AC losses in reversible niobium

Losses at 4.2 K in a cylinder o f magnetic reversible niobium subjected to a sinusoidal magnetic field within a frequency range o f 2 0 - 2 6 0 c s"1 are reported as well as waveforms related to the penetration of magnetic flux. The observed phenomena are interpreted by considering both the shielding o f the bulk by currents at the surface and the existence o f an average flux flow resistivity corresponding to the viscous damping o f the flux motion.

AC losses in reversible niobium C. S. Furtado

The use and application of superconductors in dc devices is widespread and their behaviour is reasonably well understood. However, in ac applications the situation is not so simple and further research is needed to enlarge the utilization of superconductors in ac devices. The limitation of the use of superconductors in the ac regime arises from the onset of losses due either to hysteresis or viscous damping of the movement of fluxoids. It is accepted that these losses are strongly dependent on the field of first penetration, Hfp, which is (or is nearly equal to) the first critical field, He1. Thus, materials with high value of Hfp must be used in ac applications and among them niobium-is at the present considered most favourably. There is some literature on ac losses and flux penetration in niobium. 1-12 The phenomena reported there have been explained on the basis of hysteretic models: the Buchhold 2 and critical state 13 models. So far, however, ac measurements on niobium with reversible magnetic properties have not been reported. In this paper experimental results obtained in almost ideal niobium are presented. They are interpreted in terms of damping of the flux motion by viscous forces rather than in terms of any hysteretic mechanism.

where p is the perimeter of the sample and ~, is the derivative in relation to the time of the magnetic flux, qb, across the sample. Fig. 1 shows the general arrangement for the solenoid, pick-up coil, and sample used in these measurements. The pick-up coil was wound on a tufnol former and was made of two sections: the inner one with 1 970 turns and a mean diameter of 5.8 mm approximately and the outer one with 660 turns and a mean diameter of 11.2 mm approximately.

p coil

oid

Experimental methods

I¢

Measurement technique. The loss per cycle per unit volume, Wv, is given (cgs units) by

wv =

4' cv

HedB

(1)

Jp 'coil

cle

where H e is the instantaneous value of the external magnetic field and B is the instantaneous value of the mean induction across the sample. In the case of a cylinder subjected to a periodical field of period r, appropriate transformations of relation will give the loss per cycle per cm 2 of surface, Ws: I

ws =

4•pfT"

He+dt

(2)

0

The author is now with the Laboratorio de Fisica, Universidade, Coimbra, Portugal. This research was carried out at the Clarendon Laboratory, University of Oxford, Oxford, UK. 17 August 1971.

C R Y O G E N I C S . A P R I L 1972

t|

screw

Fig.1 Sample holder and pick-up coil

129

Solenoid I

I

I

t

I L ---

L ~

Oscilloscope

-) Oscilloscope

P

Ammeter

Fig.2 Block diagram of the circuits

These two sections were connected in series opposition and designed in such a way that the product of the number of turns and the cross-sectional area was the same for both the sections within 1 part in 104. With this pick-up coil, magnetization and flux penetration measurements could be carried out in any sample with a diameter less than 4.2 mm. The magnetic field was provided either by a nitrogen cooled copper solenoid or by an NbY5ZrX5 superconducting solenoid. A schematic diagram of the electronics is given in Fig.2. The pick-up coil was compensated in amplitude by the potential divider PI and in phase by a phase-shift network. This compensation was effected at an external field approximately equal to half the field of first penetration, Hfp, in such a way that neither losses were measured nor any penetrating flux signal was displayed on the oscilloscope. Confirmation, that this compensation was correct, was further obtained by the clear evidence of portions of the oscillograms @versus time in which @ = 0 (Fig.3). The measuring system was calibrated by comparison with direct measurements of losses using a calorimetric method. The sensitivity was of the order of 0.1 erg per cycle cm2 ( loo8 J per cycle cm2) for a field of fist penetration approximately equal to 1 500 Oe (1 Oe = 79.5 A m-l). The existence of end effects was not considered since the profile of the magnitude field was such that at the ends of the sample, the magnitude of the field was considerably lower than at the centre, where the pick-up coil was located. The sample was a cylinder of niobium, 5 cm long and with a 3.03 mm diameter. It was annealed and outgassed in ultra-high vaccum (lo-lo torr [l torr = 133 N mm2]) for 24 hours at a temperature just below its melting point, having then been chemically polished in a solution of 30% HF, 70% HNO,. Its resistivity ratio (p300 KIp4.2 K in H = 8 kOe) was equal to 3 400 and the first magnetization curve and loops in quasi-static regime did not show any appreciable hysteresis. Sample.

