110

0 10 20 30 40 50

Time (s)

Tem

per

atu

re (

K)

V3

V2

C1

C2

Y. Iwasa (05/08/03) 36

Bi-2223 High Current Density Wire: Non-Reinforced

Thickness (avg): 0.21 (+/-0.02mm)Width (avg): 4.1 (+/- 0.2mm)Min. Critical Stress: 75 MPaMin. Critical Strain: 0.15%Min. Bend Dia: 100 mm

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100

Stress at 77K (MPa)

Ic/I

c(o)

0

0.0004

0.0008

0.0012

0.0016

0.002

Str

ain

Ic/Ic(o) Strain

Variable Specifications:Min. Ic: 115 A—135 APiece Length: 100 m —200 m

Slides 36-40: Based on American Superconductor Corp. Data Sheets

Y. Iwasa (05/08/03) 48

Iop=19 A; Ic=22 A

80.6

80.7

80.8

80.9

81.0

81.1

0 10 20 30 40 50

Time (s)

Tem

per

atu

re (

K) C1 (closest)

C3 (closest)

C2

Y. Iwasa (05/08/03) 49

0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

0 1 2 3 4 5 6 7 8

Time (s)

Vo

ltag

e (V

)

NZP @ 19 A & 80.6 K

PrimaryHeater pulse

V1 V2 V3

V4 100

Y. Iwasa (05/08/03) 50

0

10

20

30

40

50

60

70

80

90

50 60 70 80 90 100

Fraction I/Ic (%)

Min

imu

m Q

uen

ch E

ner

gy

(mJ)

Energy Margin vs. I/Ic (Ic =22 A @ 80.6 K )

Y. Iwasa (05/08/03) 51

NZP Velocity vs. I/Ic

0.00

0.20

0.40

0.60

0.80

1.00

50 60 70 80 90 100

I/Ic (%)

Qu

ench

Pro

pag

atio

n

Vel

oci

ty (

cm/s

)

Y. Iwasa (05/08/03) 52

Quench/Recovery Experiment & Simulation

Bath cooling @77K

Forced-flow cooling @ 2-3 atm 80-81K

Y. Iwasa (05/08/03) 53

Forced Flow Experimental Setup

PressureGauge

PressureRegulator

LiquidNitrogen

77K Hx RT Hx

77K (Styrofoam Bath)

High-Pressure (3-atm) Section

Water

N2 Gas Tank

NeedleValve

Shut/OpenValve

VolumeMeter

SampleHolder

Y. Iwasa (05/08/03) 54

Y. Iwasa (05/08/03) 55

New Forced-Flow Sample Holder

Y. Iwasa (05/08/03) 56

Y. Iwasa (05/08/03) 57

Y. Iwasa (05/08/03) 58

Y. Iwasa (05/08/03) 59

Y. Iwasa (05/08/03) 60

Sample 2: V( I ) Plot @77K [ Ic=105A ] [ Source-Measured Ic > 100A ]

-5

0

5

10

15

20

0 20 40 60 80 100 120

V [u

V]

I [A]

Y. Iwasa (05/08/03) 61

Sample 2: Forced-Flow (~81K; 5cm/s)

0

50

100

150

200

I [A

]

24A

170A

45A

0

250

500

750

1000

0 1 2 3 4 5 6

V [m

V]

Time [s]

24A

71A

65A45A

65A

71A

Y. Iwasa (05/08/03) 62

Sample 2: Forced-Flow (~81K; 3cm/s)

0

200

400

600

800

1000

0 1 2 3 4 5 6

V [m

V]

Time [s]

24A

0

50

100

150

200

I [A

]

24A

45A

45A

65A

65A

Y. Iwasa (05/08/03) 63

Sample 2: Forced-Flow (@81K)

0

200

400

600

800

1000

0 1 2 3 4 5

V [m

V]

Time [s]

170A/65A (3cm/s)

170A/65A (5cm/s)

Y. Iwasa (05/08/03) 64

Sample 2: Forced-Flow (5cm/s) & Bath

0

200

400

600

800

1000

0 1 2 3 4 5 6

V [m

V]

Time [s]

170A/75A (Bath)

170A/71A (5cm/s)

