MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING DEPARTMENT OF NUCLEAR ENGINEERING 2.64J/22.68J Spring Term 23 May 8, 23 Lecture 1: Protection & HTS Magnets Key magnet issues vs. T op ; 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 J c ( B )data @ 4.2, 1, and 2 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 (5/8/3) 1
Key Magnet Issues vs Top Cost or Difficulty Protection Conductor Mechanical Stability Cryogenics ~1 T op [K] LTS HTS Y. Iwasa (5/8/3) 2
Areas of Failure in Superconducting Magnets In the order of decreasing reported incidents. Insulation Mechanical System performance Conductor External system Coolant Y. Iwasa (5/8/3) 3
Key Quench-Induced Problems Overheating High voltage Overstressing Over pressure Y. Iwasa (5/8/3) 4
Overheating Energy Conversion B o 2 2 o h cu (T mt )-h cu (T op ) = 5.2 1 9 J/m 3 B o 115 T 1356 K 4.2 K For a uniform energy conversion over the entire winding, a quench-induced T max will remains <1 K, an upper limit to keep the differential thermal expansion stresses negligible. Y. Iwasa (5/8/3) 5
Protection Against Overheating 1. Self-Protecting Magnets Normal zone propagation speed, U nzp, 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 2 a 1 U nzp 2a 1 2a 2 B o Large magnets are not self-protecting. [U nzp ] HTS << [U nzp ] LTS : HTS magnets not self-protecting. Y. Iwasa (5/8/3) 6
An Example B o =8 T B o E mg =1 6 J.6 m Winding volume=.6 m 3 (~2 ft 3 ) Winding % T f [K] Remarks.2 m Absorbing E mg.4 m 1 55 Well below 1 K 5 7 < 1 K 1 13 Barely acceptable 1 58 Unacceptable Y. Iwasa (5/8/3) 7
Normal Zone Propagation Velocity Along Wire Axis--No Matrix C n T n t z k n T n z n J 2 (normal state) C s T s t z k s T s z (Superconducting state) T t T z z t U l T z (U l : longitudinal velocity) Normal Superconducting z Y. Iwasa (5/8/3) 8
C n U l dt n d z C s U l dt s dz d d z k n d dz k s dt n d z dt s dz Assume k n, k s, and d 2 T n /dz 2 n J 2 near z C n U l dt n dt nj 2 (z ) k s d 2 T s dz 2 C s U l dt s d t (z ) T s (z) = Ae cz T op C C s U l k s Y. Iwasa (5/8/3) 9
At z T s () = T c T s (z) = (T c T op ) e ( C s U l / k s )z T op At z k n (dt n /dz) = k s (dt s /dz) k n n J 2 C n U l C s U l (T c T op ) U l J n k n C n C s (T c T op ) Y. Iwasa (5/8/3) 1
C s C n C U l J C n k n (T c T op ) U l J U l 1/C [U l ] hts << [U l ] lts In the presence of normal metal matrix: U l C cd J m m k m (T cs T op ) Note that T cs T t Y. Iwasa (5/8/3) 11
With C n ( T ), C s ( T ), k n ( T ): U l J C n (T cs ) - n (T cs )k n (T cs ) 1 d k n (T ) T cs C s (T )dt k n (T cs ) dt T op Tcs T cs T op C s (T )d T Note that T cs T t Y. Iwasa (5/8/3) 12
1-D Adiabatic NZP Experimental & Simulation Results ~1 cm Slides 13-15: from R.H. Bellis and Y. Iwasa (Cryogenics, Vol. 34 1994) Y. Iwasa (5/8/3) 13
