MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING DEPARTMENT OF NUCLEAR ENGINEERING 2.64J/22.68J , : ( J

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1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING DEPARTMENT OF NUCLEAR ENGINEERING 2.64J/22.68J Spring Term 2003 April 24, 2003 Lecture 8: Stability Key magnet issues vs. T op Magnetic and thermal diffusion Winding pack; stability; power density equation Disturbances; energy density spectra; energy or stability margin E(J )& V(I ) characteristics of high-current superconductor Important stability issues: cryostable & adiabatic magnets Cryostability; Stekly criterion; Equal area criterion; CICC Heat transfer data High-performance (adiabatic) magnets; MPZ concept Mechanical disturbances premature quenches & training AE technique Stability of HTS Y. Iwasa (04/24/03) 1

2 Key Magnet Issues vs Top Cost or Difficulty Protection Conductor Mechanical Stability Cryogenics 0 ~100 T op [K] LTS HTS Y. Iwasa (04/24/03) 2

3 Magnetic Diffusion r r H J f r E H y E (1-D) J z z x e r B E B z y t x t 0 H y t e e 0 2 H y 2 0 H y t x 2 2 H y H D y H y mg x 2 x 2 t D mg mg e 0 1 D mg 2a 2 0 e 2a 2 D mg e 0 mg 1 D mg 2a 2 0 e 2a 2 Y. Iwasa (04/24/03) 3

4 Thermal Diffusion k 2 T x 2 C T t k C 2 T x 2 D th 2 T x 2 T t D th k C Y. Iwasa (04/24/03) 4

5 Data for Cu & Nb-Ti K [W/m K] C [J/m 3 K] [ m] D th [m 2 /s] D mg [m 2 /s] Copper ~400 ~1000 ~ ~0.4 ~ Nb-Ti ~10-3 ~500 ~ ~ ~0.5 D th Cu 5 Temperature wave travels much faster in Cu no ~2 10 temperature concentration in Cu. D th D SC Magnetic wave travels much slowly in Cu no flux ~6 10 motion induced local heating concentration in Cu. mg Cu 3 D mg SC Best to use Nb-Ti with Cu Y. Iwasa (04/24/03) 5

6 Winding Pack Structure Coolant A wpk A str A sc A m A ins A q Conductor Ins. Matrix SC Coolant Insulation Matrix (e.g. Cu) Superconductor Structure (e.g. epoxy, conduit) Superstructure Winding Pack Cross Section Y. Iwasa (04/24/03) 6

7 J c I c A sc J noncu I c A cd A m (Nb 3 Sn; HTS) J c (Nb - Ti) J eng J e I c A cd J m I op A m (Qunech propagation &protection) J overall I op A wpk Y. Iwasa (04/24/03) 7

8 Stability Stability of a superconducting magnet refers to the phenomenon of the magnet to operate reliably despite the presence of disturbance events. T cd limit set by design Disturbance may be mechanical, electromagnetic, thermal, or even nuclear in origin. Distributed: energy density [J/m 3 ] Point: energy [J] Y. Iwasa (04/24/03) 8

9 Power Density [W/m 3 ] Equation e h g k g j g d g q (6.1) f p P Cooling: cd q (T ) A cd C cd (T ) T t Disturbance: g d 2 Joule heating: cd (T )J cd Conduction: k cd (T ) T k cd (T ) x T Storage:C cd (T ) t x k cd(t ) T x cd (T )J 2 cd g d T x f P p cd q (T ) A cd Y. Iwasa (04/24/03) 9

10 Stability Concepts Derived from Eq. 6.1 ė h g k g j g d g q Application Flux jump Cryostability * 0 Dynamic stability 0 0 Equal area * MPZ * Protection * Covered in today s lecture Minimum Propagation Zone ** Normal Zone Propagation 0 0 Adiabatic NZP ** Y. Iwasa (04/24/03) 10

