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Physica C 335 Ž2000. 124–128 www.elsevier.nlrlocaterphysc
Basic approach to AC losses in HTS wires exposed to various types of electromagnetic configuration K. Funaki ) Research Institute of SuperconductiÕity, Kyushu UniÕersity, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan
Abstract AC loss in superconducting materials can be estimated, in general, by considering Poynting’s vector, electromagnetic power flow, on a closed surface surrounding the sample in a cyclic electromagnetic environment. On the basis of energy conservation, the total amount of the power flow that penetrates into the sample during the period of the electromagnetic environment is equivalent to the AC loss. By using this basic concept of the AC loss, errors in AC loss measurement with three types of pickup coil methods are first considered in relation with the geometrical configuration of the sample coil and the pickup coils. It is indicated from the analytical formulation of the AC loss measured that the error is strongly affected by the arrangement of the cancel coil and that the most proper arrangement is the coaxial type, where the sample coil is set coaxially and concentrically between the inner cancel coil and the outer main pickup coil. Secondly, the geometrical error in a simple method proposed to measure various types of AC loss is also discussed. It is suggested by the analytical consideration that this method has a high accuracy in the AC loss measurement even in comparison with the coaxial type of pickup coil method. Finally, experimental results measured by the simple method for various types of AC loss in Bi-2223 tapes are compared with numerical simulation with the measured E–J characteristic. q 2000 Elsevier Science B.V. All rights reserved. Keywords: AC loss; Poynting’s vector; Electromagnetic configuration
1. Introduction Even if superconducting composites have no heat generation for a direct current, they generate various types of AC loss in general electromagnetic environment by applying alternating current andror external magnetic field. Taking into account a large penalty factor of refrigeration, we need to measure the AC loss quantitatively for basic design of the AC applications of superconductivity. From this viewpoint, it )
Tel.: q81-92-642-4016; fax: q81-92-632-2438. E-mail address: [email protected] ŽK. Funaki..
is meaningful to be aware of an intrinsic error from the geometrical configuration especially in electromagnetic methods of AC loss measurement. In the present paper, the geometrical error in AC loss measurement by the pickup coil method is first considered in relation with the configuration of the pickup and sample coils. For a new simple method of AC loss measurement using a non-inductive double-layer sample coil, the geometrical error is also evaluated and compared with that for the pickup coil. Experimental results measured by the simple method are presented for Bi-2223 tapes in various types of electromagnetic environment.
0921-4534r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 Ž 0 0 . 0 0 1 5 6 - 8
K. Funakir Physica C 335 (2000) 124–128
125
2. Geometrical error in pickup coil method AC loss in superconducting materials can be estimated, in general, by considering Poynting’s vector S s E = H of electromagnetic power flow, the vector product of electric field E and magnetic field H, on a closed surface A surrounding the sample in a cyclic electromagnetic environment with a period T. In brief, the total amount of the power flow that penetrates into the sample during the period of the electromagnetic environment is equivalent to the AC loss per unit volume per cycle as shown in: Wsy
1
T
H d tHAd A P E = H V 0
Ž 1.
s
where Vs is the sample volume and d A is an outward vector of area element on A. This basis concept results in a quantitative evaluation of the geo-
Fig. 2. The dependence of G-factor on height ratio Ža. in coaxial arrangement, and Žb. in parallel-axial arrangement.
metrical error in AC loss measurement by the pickup coil methods and other electromagnetic ones. If the pickup coils surrounding the sample is in uniform alternating magnetic field He , apparent magnetization loss can be measured by integrating the Poynting’s vector on the surface AX of the pickup coils, which do not sufficiently surround the sample. For
Fig. 1. Geometrical configuration of pickup coil methods Ža. in coaxial arrangement, and Žb. in parallel-axial arrangement.
Fig. 3. The dependence of G-factor on a for Ža. coaxial and Žb. in parallel-axial arrangements.
K. Funakir Physica C 335 (2000) 124–128
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the configuration of pickup coils as illustrated in Fig. 1, the apparent measurement is expressed as w1x: W s ym 0 G Ž h pc ,h s , R ,a . Md He
E
Ž 2.
where M is the magnetization of the sample and a coefficient G is a function only of the geometrical parameters, h s , h pc , R and a Žindicated in Fig. 1.. This shows that the AC loss can be exactly measured for the G-factor equal to unity. Examples of analytical results for typical values of parameters w1x are represented in Fig. 2. In Fig. 2, solid lines show analytical predictions with Eq. Ž2. and symbols are experimental results for sample coils of NbTi multifilamentary wires. The good agreement shows a quantitative basis of the analytical prediction. The coaxial configuration of pickup coils can be recommended for the measurement of magnetization loss in comparison with the parallel-axial one.
3. Simple method with non-inductive double-layer sample coil A simple method has been proposed for measurement of AC loss in various types of electromagnetic environment including simultaneous application of alternating magnetic field and transport current to superconducting wires w2x. In this method, the sample coil with structure of non-inductive double-layer
Fig. 4. Comparison among experimental results of magnetization loss measured by the usual pickup coil method, simple method and calorimetric method w2x.
Table 1 Specifications of sample wire and coil Sample wire Superconductor Matrix Sizes Žwith insulator. Filament number Twist pitch Silver ratio, AgrSC Sample coil Turn number Mean diameter Height
Bi-2223 pure silver 0.205=2.89 mm Ž0.220=2.90 mm. 55 infinite 2.8 21 turnsrlayer 50 mm 65 mm
has a function of pickup coil. First, we shall consider the geometrical error in the simple method in comparison with the pickup coil method of coaxial configuration for the measurement of magnetization loss. In the double-layer coil exposed to AC magnetic field parallel to the coil axis, an electrical center line along the center of wire itself is regarded as a pickup coil. This pickup coil closely surrounds the sample part between the electric center line in the double layers. In this case, the distance a between the sample and pickup coils corresponds to a half of the distance between the electric center line in the double layer. Fig. 3 shows the dependence of the G factor on a for R s h s s h pc s 30 and 50 mm. Since the height of the sample coil is equal to that of
Fig. 5. Critical current and n-value of Bi-2223 sample wire at 77 K. The solid line is used in numerical simulation for the critical current w1x.
K. Funakir Physica C 335 (2000) 124–128
127
In order to confirm the AC loss measurement with high G factor, the magnetization loss was measured by the simple method and compared with those by the pickup coil method and a calorimetric one w3x. The sample wires were NbTi composites with fine filaments of 0.45 mm in diameter. The geometrical error estimated for the pickup coil method was less than 2% because of the height ratio 3.0. The results are plotted in Fig. 4. We have good agreement among the results measured by the three types of methods.
4. Various types of AC loss by simple method
Fig. 6. Transverse-field loss of the sample wire measured by simple method w1x. The solid and dashed lines show the numerical results at 10 and 30 Hz, respectively.
pickup coil, the geometrical error is in a maximum level as shown in Fig. 2. Although the G factor is only around 0.9

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