Nb 3 Sn Tape @ 12 K & 225 A Experimental U l =5 cm/s V 4 V 1 V 2 V 3 Temperature Simulation Simulation 15 ms V 4 25 ms 1 ms T c =16.5 K T cs =13.7 K V 1 V 2 V 3 Y. Iwasa (5/8/3) 14
Bi-2223/Ag Tape @ 14 K & 1 A Experimental [U l ] hts =1 cm/s << [U l ] lts Temperature Simulation Simulation 6 s 1 s T c =93 K T cs =44.4 K Y. Iwasa (5/8/3) 15
2. Active Protection Detect-and-Dump Widely used in large magnets. Dissipates most of the stored magnet energy into a dump resistor connected across the magnet terminals. A hot spot heated only over a brief period of current decay. Leads to another criterion for operating current density. L mg ~ V D R D r ( t ) Y. Iwasa (5/8/3) 16
L mg di(t ) d t For r(t ) << R D : L mg di(t ) d t [r(t ) + R D ]I(t ) = R D I(t ) = With g k g d g q : A cd C cd (T ) dt dt C cd (T ) A dt m (T ) m A cd I(t ) = I op exp (T) m I 2 (t) C cd (T) dt A m d t [J op ] 2 m exp 2R D t L mg dt R D t L mg m (T ) A m A cd J m (t ) = [J op ] m exp J 2 m (t ) R D t L mg T f C cd (T ) dt Z (T i, T f ) m (T ) T i A m A cd 2 [J op ] m exp 2R d t L mg dt A m A cd 2 L [J op ] mg m 2R D Z (T i, T f ) A m A cd 2 L [J op ] mg m 2R D A m [J op ] 2 E I 2 2 mg op A m m A cd 2V D I op A cd [J op ] m 2 E mg V D I op Y. Iwasa (5/8/3) 17
Z (T i, T f ) T f T i C cd (T ) m (T ) dt C cd (T ) C (T ) (T ) cd m m (T ) ~constant Z(T i, T f ) ~T ~1/T T T T i T f T Y. Iwasa (5/8/3) 18
Z(T ) Functions: 1: Ag (99.99%) 2: Cu (RRR 2) 3: Cu (RRR 1) 4: Cu (RRR 5) 5: Al (99.99%) Z [1 16 A 2 s/ m 4 ] T [K] Y. Iwasa (5/8/3) 19
Protection Criterion [J op ] m A c d A m V D I op Z (T i, T f ) E mg Cryostable Criterion [J op ] cd f p P cd A m q fm m ( A s + A m ) 2 Y. Iwasa (5/8/3) 21
Detect-and Dump : Options to improve [J op ] m 1. Increase I op Larger conductor; more expensive for given ka-m Larger current leads--greater heat input Larger ( I B ) force For a given power rating VI, higher I more expensive 2. Increase V D Increased danger of voltage breakdown, particularly > 8 V in helium environment 3. Increase Z( T f ) Better to keep T f below ~1 K-15 K Cu better than Al 4. Reduce E mg Subdivision common practice with HEP & Fusion magnets Y. Iwasa (5/8/3) 22
Detection of Non-Recovering Quench di(t ) di(t ) V 1 (t ) L 1 r(t )I(t ) V dt 2 (t ) L 2 dt V out ( t ) = V 2 ( t ) - V 1 ( t ) R 2 L 1 R 1 L 2 V out (t ) = - R 2 R 1 R 2 r(t )I(t ) I( t ) ~ V 1 ( t ) L 1 r( t ) I( t ) o V out ( t ) o R 1 R 2 V 2 ( t ) L 2 Y. Iwasa (5/8/3) 23
High Voltage Driven mode magnet, i.e., operated with its power supply generally connected, except during a dump. High voltage, i.e., V D, appears across the magnet terminals. 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 (5/8/3) 24