Experimental

He. Fig.3 shows for an external peak field of 2 200 Oe at 60 cs-1 and 4.2 K how @ varies with time together with the waveform of the external field versus time. It can be seen by the interval of time in which Cp= 0 that there is shielding of the bulk by the surface. It is worth noting that the beginning of the shielding appears later than the peak of the external field. This behaviour is different from the findings so far reported (for example, references 8 and 11). In Fig.4 the flux penetration into the sample and also the external field as function of time are also shown for He (peak) = 2 200 Oe, f = 60 and T = 4.2 K. It is clear that the maximum value of the penetrated flux is reached after the external field has passed through its peak. The flat horizontal portion observed is a result of the surface

cs-* ,

Fig.3 Time derivative of penetrated at 2 200 Oe and 60 c s.-’ (4.2 K)

flux against time [& = &

ttll

results

We have measured the losses as well as the oscillograms obtained of: (a) the flux penetration (a) into the specimen

130

versus time (t), (b) the time-derivative of this flux (a) versus time, and (c) and loops of the flux versus external field,

Fig.4 Penetrated 6Ocs-’

flux against time [@ = @ ttll at 2 200 Oe and

CRYOGENICS.

APRIL 1972

Discussion

Fig.5 Loop of penetrated flux against external field [~ = 4, (He)] at 2 200 Oe and 60 c s"1 (4.2 K) I.Oio+5

_~/-

35 cs-'

_~A

20

cs-r

.,,G-;o<.; / 1.010+4

~

bi

o 260 cs-I

//pp/ ~,a

A 11,4' I

&-'E u 1"OIo+3

t

T U

OI u Q.

LO,o+2

o

N

i:/,H/

m i.Oto+ I

As we shall see, the experimental results reported in the previous section lead to the conclusion that the losses are mainly due to the viscous forces 14 opposing the motion of fluxoids. This has not been the case of the ac losses reported so far, 1 11 the nature of which has been ascribed to a pinning mechanism. In the present case one is bound to eliminate the contribution of the pinning to the losses and to explain the results obtained on the basis of the concept of flux flow resistivity. 14 The fact that ~ becomes zero later than the peak value of the external field (Fig.3), or in other words, the maximum value of the external field is lagging behind the •peak of the external field (Figs 4 and 5), can be understood in identical terms to those involved in the skin effect in metals. 15 Also the fact that for high values of the peak field (He ~ 2 200 Oe) the loss per cycle varies as the square of the external field, which is characteristic of the response of metals to sinusoidal magnetic fields, supports the view that the losses must derive from the damping of the motion of fluxoids by viscous forces (flux flow resistivity). Finally the variation of the loss per cycle with frequency (Fig.7) shows that the mechanism causing the losses is not of hysteretic nature but instead of the eddy-current type. Furthermore, the decrease of slope of the loss-frequency curves (that is, decrease of Inll in w s ecf nl ) with the increase of the external peak field suggests the consideration of a flux flow resistivity. Of, in the terms proposed by Kim et al, 14 to explain the difffision of the fluxoids inside the sample. In fact this decrease in In1[ can be accounted by the increase in the flux flow resistivity with the external field, as it is predicted by the Kim's relation 14 B