11 Sources of Disturbance Mechanical Lorentz force; thermal contraction Wire motion/ micro-slip Structure deformation Cracking epoxy; debonding Electrical/Magnetic Time-varying current/field Current transients, includes AC current Field transients, includes AC field Flux motion, e.g., flux jump Thermal Conduction, through leads Cooling blockage (poor ventilation) Nuclear radiation Neutron flux in fusion machines Particle showers in accelerators Y. Iwasa (04/24/03) 11

12 Disturbance Energy Density Spectra Courtesy of Luca Bottura (CERN, Geneva) Y. Iwasa (04/24/03) 12

13 Energy Margin or Stability Margin: e h; e min Minimum energy density (or energy) that leads to a quench Disturbance energy < e h Disturbance T < T cs T t < 0 Stable Disturbance energy > e h Stabilized T t < 0 Stable Disturbance T > T cs Not-stabilized T t > 0 Quench Y. Iwasa (04/24/03) 13

14 E(J) & V(I) Characteristics of High-Current Superconductor E(J ) E c J J c n V ( I ) V c I I c n n: Index of a superconductor: ideal superconductor, n= E( J ) n n 1 n 2 E c J c Y. Iwasa (04/24/03) 14 J

15 Typical Values of n for Magnet-Grade Conductors Nb-Ti: ( for NMR/MRI persistent-mode magnets) Nb3Sn: ( for NMR/MRI persistent-mode magnets) BSCCO2223: Y. Iwasa (04/24/03) 15

16 Important Stability Issues Cryostable & Adiabatic Magnets Cryostable Magnets Circuit model for a well-cooled composite conductor. Current-sharing. Cryostability (Stekly) linear cooling. Cryostability nonlinear cooling. Equal Area stability. CICC Cooling data bath & forced-flow. Adiabatic Magnets Premature quenches; training. Minimum propagation zone (MPZ). Disturbance spectra. Acoustic emission (AE) technique. Y. Iwasa (04/24/03) 16

17 Cryostable Magnets Coolant bath; CCIC;pipe Matrix normal metal Normal zone size >> MPZ; in bath-cooled magnets, can extend over the entire magnet volume. Best design: sufficient cooling with the minimum coolant space. Y. Iwasa (04/24/03) 17

18 Adiabatic Magnets Matrix normal metal Structural material, e.g., epoxy Localized normal zone permitted, but its size < MPZ (~mm in most windings). Best design: elimination of all disturbances. Y. Iwasa (04/24/03) 18

19 Cryostability Circuit Model for Ideal Superconductor (n = ) I t I c V cd 0 G j V cd I t 0 R s Real o + V cd o R n Ideal ( n= ) I I c n I m =0 I t I c Matrix R m I t I c = I t 0 I c I s Superconductor R s Y. Iwasa (04/24/03) 19

20 Cryostability Circuit Model for Ideal Superconductor (n = ) I t I c V cd R m I m R m ( I t I c ) R s I c R s R m I t I c 1 At I c, superconductor will have R s between 0 and R n >> R m to satisfy the circuit requirements G j V cd I t G j R m I t (I t I c ) R s Real o + V cd o R n Ideal ( n= ) I I c n I m I t > I c Matrix R m I c 0 I c I s Superconductor R s Y. Iwasa (04/24/03) 20

21 Temperature Dependent G j (T) Stekly Model I t I c (T op ) I c 0 Ideal superconductor (n = ) I t =I c0 I c (T ) R m I t 2 G j (T ) I t I c Current-sharing I c 0 T op =T cs T c T 0 T op =T cs T c Y. Iwasa (04/24/03) 21

22 Cryostability Stekly Criterion G j (T ) G q (T ) f p P cd h q (T T b ) g q (T ) R m I t 2 f p P cd h q (T T op ) T T cs T c T cs (T cs T T c ) f p P cd h q (T T op ) A cd 2 m I c 0 T T op Note: T b T op A cd A cd A m T c T op f p P cd A m h q (T c T op ) I 1 2 m c 0 2 A I sk m c 0 m f p P cd h q (T c T op ) sk f p P cd A m h q (T c T op ) 2 m I c 0 (6.8) Note that the conventional definition of sk is upside down of Eq. 6.8 I J c0 I c J c0 0 s c0 cd A cd A s A m 1 c/s Y. Iwasa (04/24/03) 22