Operation Steps Persistent Mode Operation 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 L mg ~ Heater r ( t ) > Y. Iwasa (5/8/3) 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=l mg / r ) in NMR & MRI magnets: B(t ) B e (r / L mg )t B 1 r L mg t (for L mg /r 1hr) Y. Iwasa (5/8/3) 26
Internal Voltage In Persistent Mode Magnet No internal voltage in a uniformly (1%) resistive magnet. Internal voltage in a partially resistive magnet. Large voltages can occur when a resistive zone confined to a small section. V L 1% V R ~ r ( t ) 1% No internal voltage Y. Iwasa (5/8/3) 27
Internal Voltage in Persistent Mode ~ Extent of r ( t ) 5% 1% 1% 5% 1% Top 1% Middle 1% Top 5% Bottom 5% Bottom 1% Y. Iwasa (5/8/3) 28
Internal Voltage In Driven Mode Magnet For R D >> r ( t ), internal voltage is essentially due to the inductive voltage. The maximum inductive occurs at t = and it is equal V D. V L V D (R D >> r ) L mg ~ V D R D r ( t ) Effect of r ( t ) is neglected. Y. Iwasa (5/8/3) 29
Overstressing 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 (5/8/3) 3
Example: 2-Coil System Overstressing (& Protection) A quench in Coil 1 induces an extra current in Coil 2. 1. Helps spreading out normal zone faster and over a large volume. 2. May overstress Coil 2 I ( t ) Overstress limit I 1 I 2 I o I 1 I o R 1 L 1 I 1 r (t ) ~ M I 1 I 2 R 2 I 2 L 2 I o t I o I 1 I 2 Y. Iwasa (5/8/3) 31
Protection Circuit for an NMR Magnet + Y. Iwasa (5/8/3) Within Cryostat 32
Over Pressure 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. 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 (5/8/3) 33
HTS Magnets & Issues Hc2 [ T ] 15 YBCO HTS: YBCO; BSCCO; MgB 2 LTS: Nb-Ti; Nb 3 Sn 1 5 Nb 3 Sn BSCCO 2223 BSCCO 2212 Magnet Grade Conductors: NbTi; Nb 3 Sn; BSCCO 2223 NbTi MgB 2 2 4 6 8 1 T [K] Y. Iwasa (5/8/3) 34
HTS BSCCO 2223 currently available as magnet grade conductor. Powder in Ag tube BSCCO 2212 being developed but not easily available. YBCO, compared with BSCCO, regarded more promising for electric power devices. MgB2 also regarded promising, because of its low cost. Y. Iwasa (5/8/3) 35
Bi-2223 High Current Density Wire: Non-Reinforced Thickness (avg):.21 (+/-.2mm) Width (avg): 4.1 (+/-.2mm) Min. Critical Stress: 75 MPa Min. Critical Strain:.15% Min. Bend Dia: 1 mm Variable Specifications: Min. I c : 115 A 135 A Piece Length: 1 m 2 m Ic/Ic(o) Strain 1.2.8.16 Ic/Ic(o).6.4.12.8 Strain.2.4 2 4 6 8 1 Stress at 77K (MPa) Slides 35-39: Based on American Superconductor Corp. Data Sheets Y. Iwasa (5/8/3) 36
Bi-2223 High Strength Reinforced Tape Stainless Steel Strips Thickness (avg):.31 (+/-.2mm) Width (avg): 4.1 (+/-.2mm) Min. Critical Stress: 265 MPa Min. Critical Strain:.4% Min. Bend Dia: 7 mm Variable Specifications: Min. I c : 115 A 135 A Piece Length: 1 m 3 m Ic/Ic(o) Strain Ic/Ic(o) 1.8.6.4.2.7.6.5.4.3.2.1 5 1 15 2 25 3 35 Stress at 77K (MPa) Strain (%) Y. Iwasa (5/8/3) 37
