Method for determining transverse resistivity of multifilamentary superconducting composites with high resistivity matrix

Method for determining transverse resistivity of multifilamentary superconducting composites with high resistivity matrix M. Pol~ik, L. Jan/ifik and M. Majoro~, Institute of Electric Engineering, Slovak Academy of Sciences, Bratislava, D0bravskd cesta 9, Czechoslovakia

Received 20 September 1989; revised 19 February 1990 A simple method for determining transverse resistivity of multifilamentary composites with high resistivity matrix is described. The transverse resistivity is evaluated from magnetization curves measured at two or more amplitudes of the sinusoidal external magnetic field at one frequency.

Keywords: multifilamentary wires; measuring methods; magnetization

The transverse resistivity p ± of multifilamentary superconducting composites is an important parameter for the study of coupling losses in multifilamentary wires for 50 Hz applications. Several methods for measuring P l' are known. The method currently used consists of measuring the total losses Wat the frequencyfof the applied field and the hysteresis losses Wh at f - - O. From coupling losses W~ = W - Wh the parameter p . can be evaluated as 1

p±

-

-

2 2 wBmLp - -

47rWc where ¢0 = 2~rf, Lp is the twist pitch and B m is the amplitude of the external magnetic field. Another way of obtaining W~ is based on measurement of the total losses at two different frequencies 2. Direct measurement of p ± requires special samples 3. A method based on the selffield effect may also be used 4. In this paper a method which enables estimation of p ± from magnetization curves measured at various amplitudes at one frequency only is proposed.

Theory Let us consider a multifilamentary superconducting composite with high resistivity matrix, exposed to the sinusoidal external magnetic field B(t) = Bmsinca. The total magnetization M(t) of such a composite is the sum of the hysteresis magnetization Mh(B) due to the magnetization currents in individual filaments and the ratedependent magnetization due to the screening currents flowing through the matrix, Ms(B, B). Generally, the macroscopic screening currents may influence the magnetic field seen by the filaments. As a result, hysteresis

losses Mh become frequency dependent. Assuming that B ( t ) < < Bp/ro (where Bp is the magnetic field of full filament penetration, ro is the time constant of the macroscopic screening currents), the macroscopic screening of the composite filaments is small and the filament hysteresis losses are frequency independent 5. In the model Jc = const, the full penetration magnetic field is given by Bp = #oJcro, where Jc is the critical current density and ro is the filament radius. For NbTi composites for 50 Hz application Jc -> 5 × 109 A cm -2 and r o _< 5 X 10 -6 m . S o for these composites we get Bp ___0.03 T. The time constant ro is given by 5

T°

(1)

8~2p±

For the composites mentioned above p± _> 5 × 10 -8 ~2 m (Reference 1), L o _ 5 × 10 -3 m and from Equation (1) one obtains ro - 8 × 10 -6 s. This means that at 50Hzro< 625 T s -l. So the hysteresis losses are frequency independent for dB/dt = B(t) lower than this calculated value. For B(t) we have B(t) = wBmcoSwt. This means that, for higher amplitudes of Bm, M h can be supposed to be independent of B if we estimate M at time t far enough from zero

(t/T > 0). For a sinusoidal external magnetic field in the region of frequency independent hysteresis losses the magnetization due to the screening currents Ms(t) is given by 5

2 7"0wBm MAt)

-

(1 + Cd2To 2)

(cosc0t + C0rosinwt - e -t/7o)

(2)

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Method for determining transverse resistivity: M. Poldk e t al. For t > > ro and Wro < < 1 Equation (2) transforms to

tt = w -larcsin(B*/Bml)

(6a)

- M s ( t ) = 2w%2B(t) + 2roB(t)

t 2 = w - l arcsin(B*/Bm2)

(6b)

(3)

From Equation (3), using Equation (1), one obtains

P..t. -

#oL~ x nl- - B2 4~2 &Ms

(4)

where AMs = Ms(B, B2) - Ms(B, B1) Due to the small value of ro the measured magnetization Ms at any. time t > > ro practically corresponds to the value of B at t. The value &Ms can be obtained experimentally in the following way. The magnetization curves 1 and 2 are measured at two different amplitudes Bml and Bm2 of the sinusoidal external magnetic field (curves 1' and 2' in Figure 1). Further, we have to choose the value of magnetic field B* < Bm~ < Bin2 at which we want to evaluate the transverse resistivity. At this chosen value of B* the values of/~ for the curves 1' and 2', B, and B2are nl = wBmlCOS6Otl

(5a)