23 Stekly (continued) Dissipation: 2 m I c 0 A cd A m T T op T c T op Cooling: f p P cd h q (T T op ) A cd Power density 2 m I c 0 Acd Am Not stable Stable 0 T op T b T < Tc T Y. Iwasa (04/24/03) 23

24 General Case ( I t < I c0 or T cs > T op ) G j (T ) 0 T G j (T ) R m I t I t I c T c 0 T c T op T I c 0 I c T op t T T 2 T T G j (T ) R m I cs t T T c cs c cs (T op T T cs ) (T cs T T c ) (T cs T T c ) I c (T ) Superconductor I c0 Current-sharing R m I t 2 G j (T ) I t Matrix T T op T cs T c T op T cs T c T Y. Iwasa (04/24/03) 24

25 Nonlinear Cooling Curves f [J c 0 ] cd [J t ] cd [J op ] p P cd A m q fm f p P cd q fm cd [A/m 3 ] m (A s A m ) 2 m A m q(t ), g j (T ) q pk q(t ) q fm Stekly General g j m I t 2 f p P cd A m [w/m 2 ] Top T b T cs T c T Y. Iwasa (04/24/03) 25

26 Example 2 f p 0.5; P cd A m A s A cd ; A m = 2.6 c m ; 0.3 cm = 10; 2 ; m A m A 1 cd = cm cm; q fm 0.3 W/cm ; A s f p P cd A m q fm [J op ] cd m ( A s A m ) A/cm 2 [J op ] s (1 )[J op ] cd 69,080 A/cm 2 (0.5)(2.6cm)(0.273 cm )(0.3 W/cm ( cm)(0.3cm 2 ) 2 LHe 2 2 ) I op A cd [J op ] cd 1884 A ( = 10) 10 mm I op A cd [J op ] cd 1803 A ( = 5) 3 mm Y. Iwasa (04/24/03) 26

27 V vs. I Traces of a Composite Conductor SC alone at T = T b V V Matrix alone at T = T b R s >> R m R m 0 I 0 I 0 I c0 0 R s / R m ~ Y. Iwasa (04/24/03) 27

28 V vs. I Traces of a Composite Conductor T c (T op T ) G j (T op T ) VI R m I I c0 I R m I ( I I c T c T 0 ) op T c I c0 T T op f p P cd lh q (T T op ) f p P cd lh q T T R m I ( I I c0 )(T c T op ) f d P cd lh q (T c T op ) R m I c 0 I V R m ( I I c 0 ) R m ( I I c0 ) I c0 R I ( I I )(T m c 0 c T ) op T c T op f p P cd lh q (T c T op ) R m I c0 I 2 R m I ( I I )(T c0 c T op ) f p P cd lh q (T c T op ) R m I c0 I Y. Iwasa (04/24/03) 28

29 V vs. I Traces: Dimensionless Expressions v i V R m I c 0 I I c0 sk f p P cd lh q ( T c T op ) 2 R m I c 0 f p P cd A m h q ( T c T op ) 2 m I c 0 i( i v( i) ( i 1) sk ( v 1) i( v) v sk sk 1) i sk ( i 1) i sk Y. Iwasa (04/24/03) 29

30 Numerical Illustrations I c A;T c 5.2 K ; T op 4.2 K; A m m 2 ; m = m; 4 h q =10 W/m 2 ; P cd = m 2 f m =1: Entire conductor surface exposed to coolant sk (1)( m)( m 2 )(10 4 W/m 2 K)(5.2 K K) 10 ( m)(1000 A) v v vs. i for = 10 sk i v T T b i Y. Iwasa (04/24/03) 30

31 Numerical Illustrations f m =0.1: 10% of conductor surface exposed to coolant sk (0.1)( m)( m 2 )(10 4 W/m 2 K)(5.2 K K) 1 ( m)(1000 A) 2 v i Y. Iwasa (04/24/03) 31