g I

I.Oio + O

14OO

P / = On ttc2

l-O,o+S J 18OO

' 2200

J 2800

3600

E x t e r n a l field, Oe Fig.6 Loss--field curves at 4.2 K

screening field M/.13 Both these features appear clearly in the ~ - H e loop of Fig.5. In Fig.6 the energy loss is plotted against the peak of the external field. For comparison with previous measurements this loss is expressed in erg per cycle cm 2. The onset of the losses occurs at that value of the external field at which penetration of the flux into the specimen was observed in the q5 versus time oscillograms. It was verified that this field, called the field of first penetration, Hfp, is the same as the first critical field, Hcl, as measured 15~¢the first magnetization curves in quasi-static regime for various temperatures. The loss increases steeply (n --~ 50 in w s ccH n) with the external field until a peak value of about 1 700 Oe is reached. Then all the curves, for different frequencies, exhibit a bend, until for an external field of about 2 200 Oe, they begin to increase again linearly with He(n ~- 2

=2192 Oe H855

)1710 Oe

IU

i E ,<

g

d623 O¢ o; O

O ]1577 Oe

1Oio+ I -

in ws=nn). In Fig.7 the loss per cycle cm 2 is shown against frequency f, for different values of external peak field. Considering a dependence of the type w s ocf nl one can see that n 1 is always negative and that its modulus decreases with the peak field.

CRYOGENICS

. APRIL

1972

Oe

,1490 Oe 1446 Oe IOl°+Cl6

20

35

60 120 Frequency, c s -~

260

Fig.7 Loss--frequency curves at 4.2 K

131

iO s

.

has been considered applicable since the skin depth 6L corresponding to the flux flow resistivity pfis much smaller than the radius of the sample, R. Even at the lowest value of the frequency range, 20 c s"l , and for the normal resistivity at 4.2 K, the skin depth 6n is smaller than the radius of the sample. The boundary condition imposed on equation 3 was evaluated by subtracting from the external field the field produced by the surface currents. Fig.8 shows together with the experimental curve, some loss-field curves evaluated by assuming different values of the average flux flow resistivity. The experimental curve roughly agrees with the evaluated one for the high values of the external peak field (2 4 0 0 - 3 400 Oe). Nevertheless we conclude that the model will be acceptable if the average flux flow resistivity, ~-f, is considered to vary with the external peak field according to a relationship defined by the intersection of the observed and evaluated curves. For the present case this dependence is shown in Fig.9.

IO-9

(5 I°

104

/ •

,

/

/

~

l(Sil

?

103

I

II t-

'E u

L iO 2

Conclusions

o~

The ac losses reported here were mainly due to viscous forces opposing the movement of fluxoids in the bulk of the specimen. A simple model considering an average flux flow resistivity constant for each peak of the external field gives a reasonable account of the observed phenomena. This leads to the acceptance of the flux flow resistivity concept not only in situations in which the external conditions are static (Kim's experiment) but also for those, as presented here, under dynamic external conditions.

/ iO I

,o°

"

1400

I

1800

I

I

2400 3400 H e , O e (I Oe=79.4 Am -I )

,0-9 Fig.8 Loss--fieldcurvesat 4.2 K; experimental -- dotted line, evaluated -- full line

An important point to be taken into consideration in type II superconductors with low negative surface tension (low Ginzburg-Landau parameter K), as in the present case, is that of the existence of Meissner currents. If for hard superconductors the surface currents can in many cases be disregarded, this is not so in the case of low K materials because the magnetization due to Meissner currents is of the order of the external field. This partly accounts for the steep slope of the loss-field curves at the onset of the losses (Fig.6). Furthermore irreversible currents are set up at the surface as the flat portions of the curves of Figs 3, 4, and 5 show. It should be mentioned here that, contrary to what has been suggested as, for example, in reference 16, no surface screening field AH was found just below Hcl, once the field of first penetration, Hfp, has coincided with Hcl for different values of temperature. A simple model considering an average flux flow resistivity ~-fas constant for a given external peak field and taking into account the surface currents (Meissner and irreversible ones) has been used. The field equation O2B

aX 2 -

132

4n

id °

E u O~

1(5II

L

'i(~-

-12

IO

1500

2000 He , O e (I O e = 7 9 . 4 A m -I)

2500

OB

C P--fall

(3)

