2. Dissipation mechanisms: Resistive Eddy currents Flux pinning Coupling currents

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1 AC loss par I Fedor Gömöry Insiue of Elecrical Engineering Slovak Academy of Sciences Dubravska cesa 9, raislava, Slovakia elekgomo@savba.sk

2 Ouline of Par I: 1. Wha is AC loss 2. Dissipaion mechanisms: Resisive Eddy currens Flux pinning Coupling currens 3. Possibiliies for AC loss reducion 4. Mehods o measure AC loss

3 Ouline of Par I: 1. Wha is AC loss 2. Dissipaion mechanisms: Resisive Eddy currens Flux pinning Coupling currens 3. Possibiliies for AC loss reducion 4. Mehods o measure AC loss

4 Wha is undersood under AC loss = amoun of hea released during operaion in cyclic (or ransien) regime i does no appear in DC regime is no a propery of maerial bu of a (superconducing) objec operaing in well defined condiions (emperaure, ranspored curren, applied magneic field)

5 Ouline of Par I: 1. Wha is AC loss 2. Dissipaion mechanisms: Resisive Eddy currens Flux pinning Coupling currens 3. Possibiliies for AC loss reducion 4. Mehods o measure AC loss

6 P [W/m] Resisive AC loss does no fall under he definiion of AC loss because i is due o saic E(j) relaion E can be calculaed from E(j) j 1.E+02 1.E+01 1.E+00 1.E-01 1.E-02 P res P mag P ran - daa P ran - model 36 Hz 72 Hz 144 Hz 36 Hz 72 Hz 144 Hz 36 Hz 72 Hz 144 Hz 1.E-03 1.E I rms [A] should be marginal in nominal operaing regime

7 Ouline of Par I: 1. Wha is AC loss 2. Dissipaion mechanisms: Resisive Eddy currens Flux pinning Coupling currens 3. Possibiliies for AC loss reducion 4. Mehods o measure AC loss

8 Eddy curren loss induced currens in meallic pars reaed in exbooks of elecromagneism (skin effec, inducive heaing) peneraion deph d 2 0 meal resisiviy frequency (angular) magneic permeabiliy of vacuum shielding of magneic field if d << wall hickness negligible if d >> hickness of meallic objec should be marginal in nominal operaing regime

9 Ouline of Par I: 1. Wha is AC loss 2. Dissipaion mechanisms: Resisive Eddy currens Flux pinning Coupling currens 3. Possibiliies for AC loss reducion 4. Mehods o measure AC loss

10 Hyseresis loss in superconducor because of magneic flux pinning in superconducor (he mechanism securing high curren ranspor capaciy i.e. large criical curren densiy in magneic fields >> 1 T ) hard = ype II superconducor wih flux pinning criical sae model Ch. P. ean 1962: j 0 in he places ha never experienced elecrical field j c elsewhere simples version: j c independen of E, j c = cons. someimes call he ean model

11 Transpor of elecrical curren e.g. he criical curren measuremen I 0 A 20 A 100 A j =0 j =+ j c 80 A 20 A 0 A j =- j c

12 Transpor of elecrical curren AC cycle wih I a less han I c : neural zone A

13 AC ranspor in hard superconducor : is i sill wihou dissipaion? Q T IUd Id neural zone: j =0, E = 0 U check for hyseresis in I vs. plo U Φ

14 [Vs/m] AC ranspor loss in hard superconducor 1.5E E E E E E E-05 I [A] hyseresis dissipaion AC loss

15 [Vs/m] AC ranspor loss in hard superconducor 1.5E E E E E E E-05 I [A] hyseresis dissipaion AC loss

16 Hard superconducor in changing magneic field mt mt

17 Hard superconducor in changing magneic field dissipaion because of flux pinning a y x volume loss densiy Q [J/m 3 ] magneizaion: M S Q V x. j( x, a d M y)dxdy

18 M [A/m] Round wire from hard superconducor in changing magneic field M s 3.E+04 2.E+04 1.E+04 0.E+00 p -1.E+04-2.E+04-3.E [T] M s sauraion magneizaion, p peneraion field

19 M [A/m] Round wire from hard superconducor in changing magneic field 3.E+04 esimaion of AC loss a a >> p 2.E+04 1.E+04 0.E+00-1.E+04-2.E+04-3.E [T] Q 4 M a s V

20 Slab in parallel magneic field analyical soluion Q 4 a M s j peneraion field w 2 0 w j c p p a p p a V Q p c s w j M

21 Q/V [J/m] Slab in parallel magneic field analyical soluion 1.E+05 1.E+04 Q 4 a M s 1.E+03 1.E+02 1.E+01 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 1.E-08 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 a [T] jc=10^8 A/m2, w=1 mm (p = 63 mt) jc=10^8 A/m2, w=0.1 mm (p = 6.3 mt) jc=10^7 A/m2, w=1 mm (p = 6.3 mt) jc=10^7 A/m2, w=0.1 mm (p = 0.63 mt)

22 Ouline of Par I: 1. Wha is AC loss 2. Dissipaion mechanisms: Resisive Eddy currens Flux pinning Coupling currens 3. Possibiliies for AC loss reducion 4. Mehods o measure AC loss

23 Coupling loss - wo parallel superconducing wires in meallic marix a coupling currens in he case of a perfec coupling: mt

24 M [A/m] Magneizaion of wo parallel wires 2.E+05 1.E+05 5.E+04 0.E+00 uncoupled: -5.E+04-1.E+05 coupled: -2.E [T] how o reduce he coupling currens?