32 Numerical Illustrations f m =0.05: Only 5% of conductor surface exposed to coolant v vs. i for = 0.5 sk v i v i 0.5( i 1) 0.5(v 1) or v 0.5 i 0.5 v 1 i v i Y. Iwasa (04/24/03) 32

33 Y. Iwasa (04/24/03) 33

34 Equal-Area Criterion 0 g k (T ) g j (T ) 0 g q (T ) g k (T ) ds(t ) dx S(T ) ds(t ) dt 1 2 S 2 (T 2 ) d dx k cd (T ) dt dx g q (T ) g j (T ) k cd (T ) g q (T ) g q (T ) g j (T ) S (T ) k cd (T ) dt dx ds(t ) dt T 2 dt dx ds(t ) dt S 2 (T 1 ) k 0 g q (T ) g j (T ) T 1 g j (T ) S (T ) k cd (T ) dt S(T 1 ) S (T 2 ) 0because dt/ dx x1 dt/ dx x 2 0 T 2 gq (T ) T 1 g j (T ) dt 0 Y. Iwasa (04/24/03) 34

35 Equal Area (continued) 2-D Case k cd (T ) T d dr k (T ) cd dt dr d dr k cd (T ) dt dr g q (T ) g j (T ) 1 r k cd (T ) dt dr 1 r k dt cd (T ) dr Because the last term dt/dr is negative, it has the same effect as that of increasing cooling or decreasing Joule heating. Y. Iwasa (04/24/03) 35

36 q(t ), g j (T ) q pk q(t ) Equal Area q fm Stekly Stekly (T cs >T op ) 2 m I g c 0 j f p P cd A m T op T b T cs T c T [I c0 ] equal area > [I c0 ] Stekly Y. Iwasa (04/24/03) 36

37 Recovery Processes Stekly T x T Equal Area x Y. Iwasa (04/24/03) 37

38 CICC Transposed 37-Strand Cable (c. 1970) Courtesy of Luca Bottura (CERN, Geneva) Y. Iwasa (04/24/03) 38

39 Power Density Equation CICC Conduit Fluid Composite V fl (T ) C cd (T ) T t x k cd(t ) T x 2 cd(t )J cd g d f p P cd A cd q(t ) C fl (T ) T fl t h fl f p P cd A fl q (T ) k fl D hy Re 0.8 Pr 0.4 T fl T f p P cd A fl h fl (T T fl ) Y. Iwasa (04/24/03) 39

40 Stability Margin vs. Current in CICC ~1000 e h [mj/cm 3 ] Well-Cooled Dual Stability* Ill-Cooled ~100 ~10 0 I lim I op * J.W. Lue, J.R. Miller, L. Dresner (J. Appl. Phys. Vol. 51, 1980) Y. Iwasa (04/24/03) 40

41 Stability Approach for CICC Because CICC is mostly applied for large ( expensive ) magnets, cryostability (Stekly) is the accepted approach. Choose I op I lim given by: I lim f p P cd A m h q (T c T op ) m Y. Iwasa (04/24/03) 41

42 Helium Heat Transfer Data Nucleate & Film Boiling 10 q(t ) [W/cm 2 ] q pk q fm Approximate N 2 data multiply: y-scale by x-scale by T [K] Based on data from Luca Bottura (CERN, Geneva) Y. Iwasa (04/24/03) 42

43 Helium Heat Transfer Coefficient Data 10 h q (T ) [W/cm 2 ] q pk T [K] Based on data from Luca Bottura (CERN, Geneva) Y. Iwasa (04/24/03) 43

44 Computation of I lim for ITER CS (Central Solenoid) CICC Strand dia. (d st ) 0.81 mm Cu/non-Cu (γ) 1.45 Cable # Strands (N st ) 1152 A m = A cu m 2 f p 5/6 P cd = P st h q T c (13 T); Tb m (13 T) 2.93 m 600 W/m 2 K 11.2 K; 4.5 K Ω m A cu 2 d st 4 N st 1 P st d st N st Y. Iwasa (04/24/03) 44

