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Basic approach to AC losses in HTS wires exposed to various types of electromagnetic configuration
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
126
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 0.93 in the coaxial configuration of the pickup coil method for a s 2 to 3 mm, the level attains to about 0.99 in the simple method for a s 0.1 to 0.2 mm. This means that the simple method corresponds to a limiting case extrapolated from the pickup coil method to measure the magnetization loss with high accuracy.
In the simple method, for example, both components of magnetization loss and transport-current one can be measured individually using the terminal voltage of the sample coil in case of simultaneous application of alternating transverse magnetic field and transport current w2x. In this section, we shall evaluate the results of AC losses measured by the simple method in comparison with numerical simulation w1x. Specifications of the sample wire and coil are listed in Table 1. For this simulation, the magnetic field dependence of critical current and n-value was measured. The results are shown in Fig. 5, where the critical current is defined by a criterion of 10y1 2 V m.
Fig. 7. Various types of AC loss measured by the simple method in simultaneous application of alternating transverse magnetic field and transport current, Ža. magnetization loss, Žb. transport-current loss and Žc. total AC loss w1x. The solid and dashed lines show the numerical results at 10 and 30 Hz, respectively.
128
K. Funakir Physica C 335 (2000) 124–128
In the simple method, the total AC loss and the components can be evaluated from the terminal voltages of the sample coil and the search coils for the external magnetic field and the transport current. The measurement procedures are presented in detail in Refs. w1,2x. In order to confirm the numerical simulation, the experimental and numerical results are compared for the transverse-field loss in Fig. 6, where only the alternating transverse field is applied parallel to the flat surface of the sample wire. The good agreement shows that the numerical procedure gives proper results. In the simultaneous application of alternating transverse field and transport current, the magnetization loss, the transport-current loss and the total AC loss measured are plotted for the amplitude of external field in Fig. 7. The numerical results are also indicated up to the level of the field amplitude, where the transport current is equivalent to the critical current. We can see good agreement in Fig. 7.
methods was quantitatively estimated with the G factor. It is shown that the pickup coil method in the coaxial arrangement gives higher G factor than other types, because the cancel coil in the coaxial arrangement also catches the Poynting’s vector in a proper way. From the comparison with the geometrical structure of the pickup coil method, it is furthermore indicated that the simple method has an accuracy in AC loss measurement superior to the pickup coil one. This result comes from a peculiar configuration in the simple method where the equivalent pickup coil closely surrounds the sample coil. On the basis of the geometrical error, various types of AC loss were measured by the simple method for the non-inductive double-layer sample coil of Bi-2223 tape exposed simultaneously to alternating transport current and AC magnetic field parallel to the coil axis. The comparison with the numerical simulation supports the high accuracy in AC loss measurement.
5. Concluding remarks
References
From the basic relation between the AC loss and the Poynting’s vector, the geometrical error in the magnetization loss measurement by pickup coil
w1x K. Kajikawa, et al., Proc. of ASC98, in press. w2x K. Funaki et al., Adv. Cryog. Eng. 43 Ž1998. 341. w3x K. Kuroda, Cryogenics 26 Ž1986. 566.
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
126
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 0.93 in the coaxial configuration of the pickup coil method for a s 2 to 3 mm, the level attains to about 0.99 in the simple method for a s 0.1 to 0.2 mm. This means that the simple method corresponds to a limiting case extrapolated from the pickup coil method to measure the magnetization loss with high accuracy.
In the simple method, for example, both components of magnetization loss and transport-current one can be measured individually using the terminal voltage of the sample coil in case of simultaneous application of alternating transverse magnetic field and transport current w2x. In this section, we shall evaluate the results of AC losses measured by the simple method in comparison with numerical simulation w1x. Specifications of the sample wire and coil are listed in Table 1. For this simulation, the magnetic field dependence of critical current and n-value was measured. The results are shown in Fig. 5, where the critical current is defined by a criterion of 10y1 2 V m.
Fig. 7. Various types of AC loss measured by the simple method in simultaneous application of alternating transverse magnetic field and transport current, Ža. magnetization loss, Žb. transport-current loss and Žc. total AC loss w1x. The solid and dashed lines show the numerical results at 10 and 30 Hz, respectively.
128
K. Funakir Physica C 335 (2000) 124–128
In the simple method, the total AC loss and the components can be evaluated from the terminal voltages of the sample coil and the search coils for the external magnetic field and the transport current. The measurement procedures are presented in detail in Refs. w1,2x. In order to confirm the numerical simulation, the experimental and numerical results are compared for the transverse-field loss in Fig. 6, where only the alternating transverse field is applied parallel to the flat surface of the sample wire. The good agreement shows that the numerical procedure gives proper results. In the simultaneous application of alternating transverse field and transport current, the magnetization loss, the transport-current loss and the total AC loss measured are plotted for the amplitude of external field in Fig. 7. The numerical results are also indicated up to the level of the field amplitude, where the transport current is equivalent to the critical current. We can see good agreement in Fig. 7.
methods was quantitatively estimated with the G factor. It is shown that the pickup coil method in the coaxial arrangement gives higher G factor than other types, because the cancel coil in the coaxial arrangement also catches the Poynting’s vector in a proper way. From the comparison with the geometrical structure of the pickup coil method, it is furthermore indicated that the simple method has an accuracy in AC loss measurement superior to the pickup coil one. This result comes from a peculiar configuration in the simple method where the equivalent pickup coil closely surrounds the sample coil. On the basis of the geometrical error, various types of AC loss were measured by the simple method for the non-inductive double-layer sample coil of Bi-2223 tape exposed simultaneously to alternating transport current and AC magnetic field parallel to the coil axis. The comparison with the numerical simulation supports the high accuracy in AC loss measurement.
5. Concluding remarks
References
From the basic relation between the AC loss and the Poynting’s vector, the geometrical error in the magnetization loss measurement by pickup coil
w1x K. Kajikawa, et al., Proc. of ASC98, in press. w2x K. Funaki et al., Adv. Cryog. Eng. 43 Ž1998. 341. w3x K. Kuroda, Cryogenics 26 Ž1986. 566.