25 Composie wires wised filamens l p good inerfaces bad inerfaces m m S S SC m j j l p 2

26 Composie wires wised filamens coupling currens (parially) screen he applied field i l 0 p ime consan of magneic flux diffusion A.Campbell (1982) Cryogenics 22 3 K. Kwasniza, S. Clerc (1994) Physica C K. Kwasniza, S. Clerc, R. Flukiger, Y. Huang (1999) Cryogenics Q V 2 max Q V 2 max round wire fla wire round 0 2 A

27 Ouline of Par I: 1. Wha is AC loss 2. Dissipaion mechanisms: Resisive Eddy currens Flux pinning Coupling currens 3. Possibiliies for AC loss reducion 4. Mehods o measure AC loss

28 Hyseresis loss: a large fields proporional o p ~ j c w = loss reducion by eiher lower j c or reduced w widh of superconducor (perpendicular o he applied magneic field) lowering of j c would mean more superconducing maerial required o ranspor he same curren hus only plausible way is he reducion of w

29 M [A/m] effec of he field orienaion perpendicular field 2.E+05 parallel field 1.E+05 5.E+04 0.E+00-5.E+04-1.E+05-2.E [T] Q 4 M a s V

30 Q/V [J/m 3 ] Magneizaion loss in srip wih aspec raio 1: E+07 1.E+06 1.E+05 H 1.E+04 1.E+03 1.E+02 H 1.E+01 1.E+00 1.E-01 1.E-02 1.E-03 parallel 1.E-04 1.E-05 perpendicular 1.E-06 1.E-07 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 H max [A/m] Q 4 M a s V

31 in he case he ape orienaion is no a free parameer = reducion of he ape widh sriaion of CC apes ~ 6 imes lower hyseresis loss

32 sriaion of CC apes bu in operaion he filamens are conneced a magne erminaions coupling loss will be he main issue

33 Coupling loss: a low frequencies proporional o l 0 p ransposiion lengh effecive resisiviy = filamens (in single ape) or apes (in a cable) should be ransposed = low loss requires high iner-filamen or iner-ape resisiviy bu good sabiliy needs he opposie

34 Ouline of Par I: 1. Wha is AC loss 2. Dissipaion mechanisms: Resisive Eddy currens Flux pinning Coupling currens 3. Possibiliies for AC loss reducion 4. Mehods o measure AC loss

35 Experimenal mehods for AC loss deerminaion Tape Cable Magne

36 Experimenal mehods for AC loss deerminaion Shape of he exciaion field (curren) pulse ransiion unipolar harmonic relevan informaion can be achieved in harmonic regime final esing necessary in acual regime

37 Experimenal mehods for AC loss deerminaion 1.Thermal a) cooling power (large devices) b) boil-off c) emperaure profile 2. Elecrical - lock-in echnique - Y(I) hyseresis loop regisraion

38 Uc[uV] P [W/m] emperaure profile mehod Curren DC, AC Volage aps 1.E-01 1.E-02 P hermal P elecrical 1.E-03 1.E-04 Thermal insulaion 1.E-05 Thermocouple 1.E I rms [A] 6 5 Series1 Linear (Series1) P~T 4 y = x P = (Uc-.145)/ P [mw/m]

39 Elecrical mehod AC power supply AC power flow AC loss in SC objec Q 1 AC cycle Power.d Q T U()I().d Power meer Lock-in amplifier

40 Elecrical mehod Lock-in amplifier (phase sensiive deecion a fundamenal componen) so called in-phase and ou-of-phase signals U U S C u u m m ( )sin d ( )cosd u m - measured volage reference signal necessary o se he frequency phase aken from AC curren

41 Fundamenal problem of elecrical mehods for AC loss deerminaion AC power supply AC power flow AC loss in SC objec

42 Soluion 1- deecion of power flow o he sample AC power supply AC power flow AC loss in SC objec

43 Soluion 2- eliminaion of parasiic power flows AC power supply AC power flow AC loss in SC objec

44 ideal magneizaion loss measuremen: a ex cos Area A ) ( ) ( )d ( 1 ) ( d ) ( d d ) ( d ) ( in M A A A u ex A m m pick-up coil wrapped around he sample induced volage u m () macroscopic magneizaion of he sample conains higher harmonics d dm d d A u ex m ) ( ) ( ) ( ( ) 1 "sin 'cos ) ( n n n a n n M M M Q T a T )d "cos( ) cos( d d d ) ( 1 d H M = 0 = = /2 = 3/2 " 0 2 Q a Lock-in amplifier

45 Real magneizaion loss measuremen: Pick-up coil Calibraion necessary sample M C ud by means of: measuremen on a sample wih known properries calibraion coil numerical calculaion

46 Loss measuremen from he side of AC power supply: LOCK-IN channel A channel Rogowski coil LN 2 generaor AMPLIFIER ransformer I m sample power supply P I sample m U

47 Loss measuremen from he side of AC power supply: Y(I) hyseresis loop regisraion for superconducing magne (Wilson 1969) Ud Y y x RI I

µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ

µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high