45 (5/6)(2.93 m)( m 2 )(600 W/m 2 K)(11.2 K K) I lim m) 71kA I (40-46 ka) < I op lim c I (96 ka) This CICC design as with CICC designs for the rest of ITER coils are highly stable, i.e. very conservative. Y. Iwasa (04/24/03) 45

46 High-Performance ( Adiabatic ) Magnet J over enhanced by: Combining superconductor and high-strength normal metal (stability; protection; mechanical). Eliminating local coolant* and impregnating the entire winding space unoccupied by conductor with epoxy, making the entire winding as one monolithic structural entity. (Presence of cooling in the winding makes the winding mechanically weak and takes up the conductor space.) High-performance approach universally used for NMR, MRI, HEP dipoles & quadrupoles in which R J B manageable with a combination of composite conductor & monolithic entity. * The conductor always requires cooling but not necessarily exposed directly to the coolant. Y. Iwasa (04/24/03) 46

47 MPZ Concept* Even in an adiabatic magnet, a small normal-state region may remain stable: g j is balance by thermal conduction to the outside region. Corollary: Even an adiabatic magnet can tolerate a disturbance without being driven to a quench How large is this normal state region, R mz, and a permissible disturbance energy? y Region 1 Region 2 ( r> R mz ) R mz x * A.P. Martinelli, S.L. Wipf (IEEE, 1971) Y. Iwasa (04/24/03) 47

48 0 g k k wd r 2 k wd r 2 T 1 (r ) d dr d dr g j r 2 dt 1 dr r 2 dt 2 dr 0 0 g j 6k wd r 2 g j (Region 1) 0 (Region 2) A r Boundary conditions: B; T 2 ( r ) At r, T 2 T op D T op ; r 0, T 1 dt 1 dr r Rmz g j R mg 3k wd dt 2 dr r Rmz C 2 R mz C r C D A 0; r R mz, dt 1 / dr dt 2 / dr : 3 g j R mz 3k wd At r R mz, T 1 T 2 T 1 (r ) B g j r 2 6k wd ; T 2 (r ) T op 3 g j R mz 3k wd r B T op 2 g j R mz 2k wd T 1 (r ) T op 2 g j R mz 2k wd r R mz 2 Y. Iwasa (04/24/03) 48

49 Total Joule Heating G j G j 3 4 pr mz 3 g j 3 4 pr mz 3 k wd dt 1 dr r R mz 2 4 pr mz k wd 2 g j R mz 2 2k wd 3R mz 4 R 3 3 mz g j Because g j 2 2 m J T c T m R mz op 3k wd m J 2 m and T 1 T c at r R mz : R mz 3k wd (T c T op ) J 2 m m With k wd 400W/mK;T m m; J m A/m 2 c 6K; T op 4K; : R mz 1 3(400W/mK)(6K -4K) ( m)( A/m 2 ) 12mm k R wd 2 0.1W/mK mz 2 R mz 1 R mz 1 0.2mm 400W/mK k wd 1 Y. Iwasa (04/24/03) 49

50 With k wd 400 W/mK; T m m; J m A/m 2 c 6K;T op 4K; : R mz 1 3(400W/m K)(6K-4K) ( m)( A/m 2 ) 12mm R mz 2 k wd 2 0.1W/m K R k mz 1 R mz 1 wd 1 400W/m K 0.2mm 2R mz2 2R mz1 Y. Iwasa (04/24/03) 50

51 Energy margin or stability margin, E h : T c R mz1 ) Eh mz C wd (T )dt T op With R mz 2 and h(t op mz 4 ) m, R cu (2 1.3kJ/m 3 : 2 4 R mz 2 3 mz m) 2 ( m) 3 h(t c ) h(t op cu 10 2 m, h(t c ) cu 3.9kJ/m 3, m 3 E h J~ 10 J e h 2.6kJ/m 3 2.6mJ/cm 3 Y. Iwasa (04/24/03) 51