Y. Iwasa (05/08/03) 65

Simulation

3.08.0 PrRe023.0=Nu

( )( )[ ] 3/2PrRe/04.01

PrRe/0668.066.3

LD

LDNu

++=

3000Re ≥

3000Re <

0.849°10-20.5791°10-513768.62884.0

0.12470.1228°10-32079779.983.0

κ(W/m K)µ(Pa s)Cp(j/kg K)ρ(kg/m3)T(K)

Nitrogen Properties at 2 bar( From Handbook of Cryogenic Engineering, I. G. WeisendΙΙ, 1998)

, turbulent flow

, laminar flow

Q = h Tw =hAs(Tw-Tf)

h=kNu/D

Y. Iwasa (05/08/03) 66

Sample 2: Bath @77 K & Simulation

0

200

400

600

800

1000

1200

V [m

V]

MeasurementSimulation

45A

24A

65A

65A

45A

24A

0

50

100

150

200

250

300

350

0 1 2 3 4 5

T [K

]

Time [s]

75A

20A

40A

60A

Y. Iwasa (05/08/03) 67

Sample 2: Forced-Flow (3 cm/s) & Simulation

0

50

100

150

200

250

300

350

0 1 2 3 4 5

T [K

]

Time [s]

Entrance Middle

65A

45A

24A

Exit

0

200

400

600

800

1000

1200V

[mV

]MeasurementSimulation

45A

24A

65A

65A

45A

24A

Y. Iwasa (05/08/03) 68

Sample 2: Forced-Flow (5 cm/s) & Simulation

0

50

100

150

200

250

300

350

0 1 2 3 4 5

T [K

]

Time [s]

45A

65A

71A

24A

Entrance Middle Exit

0

200

400

600

800

1000

1200

V [m

V]

45A

24A

65A

71A

71A

65A45A

24A

MeasurementSimulation

Y. Iwasa (05/08/03) 69

YBCO Samples in a Conduction Cooling Setup

• The sample was mountedbetween a Kapton-tape-insulated Cu-block and a G-10block.

• It was affixed to the first- stagecold-head of a Cryomech GB-37cryocooler for conductioncooling to about 40 K.

• A copper shield was addedaround the G-10 block to ensurea better uniform temperature ofthe tape.

• A heater was affixed to thecopper base,and three PRTThermometers are placed onthe YBCO top surface.

Slides 69-78: Based on Winston Lue ( ASC2002, August 2002 )

Y. Iwasa (05/08/03) 70

Over-Current Pulse Induced NZP

• At each operating current, Iop aninitial over-current pulse wasapplied. The transient pulse energywas varied by changing themagnitude, Ip or the duration of thepulse.

• The figures show at T= 45 K, and atan Iop of 33.7-A and 2-s over-currentpulse duration, an Ip of 117.4 Acaused a quench while 116.5 A didnot.

• Distinctive normal zone propagationwas observed when there was aquench.

• The inserts show the temperaturesmeasured by a PRT at the center ofthe sample.

0

30

60

90

120

150

180

0

50

100

150

0 4 8 12 16 20 24

V1

V2

V3

V4

V5

V6

V7

V8

I [A]

U [mV]

t [s]

45

55

65

75

85

0 4 8 12 16 20 24

T [K]

t [s]

0

50

100

150

200

0

20

40

60

80

100

0 3 6 9 12 15 18

V1

V2

V3

V4

V5

V6

V7

V8

I [A]

U [mV]

t [s]

45

46

47

48

49

50

51

52

53

54

0 3 6 9 12 15 18

T [K]

t [s]

Ip = 117.4 A

Ip = 116.5 A

Y. Iwasa (05/08/03) 71

Stability Margins in the Range 45—80 K

• To measure the stability margin, theoperating current was set near the lowestzone Ic at a particular temperature.

• At the highest recovery pulse current, theV-I product integrated over the initial pulsedivided by the zone volume is used toestimate the stability margin.

• The measured stability margins rangedfrom 16 to 120 J/cm3 as temperature lowersfrom 80 to 45 K.

• Comparison with the specific heat integralsindicated better fit to Tc than to Tcs for theHTS tapes.

• The higher margins measured at lowertemperatures are attributed to the higherconduction cooling.( )( )coptopcopcs IITTTT −−+= 1

0

20

40

60

80

100

120

45 50 55 60 65 70 75 80 85

Measured

Stability marg

3]

T [K]

Y. Iwasa (05/08/03) 72

Minimum Propagation Currents

• At 45.4 K, the sample wassubjected to an initial over-current pulse of 118 A for 2 swhile increasing the operatingpropagation in 1 A steps.