Scaling Ratio to 77K (self-field) in // External Field 6 Scaling Ratio, Ic(T,B)/Ic(77K,) 5 4 3 2 2 35 5 1 1 2 3 4 5 6 7 8 Parallel Magnetic Field (Tesla) Y. Iwasa (5/8/3) 38
Scaling Ratio to 77K (self-field) in External Field 6 Scaling Ratio, Ic(T,B)/Ic(77K,) 5 4 3 2 2K 35K 5K 1 1 2 3 4 5 6 7 8 Perpendicular Magnetic Field (Tesla) Y. Iwasa (5/8/3) 39
Scaling Ratio, 77K to 4.2K 6. 5. Bpar, 4.2K Bperp, 4.2K 4. 3. 2. 1.. 2 4 6 8 1 12 Magnetic Field, Tesla Y. Iwasa (5/8/3) 4
1-D NZP in YBCO Composite Energy Margin & NZP Velocity Keithley 21 DMM* Keithley 21 DMM* Keithley 21 DMM* Keithley 2 DMM Keithley 2 DMM Keithley 2 DMM V 3 V 2 V 1 V cernox1 V cernox2 V cernox3 HTS sample NiCr heater HP 6286A DC-P/S Keithley 2 DMM* V tot HP 8112A pulse generator 5 A / 1 mv V(I) HP 6681A DC-P/S Keithley 2 DMM Keithley 21 DMM* GPIB *set on buffer read for increased speed/resolution Slides 45-51: Based on Justin Schwartz ( DOE Meeting July 22) Y. Iwasa (5/8/3) 45
Bi2223 tape: Recovery.8 Voltage (V).6.4.2 V 1 V 2. V 3 6 7 8 9 1 11 12 13 14 15 Time (s) 11 Temperature (K) 1 9 C 2 C 1 8 1 2 3 4 5 Time (s) Y. Iwasa (5/8/3) 46
Bi-2223 High Current Density Wire: Non-Reinforced Thickness (avg):.21 (+/-.2mm) Width (avg): 4.1 (+/-.2mm) Min. Critical Stress: 75 MPa Min. Critical Strain:.15% Min. Bend Dia: 1 mm Variable Specifications: Min. I c : 115 A 135 A Piece Length: 1 m 2 m Ic/Ic(o) Strain 1.2.8.16 Ic/Ic(o).6.4.12.8 Strain.2.4 2 4 6 8 1 Stress at 77K (MPa) Slides 36-4: Based on American Superconductor Corp. Data Sheets Y. Iwasa (5/8/3) 36
I op =19 A; I c =22 A 81.1 Temperature (K) 81. 8.9 8.8 8.7 8.6 C 1 (closest) C 2 C 3 (closest) 1 2 3 4 5 Time (s) Y. Iwasa (5/8/3) 48
NZP @ 19 A & 8.6 K 3.E-2 2.5E-2 Voltage (V) 2.E-2 1.5E-2 1.E-2 5.E-3 Primary Heater pulse V 1 V 2 V 3 V 4 1.E+ 1 2 3 4 5 6 7 8 Time (s) Y. Iwasa (5/8/3) 49
Energy Margin vs. I/I c (I c =22 A @ 8.6 K ) Minimum Quench Energy (mj) 9 8 7 6 5 4 3 2 1 5 6 7 8 9 1 Fraction I/I c (%) Y. Iwasa (5/8/3) 5
NZP Velocity vs. I/I c Quench Propagation Velocity (cm/s) 1..8.6.4.2. 5 6 7 8 9 1 I/Ic (%) Y. Iwasa (5/8/3) 51
Quench/Recovery Experiment & Simulation Bath cooling @77K Forced-flow cooling @ 2-3 atm 8-81K Y. Iwasa (5/8/3) 52
Forced Flow Experimental Setup Pressure Gauge Pressure Regulator Needle Valve Shut/OpenVolume Valve Meter Liquid Nitrogen Water N 2 Gas Tank 77K Hx Sample Holder 77K (Styrofoam Bath) RT Hx High-Pressure (3-atm) Section Y. Iwasa (5/8/3) 53
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New Forced-Flow Sample Holder Y. Iwasa (5/8/3) 55
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Sample 2: V( I ) Plot @77K [ I c =15A ] [ Source-Measured I c > 1A ] 2 15 V [uv] 1 5-5 2 4 6 8 1 12 I [A] Y. Iwasa (5/8/3) 6
Sample 2: Forced-Flow (~81K; 5cm/s) 2 15 17A I [A] 1 5 24A 45A 65A 71A 1 75 71A V [mv] 5 25 65A 45A 24A 1 2 3 4 5 6 Time [s] Y. Iwasa (5/8/3) 61