52 Cryostable vs. Adiabatic (High-Performance ) Magnets Basic power density equation: e h g k g j g d g q Cryostable Magnets e h 0; g k g j ; g d g j g j g q J c 0 cd f p P cd A m q fm m ( A s A m ) J c 0 s Y. Iwasa (04/24/03) 52

53 Cryostable Magnets (continued) Observations [J c0 ] cd determined by external parameters. Applied for large magnets (e.g. fusion) in which non-conducting structural materials occupy a significant fraction of the winding pack, making the condition [J c0 ] cd << [J c0 ] s not as important as in adiabatic magnets. Note that coolant, though a key component in a cryostable magnet, is a structural detriment. Y. Iwasa (04/24/03) 53

54 Adiabatic (High-Performance) Magnets e h g k g j g d g q 0 Observations Elimination of coolant within the winding: 1) enhances the overall current density; 2) makes the winding pack structurally robust. [J c0 ] cd no longer limited by external parameters but primarily by [J c0 ] s. Disturbances (g d ) must be eradicated or their energies minimized impregnation of the winding with epoxy resin a widely used technique. High-performance magnets: NMR, MRI, HEP. Y. Iwasa (04/24/03) 54

55 Mechanical Disturbances Premature Quenches & Training Important for adiabatic magnets; not so for cryostable magnets. Through the use of AE (acoustic emission) technique, it has been demonstrated that virtually every premature quench in adiabatic magnets is induced by a mechanical event, primarily either conductor motion or epoxy fracture. Mechanical events usually obey the Kaiser effect, mechanical behavior in cyclic loading in which mechanical disturbances, e.g., conductor motion, epoxy fracture, appear only when the loading responsible for events exceeds the maximum level achieved in the previous loading sequence. An adiabatic magnet thus generally trains and improves its performance progressively to the point where it finally reaches its design operating current. Y. Iwasa (04/24/03) 55

56 Training Sequence for an SSC Dipole S. Ige (MIT ME Dept. Ph.D. Thesis, 1989) Y. Iwasa (04/24/03) 56

57 AE Technique Acoustic signals emitted by sudden mechanical events in a body being loaded or unloaded, e.g., a magnet being charged or discharged; useful for detection and location of a premature quench caused by conductor motion or epoxy fracture event in adiabatic magnets. Piezoelectric Effect The coupling of mechanical and electric effects in which a strain in a certain class of crystals, e.g. quartz, induces an electric potential and vice versa. Discovered by P. Curie in Y. Iwasa (04/24/03) 57

58 AE Sensor Commercially available sensor: expensive ($500-$1000) and even those claimed to be for use in low temperatures generally fail. Home-made (FBML) differential sensor: reasonable ($50/disk + labor); withstands 4.2 K RT cycles. Differential Sensor from Copper pipe cap + + Sensor: two half-disks Cu foil (~25 m) Brass foil (~75 m) Y. Iwasa (04/24/03) 58

59 AE Instrumentation LabVIEW Oscilloscope AE Sensor Filter 10k 1MHz Pre-amp e.g. 40 db Filter 200k 230kHz Amplifier e.g. 43 db Discriminator <0.1 V Counter Recorder Y. Iwasa (04/24/03) 59

60 Identification of Quench Causes A combination of voltage and AE monitoring permits identification of three distinguished causes of a quench in adiabatic magnets. Conductor motion: a voltage spike and the start of AE signals. Epoxy fracture: no voltage spike but AE signals. Critical current: no voltage spike nor AE signals. Y. Iwasa (04/24/03) 60

61 Three Causes of Quench Epoxy cracking NO voltage pulse AE Conductor-motion Critical current Voltage pulse AE O. Tsukamoto, J.F. Maguire, E.S. Bobrov, Y. Iwasa (Appl. Phys. Lett. Vol. 39, 1981) Y. Iwasa (04/24/03) 61

62 A Conductor-Motion Induced Quench Isabella Dipole AE AE V 5 ms 50 ms O. Tsukamoto, M.F. Steinhoff, Y. Iwasa (IEEE, 1981) Y. Iwasa (04/24/03) 62