/12 = 6°Bm2c°swt2

(5b)

and the corresponding values of t~ and t2 are

Thus we can plot the total magnetization M at B = B* corresponding to two different values of B given by Equations (5a) and (5b) as shown in Figure 2. Extrapolating the straight line conne,cting points 1 and 2 to B = 0 we obtain practically the hysteresis magnetization Mh, because the contribution of the first term in Equation (3) is negligibly small. Subtracting this Mh value from the total magnetization M(1) and M(2), we obtain M,(B1) and Ms(B2), respectively. Using Equation (4) we can determine p ±. Measurement of M a n d e v a l u a t i o n of p . multifilamentary composite

for a

For measurement of M(t) we used a method similar to that described in Reference 6, which is shown schematically in Figure 3. The time dependence of the voltage difference AU from two pick-up coils, one of which contains the sample, is electronically integrated and registered by transient recorder. The time dependence of the voltage UB on the resistor Rs, proportional to the external magnetic field, is simultaneously recorded (see Figure 3). Finally, the value M - J AU dt is plotted as a function of UB -- B. As an example we present results obtained on the multi filamentary composite Alsthom Atlantique CCN

P2 L ~ " ~

q

B=

P~

0

8,

t

Figure 2 Total magnetization M at two values B"1 and B"2 estimated at the chosen external magnetic field B = B*. Extrapolation of the straight line connecting points 1 and 2 to B -- 0 gives the hysteresis magnetization M h

S ~'Ui d[

-I Figure 1 Magnetization curves 1 and 2 measured at amplitudes of the sinusoidal external magnetic field Brnl and Bm2, respectively. The time dependence of the external magnetic field corresponding to amplitudes Bml and Bin2 is represented by the curves 1' and 2" respectively. At points P1 and P2 the instantaneous values of B" are B'I and /3"2, respectively

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Figure 3 Block diagram of the experimental apparatus. 1, 2, Pickup coils; 3, measured sample; 4, coil generating external magnetic field

Method for determining transverse resistivity: M. Pol~k e t al.

5xlO

2

/ oI

/ IOO

J

I

f I-Ol ~,

I 200 BIT s"i)

Figure 5 Total magnetization at B* = 0.4 T as a function of B" estimated from Figure 4 i

¢

i

i

,

0

i

~

~

I

015

,

i

B [T]

Figure 4 Magnetization curves of the multifilamentary wire Alsthom Atlantique CCN 14000LL measured at various external magnetic field amplitudes 14 000 L L containing 14 496 NbTi filaments of diameter 1.4/zm in a CuNi/Cu matrix. The composite diameter was 0.30 mm, the twist pitch length Lp = 5 mm. The measured M = fiB) curves at 11 amplitudes of the external magnetic field up to Bm = 0.7 T are shown in Figure 4. The dependence M = f(B) estimated from Figure 4 at B* = 0.4 T is shown in Figure 5. For Mh we obtained 1.4 x 10-2 T; it can be seen that Ms depends linearly on B, which proves the applicability of the present method. At B = 200 T s -~ we obtain Ms = 3 × 10 -3 T and using Equation (4) we get P i = 5.3 × 10 -s fl m. Conclusions

The method described enables the determination of the transverse resistivity of multifilamentary composites with

high resistivity matrix from magnetization curves measured at two different amplitudes of the sinusoidal external magnetic field at one frequency. It can be used easily when the rate-dependent magnetization M, is not much lower than hysteretic magnetization Mh. The advantage of this method over others is that it enables p~ to be determined by simple magnetization measurement on standard samples at one frequency only, without measurement of the hysteresis magnetization.

References 1 Hl~nik, I. and Seibt, W. J Phys Paris (1984) 45 C1-459 2 Hldsnik,I., ~ , J., Majoro~,M., PoMk,M., Cesnak, L., Jan~k, L., Gdbor, M., Gomory, F., Klimenko, E.J., Novikov, S.I., Burjak, V.P. and Klabik, V. Elektrotech ~as (1985) 36 858 3 Drobin, V.M., Dyachkov, E.I., Khukhareva, LS., Lupov, V.G. and

Nichitiu, A. Cryogenics (1982) 22 115 4 Turck, B., Wake, M. and Kobayashi, M. Cryogenics(1977) 17 217 5 Gurevich,A.V., Mints, R.G. and Rakhmanov, A.L. Physicsof Composite Superconductors (in Russian) Nauka, Moscow(1987) 6 Pol6k, M. and Krempask~, L. Elektrotech ~as (1982) 33 342

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