Fig.9 Average flux flow resistivity against peak external field

(4.2K, 60cs "1)

C R Y O G E N I C S . A P R I L 1972

It has been found further that the surface starts to shield the bulk only when the fluxoids begin to change the direction of their movement across the surface and not when the external field reaches its peak.

4. 5. 6.

I wish to express my gratitude to Dr K. Mendelssohn, FRS, for his encouragement and for suggesting this work. I would also like to thank Mr A. Garratt-Reed for preparing the sample and Mr T. S. l~adhakrishnan for the literary correction of the manuscript. It is a pleasure to acknowledge the scholarship provided by the Calouste Gulbenkian Foundation and the lnstituto de Alta Cultura (Portugal) for granting leave of absence from the Physics Department of the University of Coimbra (Portugal).

7. 8. 9. 10. 11.

REFERENCES 1. 2. 3.

BUCHHOLD, T. A., and MOLENDA, P. J. Cryogenics 2, 344 (1962) BUCHHOLD, T. A. Cryogenics 3, 141 (1963) RHODES, R. G., ROGERS, E. C., and SEEBOLD, R. J. A. Cryogenics 4, 206 (1964)

12. 13. 14. 15.

16.

ROCHER, Y. A., and STEPFONDS, J. Cryogenics 7, 96 (1967) EASSON, R. M., and HLAWlCZKA, P. BritJAppl Phys 18, 1237 (1967) DAMMAN, C., SANTAMARIA, E., MALDY, J., and DONADIEU, L. Phys Lett 24A, 575 (1967) TAKANO, N. Proc ICEC1, Kyoto, 1967, p 184 (Heywood-Temple, 1968) EASSON, R. M., and HLAWICZKA, P. Brit J Appl Phys (J Phys D) 1, 1477 (1968) BEALL, W. T., Jr, and MEYERHOFF, R. W. Jr. Appl Phys 40, 2052 (1969) SALMON, D. R., and CATTERALL, J. A. BritJ Appl Phys (J Phys D) 3, 1023 (1970) LINFORD, R. M., and RHODES, R. G. JAppl Phys 42, 10(1971) BEAN, C. P. Rev Mod Phys 36, 31 (1964) ULLMAIER, H. A. PhysStatSol 17, 631 (1966) KIM, Y. B., HEMPSTEAD, C. F., and STRNAD, A. R. Phys Rev 139, A1163 (1965) LANDAU, L. D., and LIFSHITZ, E. M. Electrodynamics of Continuous Media, Ch 7 (Pergammon, 1960) WlPF, S. L. Proc Summer Study on Superconducting Devices, Brookhaven, p 511 (1968)

Low Temperature Physics Conference The Low Temperature Division of the European Physical Society are organizing a special flight to the 13th International Low Temperature Physics Conference taking place in Boulder, Colorado on 2 0 - 2 6 August 1972. The planned schedule is: 20 August - leave Amsterdam, arrive Denver in afternoon 2 1 - 2 5 August - attend Low Temperature Conference 3 - 4 September - return flight New York-Amsterdam The price of the entire trip Amsterdam-New Y o r k - D e n v e r - N e w York-Amsterdam will be fl 1680 (£205). This price is based on a minimum of 30 participants. Participants must travel as a group on the transatlantic part of the flight but once inside the USA they are free to make their own flight arrangements, but intermediate stop-offs on the Denver-New York flights may increase the price of the air ticket. Anyone interested in taking part in this flight should contact: Dr J. N. Haasbrock Kamerlingh Onnes Laboratorium N ieuwsteeg 18 Leiden The Netherlands

CRYOGENICS. APRIL 1972

133