Sample 2: Forced-Flow (~81K; 3cm/s) 2 15 I [A] 1 5 24A 45A 65A 1 8 V [mv] 6 4 65A 2 45A 24A 1 2 3 4 5 6 Time [s] Y. Iwasa (5/8/3) 62
Sample 2: Forced-Flow (@81K) 1 8 17A/65A (3cm/s) V [mv] 6 4 17A/65A (5cm/s) 2 1 2 3 4 5 Time [s] Y. Iwasa (5/8/3) 63
Sample 2: Forced-Flow (5cm/s) & Bath 1 8 17A/71A (5cm/s) V [mv] 6 4 2 17A/75A (Bath) 1 2 3 4 5 6 Time [s] Y. Iwasa (5/8/3) 64
Simulation Re 3, turbulent flow Q = h T w =ha s (T w -T f ) h=knu/d Nu =.23Re.8 Pr Re < 3, laminar flow.668 Nu = 3.66 + 1+.4.3 ( D / L) Re Pr [( D / L) Re Pr] 2/ 3 T(K) Nitrogen Properties at 2 bar ( From Handbook of Cryogenic Engineering, I. G. WeisendΙΙ, 1998) ρ(kg/m 3 ) Cp(j/kg K) µ(pa s) κ(w/m K) 83. 779.9 279.1228 1-3.1247 84. 8.628 1376.5791 1-5.849 1-2 Y. Iwasa (5/8/3) 65
Sample 2: Bath @77 K & Simulation 35 3 75A 6A T [K] 25 2 15 1 5 4A 2A 12 1 2 3 4 5 Time [s] V [mv] 1 8 6 4 65A 65A Measurement Simulation 45A 2 45A 24A 24A Y. Iwasa (5/8/3) 66
Sample 2: Forced-Flow (3 cm/s) & Simulation 12 V [mv] 1 8 6 4 65A 65A Measurement Simulation 45A 2 35 45A 24A 24A T [K] 3 25 2 15 1 65A Entrance Middle Exit 45A 24A 5 1 2 3 4 5 Time [s] Y. Iwasa (5/8/3) 67
Sample 2: Forced-Flow (5 cm/s) & Simulation 12 1 8 71A 65A Measurement Simulation 71A V [mv] 6 4 2 24A 45A 65A 24A 45A 35 3 25 71A 65A Entrance Middle Exit T [K] 2 15 45A 1 24A 5 1 2 3 4 5 Time [s] Y. Iwasa (5/8/3) 68
YBCO Samples in a Conduction Cooling Setup The sample was mounted between a Kapton-tapeinsulated Cu-block and a G-1 block. It was affixed to the first- stage cold-head of a Cryomech GB-37 cryocooler for conduction cooling to about 4 K. A copper shield was added around the G-1 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 ( ASC22, August 22 ) Y. Iwasa (5/8/3) 69
Over-Current Pulse Induced NZP 18 15 ] A12 [ 9 I 6 3 2 15 ] A [ 1 I 85 75 ] K [ 65 T 55 45 4 8 12 16 2 24 t [s] V 1 V 2 V 3 V 4 V 5 V 6 V 7 V 8 4 8 12 16 2 24 5 I p = 117.4 A 54 53 52 ] 51 K [ 5 T49 48 47 46 45 t [s] 3 6 9 12 15 18 t [s] I p = 116.5 A V 1 V 2 V 3 V 4 V 5 V 6 V 7 V 8 3 6 9 12 15 18 t [s] 15 1 5 1 8 6 4 2 U [ m V ] U [ m V ] At each operating current, I op an initial over-current pulse was applied. The transient pulse energy was varied by changing the magnitude, I p or the duration of the pulse. The figures show at T= 45 K, and at an I op of 33.7-A and 2-s over-current pulse duration, an I p 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. Y. Iwasa (5/8/3) 7
Stability Margins in the Range 45 8 K g r12 a m 1 y t 8 i l i 6 b a 4 t S 2 3 ] 45 5 55 6 65 7 75 8 85 T cs op ( T T )( I I ) = T + 1 c T [K] op Measured t cop To measure the stability margin, the operating current was set near the lowest zone I c 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 12 J/cm 3 as temperature lowers from 8 to 45 K. Comparison with the specific heat integrals indicated better fit to T c than to T cs for the HTS tapes. The higher margins measured at lower temperatures are attributed to the higher conduction cooling. Y. Iwasa (5/8/3) 71