• The figures show recovery atan operating current of 27.4 Aand propagation at 28.4 A - aminimum propagation current.

• The initial heat input to zone 4was about 4.6 J or 350.4 J/cm3

- about 3 times the stabilitymargin.

0

50

100

150

200

0

50

100

150

200

-2 6 14 22 30 38 46 54 62

V1

V2

V3

V4

V5

V6

V7

V8

I [A]

U [mV]

t [s]

45

50

55

60

65

70

75

0 10 20 30 40 50 60

T [K]

t [s]

0

30

60

90

120

150

180

0

50

100

150

200

-2 6 14 22 30 38 46 54 62

V1

V2

V3

V4

V5

V6

V7

V8

I [A]

U [mV]

t [s]

40

50

60

70

80

90

100

110

0 10 20 30 40 50 60

T [K]

t [s]

Iop = 27.4 A

Iop = 28.4 A

Y. Iwasa (05/08/03) 73

Minimum Propagation Current vs. Temperature

• Minimum propagationcurrents were also determinedby extrapolating the velocityversus current plots to zerovelocity.

• Minimum propagationcurrents of 12 to 27 A wereobserved at 80.8 to 45.4 K.

• The existence of minimumpropagation current is thoughtto be the result of conductioncooling.

10

15

20

25

30

45 50 55 60 65 70 75 80 85

measured

extrapolated

fitted average

I mp

[A]

T [K]

Y. Iwasa (05/08/03) 74

NZP Velocity vs. Iop

• NPZ always starts from themiddle (zone 4) of this sample.

• NZP velocities were found to beincreasing linearly with thecurrent.

• No more than 20 mm/s of NZPvelocity was measured when Iopwas set below Ic.

• The outer zones which receivedbetter cooing resulted in lowerNZP velocity and higherminimum propagation current.

0

5

10

15

20

25

30

10 15 20 25 30 35

v2-1

v3-2

v7-8

Quench propagati

Iop

[A]

T=76.4-KIc2

=22.3-A

Ic3

=20.4-A

Ic7

=18.7-A

0

2

4

6

8

10

20 25 30 35 40 45 50

v2

v6

v7

Quench propagati

Iop

[A]

T=45.8 KIc2

=68.8 A

Ic6

=64.9 A

Ic7

=61.5 A

Y. Iwasa (05/08/03) 75

NZP Velocity vs. Temperature

• NZP velocities weremeasured at fivedifferent temperatures.

• NZP velocities at anoperating current of 30.3A were found at thedifferent temperaturesand plotted in the figure.

• NZP velocity vs.temperature shows asimilar dependence asthe ratio of operating tocritical current.

0

5

10

15

20

0.5

1

1.5

2

2.5

45 50 55 60 65 70 75 80

v2

v7

T [K]

Iop

=30.3 A

I op/

Ic7

Quench propagati

Y. Iwasa (05/08/03) 76

Modified Adiabatic Theories of NZP Velocity

1. Constant material properties (Dresner)

2. Variable material properties (Zhao and Iwasa)

3. Constant material properties with a different transition temperature(Bellis and Iwasa)

vA

I Imp

A C p

k

Tc Top

vB

I Im p

A

kn n

Cs dT Cn

1

kn

dkn

dTCs

Top

T c

dTT op

Tc

vC

I Im p

A

kn

CnCs Tt Top Tt Tcs

1

2Tc Tcs

Y. Iwasa (05/08/03) 77

NZP velocities: Experiment & Modified Adiabatic Theories

• Inclusion of a minimumpropagation current isnecessary to achieve betteragreement with the data.

• The agreement of the twoIwasa’s theories indicatedthe validity of a newtransition point for HTS,

• Fair agreement is foundbetween the data themodified theory of Iwasa.

0

5

10

15

20

45 50 55 60 65 70 75 80

vB

vC

vA

vm (Fig. 9)

Quench propagati

T [K]

Iop

=30.3 A

Y. Iwasa (05/08/03) 78

ORNL Conclusion

• Stability margins ranged from 16 to 120 J/cm3 as temperature lowersfrom 80 to 45 K. Comparison with the specific heat integrals indicatedbetter fit to Tc than to Tcs for the HTS tapes.

• Distinctive NZP in YBCO was observed at each of the measuredtemperatures.

• Minimum propagation current as a function of temperature wasmeasured. 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 tocritical current and agrees with a modified adiabatic theory.