63 Conductor-Motion Induced & Critical-Current Quenches An SSC Dipole AE AE Located farthest from the source Due to heating AE Voltage Voltage scale too large for a spike I q = 6510 A NO AE signals! Voltage I c = 6828 A S. Ige (MIT ME Dept. Ph.D. Thesis, 1989) Y. Iwasa (04/24/03) 63

64 Conductor Motion Frictional heating energy release, e f, due to a Lorentz-force induced conductor motion ( slip ) of r f : e f f f r f f J B z r f With f 0.3, J A/m 2, B z 5T, ande f h cu (5.2K) - h cu (4.2K) = 1300J/m r f 3 : Lr e f f J B z (1300J/m 3 ) (0.3)( A/m 2 )(5T) 20 m Actually a conductor slip as small as ~1 m ( microslip ) can drive a short length of the conductor to the normal state, leading to a premature quench. Y. Iwasa (04/24/03) 64

65 Friction/Quench Experiment F t AE Sensor F n G705 B (5 T) F n F n F t AE Sensor Search Coil Conductor Braid I I F t I B Helmholtz Coil F n Based on O. Tsukamoto, H.Maeda, Y. Iwasa (Appl. Phys. Lett. Vol. 40, 1982) Y. Iwasa (04/24/03) 65

66 Slip Distance from Extensionmeter V ( t ) z d dnab dt dt V ( t ) dt NA db dz known mea NA db dz dz dt Search coil (N, A) V(t ) z (t ) B(z ) Slip Distance from Voltage Pulse V(t ) V ( t ) z d d lzb dt dt V ( t ) dt lb known mea lb dz dt I l F t ; z B Y. Iwasa (04/24/03) 66

67 Friction Experiment Quench Experiment Search Coil Slip-Induced voltage spike 2 mv AE 1 ms Slip distance: ~1 m Peak slip velocity: ~ 1 cm/s F n =2000 N; F t ~400 N Slip distance: ~1 m Peak slip velocity: ~ 3 cm/s F n =2000 N; F t =500 N [=(0.025 m)(4000 A)(5 T)] Y. Iwasa (04/24/03) 67

68 Observation of Kaiser Effect Friction Experiment Quench Experiment H. Maeda, O. Tsukamoto, Y. Iwasa (Cryogenics Vol. 22, 1982) Y. Iwasa (04/24/03) 68

69 Y. Iwasa (04/24/03) 69

70 Epoxy Cracking Inducted Heating Stored elastic energy density, e el, typical epoxy resin: e el 2 el ( Pa) J/m 3 2 E el 2(10x10 9 ) 2 e f Nb-Ti/Cu composite Epoxy coating Y. Iwasa (04/24/03) 70

71 Epoxy Cracking Inducted Heating Experimental Results T 1 F t T 1 Nb-Ti/Cu composite T 2 T 2 max T 3 Epoxy coating 1K T 4 AE Sensor max T 3 T 4 AE from Y. Yasaka, Y. Iwasa (Cryogenics Vol. 24, 1984) Time [ms] Y. Iwasa (04/24/03) 71

72 Stability of HTS Operating Temperature Ranges 0 ~10 ~100 T op [K] LTS HTS [T cs T op ] HTS > ~10 [T cs T op ] LTS Y. Iwasa (04/24/03) 72

73 Heat Capacity Data [C p (T op Range)] HTS 1 [C p (T op Range)] LTS A. Helium (10 atm) B. Helium (1 atm) C. GE varnish D. Stainless steel E. Nb-Ti F. Epoxy G. Silver H. Copper I. Aluminum Y. Iwasa (04/24/03) 73

74 Enthalpy Data [e min ] HTS 1 [e min ] LTS 1. Silver 2. Copper 3. Aluminum Y. Iwasa (04/24/03) 74

75 Minimum Thermal Energy Density C p (T): copper; T c : Superconductor e min = e min Top+ T Top T op Cp(T )dt T op T op ( T )dt C cd Y. Iwasa (04/24/03) 75

76 HTS Stability >> LTS Stability Y. Iwasa (04/24/03) 76