Minimum Propagation Currents 2 15 ] A [ 1 I 5 18 15 ] 12 A [ 9 I 75 7 ] K 65 [ 6 T 55 5 45 1 2 3 4 5 6 t [s] V 1 V 2 V 3 V 4 V 5 V 6 V 7 V 8-2 6 14 22 3 38 46 54 62 6 3 I op = 27.4 A 11 1 9 ] K [ 8 T 7 6 5 4 t [s] 1 2 3 4 5 6 t [s] I op = 28.4 A V 1 V 2 V 3 V 4 V 5 V 6 V 7 V 8 2 15 1 5 2 15 1 5 ] V m [ U ] V m [ U 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 35.4 J/cm 3 - about 3 times the stability margin. -2 6 14 22 3 38 46 54 62 t [s] Y. Iwasa (5/8/3) 72
Minimum Propagation Current vs. Temperature 25 ] A [ 2 I m p 3 15 measured extrapolated fitted average 1 45 5 55 6 65 7 75 8 85 T [K] 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 8.8 to 45.4 K. The existence of minimum propagation current is thought to be the result of conduction cooling. Y. Iwasa (5/8/3) 73
i t 1 a g a 8 p o r 6 p h c n e u Q 4 2 2 25 3 35 4 45 5 I i op [A] t 3 a g I =22.3-A T=76.4-K 25 c2 a I =2.4-A p c3 o 2 I =18.7-A c7 r p v 2-1 15 h c 1 n e u 5 Q I c2 =68.8 A I c6 =64.9 A I c7 =61.5 A v 2 v 6 v 7 v 3-2 v 7-8 T=45.8 K 1 15 2 25 3 35 I [A] op NZP Velocity vs. I op 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 2 mm/s of NZP velocity was measured when I op was set below I c. The outer zones which received better cooing resulted in lower NZP velocity and higher minimum propagation current. Y. Iwasa (5/8/3) 74
i t a g a p o r p h c n e u Q 2 15 1 5 v 2 v 7 NZP Velocity vs. Temperature I op =3.3 A 2.5 1.5.5 45 5 55 6 65 7 75 8 T [K] 2 1 I 7 c / p I o NZP velocities were measured at five different temperatures. NZP velocities at an operating current of 3.3 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. Y. Iwasa (5/8/3) 75
Modified Adiabatic Theories of NZP Velocity 1. Constant material properties (Dresner) v A I I mp A C p T c k T op 2. Variable material properties (Zhao and Iwasa) v B I I mp A T c T op k n 1 dk C s dt C n n k n dt n T c T op C s dt 3. Constant material properties with a different transition temperature (Bellis and Iwasa) v C I I m p A k n C n C s T t T op T t T cs 1 2 T c T cs Y. Iwasa (5/8/3) 76
i t 2 a g a p15 o r p 1 h c n e 5 u Q NZP velocities: Experiment & Modified Adiabatic Theories v A v B v C v m (Fig. 9) I op =3.3 A 45 5 55 6 65 7 75 8 T [K] 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. Y. Iwasa (5/8/3) 77
ORNL Conclusion Stability margins ranged from 16 to 12 J/cm 3 as temperature lowers from 8 to 45 K. Comparison with the specific heat integrals indicated better fit to T c than to T cs 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 2 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 (5/8/3) 78