1. AC Losses Measurements at SOTON 1

2. Objectives 2  Comparison between twisted and non-twisted  Decoupling by twisting: effective diameter of (de)coupling  Characteristics of the coupling current: o Time constant o Transverse resistivity o Flux fill factor

3. Method 3 B 0 cos(2πft)  Applied sinusoidal field o B 0 ≤ 0.2 T o 5Hz ≤ f ≤ 2kHz  Measurements o 3K ≤ T ≤ 100K o Single-turn saddle pick-up coil o Sample length L ≤ 100mm L ≤ 100mm  Strength:Wide frequency range for detailed probing of the coupling current: essential for twisted filaments.  Limitation: No DC field  Mitigation: Extended range of temperature

4. Work so far: OST’s Twisted Bi2212 Round Wires 4 X-Ray Tomography  Diameter 1.2mm  1530 filaments in 85x18 configuration  Twist pitch: 8mm, 12mm, ∞ (no twist)

5. Summary: Details at ASC 2MOr2B- 02 1.Coupling current loss and hysteretic loss resolved 2.Coupling current time constant directly measured 3.Effective size of coupled diameter determined 4.Matrix transverse resistance determined 5.Classical theory works well, if low flux fill factor is considered. 5

6. Twisting is still necessary for striated YBCO: Based on the data from Amemiya 6 At 0.5 mT, 10-1k Hz, the measured loss and calculated loss is compared to determined the transverse resistance between filaments. R t =4.8  m → ρ t ~ 1  m Rutherford Criterion for coupling length: λJ c =J e ~ 5x10 8 A/m 2 a = w f = 0.2mm L c (10mT/s)~13m L c (100mT/s)~4m Note that reduction of filament size w f will reduce the coupling length even further. In real coils, filaments in a striated conductor will couple together.

7. Proposal for Roebel conductors 7 Step 1: single strand Three pick-up loops: decoupling at the corner? Step 2: Double strands Insulated at crossing Pressure contact at crossing Soldered at crossing Step 3: Roebel segments of several layers Looking forward to receiving strands (offcuts really!) from KIT to start step 1&2

8. Untwisted Wire: Monolithic behaviour i.e. fully coupled 8 Rutherford Criterion for coupling length: Jc < 5000 A/mm 2 D sw ≤ a ≤ D Sinusoidal field L c max (1mT,20Hz/90mT/s)=75mm Fully coupled in 100mm Sweep DC magnetisation L c max (1mT,1Hz/4.5mT/s)~500mm Likely decoupled

9. Untwisted Wire: Loss factor and full penetration field B p 9 Loss factor reveals more details. with full penetration field at peak: and scales with normalized field Obtain B p without saturation

10. Twisted Wire: decoupling evident 1.Uncoupling seen in the twisted wire below and above the saturation field B p. 2.Loss reduced above B p as desired o Found at 60K o B p not reached at 5K 3.Loss increased below B p : o Inevitable o Applications always in B>B p 4. Q(B 0 ) visibly less steep at low field: coupling current? 10

11. Twisted Wire: Loss factor and coupling current loss  Flowing parallel to the field in the matrix, the coupling current is an eddy current.  Its loss is proportional to B 0 2,  Hence a constant loss factor 11

12. Twisted wire: Temperature effects Coupling current loss increases at low temperature and saturates for T <= 20K where resistance settles at the residual level. Loss at higher field appears from uncoupling sub-wires:  Hysteresis loss “like”  With a full penetration field B p  B p low than non-twisted  Loss factor scales with normalized field β=B 0 /B p. 12

13. Twisted Wires: different twist pitch and Loss factor scaling 13 Hysteresis loss independent of pitch:  no Jc degradation at a shorter pitch  no change in the size of uncoupled bundle. Coupling current loss reduces twist pitch, ~ L P 2

14. Effective Diameter of Coupling 14 X 2.5  B p of twisted wire is 40% of non-twisted wire.  Hence D eff ~ 1.6D i ~ 0.4mm.  Not unexpected: filaments not twisted relatively within sub- wire.

15. Coupling Current Coupling current loss is frequency dependent: with a time constant: Identified by the peak position 2πfτ f =1. Evident before hysteresis loss fully takes over. 15 The peak loss of 0.16= π λ f /2 suggests a low flux fill factor of λ f ~ 0.1 consistent with uncoupling at sub-wire level: large diamagnetic moment within.

16. Time constant and effective transverse resistance 16 Time constant is in milliseconds! And scales with L p 2 Transverse resistance ρ et  Independent of twist  Consistent with Ag resistivity of RRR~100  Resistivity within the sub-wire irrelevant  Low constant resistance between sub-wires