IEC 61788-26:2020
(Main)Superconductivity - Part 26: Critical current measurement - DC critical current of RE-Ba-Cu-O composite superconductors
Superconductivity - Part 26: Critical current measurement - DC critical current of RE-Ba-Cu-O composite superconductors
IEC 61788-26:2020 specifies a test method for determining the DC critical current of short RE (rare earth)-Ba-Cu-O (REBCO) composite superconductor specimens that have a shape of straight flat tape. This document applies to test specimens shorter than 300 mm and having a rectangular cross section with an area of 0,03 mm2 to 7,2 mm2, which corresponds to tapes with width ranging from 1,0 mm to 12,0 mm and thickness from 0,03 mm to 0,6 mm.
This method is intended for use with superconductor specimens that have critical current less than 300 A and n-values larger than 5 under standard test conditions: the test specimen is immersed in liquid nitrogen bath at ambient pressure without external magnetic field during the testing. Deviations from this test method that are allowed for routine tests and other specific restrictions are given in this document.
Supraconductivité - Partie 26: Mesurage du courant critique - Courant critique continu des composites supraconducteurs de RE-Ba-Cu-O
L’IEC 61788-26:2020 spécifie une méthode d'essai pour la détermination du courant critique continu des échantillons de composites supraconducteurs RE (terre rare)-Ba-Cu-O (REBCO) courts en forme de ruban plat et rectiligne. Le présent document s'applique aux échantillons d’essai d'une longueur inférieure à 300 mm et d'une superficie de section rectangulaire de 0,03 mm2 à 7,2 mm2, ce qui correspond aux rubans d’une largeur de 1,0 mm à 12,0 mm et d’une épaisseur de 0,03 mm à 0,6 mm.
Cette méthode est destinée à être utilisée avec des échantillons de supraconducteurs caractérisés par un courant critique inférieur à 300 A et des valeurs n supérieures à 5 dans les conditions d’essai normalisées: l’échantillon d’essai est immergé dans un bain d’azote liquide à pression ambiante sans champ magnétique externe pendant l’essai. Le présent document spécifie les écarts par rapport à cette méthode d’essai qui sont admis dans les essais individuels de série, ainsi que d'autres restrictions spécifiques.
General Information
Standards Content (Sample)
IEC 61788-26 ®
Edition 1.0 2020-06
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Superconductivity –
Part 26: Critical current measurement – DC critical current of RE-Ba-Cu-O
composite superconductors
Supraconductivité –
Partie 26: Mesurage du courant critique – Courant critique continu des
composites supraconducteurs de RE-Ba-Cu-O
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IEC 61788-26 ®
Edition 1.0 2020-06
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Superconductivity –
Part 26: Critical current measurement – DC critical current of RE-Ba-Cu-O
composite superconductors
Supraconductivité –
Partie 26: Mesurage du courant critique – Courant critique continu des
composites supraconducteurs de RE-Ba-Cu-O
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 17.220.20; 19.080; 29.050 ISBN 978-2-8322-8436-0
– 2 – IEC 61788-26:2020 © IEC 2020
CONTENTS
FOREWORD . 4
INTRODUCTION . 6
1 Scope . 7
2 Normative references . 7
3 Terms and definitions . 7
4 Principle . 8
5 Apparatus . 8
5.1 General . 8
5.2 Critical current measuring system . 8
6 Specimen preparation and setup . 8
6.1 Length . 8
6.2 Mounting of the specimen . 9
7 Critical current measurement . 9
8 Calculation of results . 9
8.1 Critical current criteria. 9
8.2 n-value (optional) . 11
9 Uncertainty of measurement . 11
10 Test report . 11
10.1 Identification of test specimen . 11
10.2 Reporting of I values . 11
c
10.3 Reporting of I test conditions . 11
c
Annex A (informative) Additional information relating to measurement, apparatus, and
calculation . 12
A.1 General information . 12
A.2 Measurement condition . 12
A.3 Apparatus . 13
A.3.1 Measurement holder material . 13
A.3.2 Measurement holder construction . 13
A.4 Specimen preparation . 14
A.5 Measurement procedure . 14
A.5.1 Voltage leads . 14
A.5.2 Cooling process . 14
A.5.3 Temperature of liquid nitrogen bath . 14
A.5.4 System noise and other contributions to the measured voltage . 15
A.6 Calculation of n-value . 16
Annex B (informative) Evaluation of combined standard uncertainty for REBCO
I measurement [8] . 17
c
B.1 Practical critical current measurement . 17
B.2 Model equation . 18
B.3 I measurement results . 19
c
B.4 Combined standard uncertainty [11] . 21
B.5 Type B uncertainty evaluation . 22
B.5.1 General . 22
B.5.2 Uncertainty of L measurement . 22
B.5.3 Uncertainty of voltage measurement . 22
B.5.4 Uncertainty of current measurement . 23
B.5.5 Uncertainty of temperature measurement . 23
B.5.6 Uncertainty coming from intrinsic non-uniformity of I . 24
c
B.5.7 Comparison between types A and B combined standard uncertainties . 25
B.6 Influence of current ramp rate on the total uncertainty . 26
Bibliography . 27
Figure 1 – Schematic view of measurement setup . 9
Figure 2 – Intrinsic U-I characteristic . 10
Figure 3 – U-I curve with a current transfer component . 10
Figure A.1 – Illustration of a measurement configuration for a short specimen of a few
hundred amperes class REBCO conductor . 13
Figure A.2 – Temperature dependence of I for commercial REBCO superconductors
c
(data from [9]) . 14
Figure A.3 – Pressure dependence of boiling temperature of liquid nitrogen . 15
Figure B.1 – Typical circuit to measure I . 17
c
Figure B.2 – Typical voltage–current (U-I) characteristic of a superconductor . 18
Figure B.3 – Ramp time dependence of total RSU of I for conductors B, C, and D . 26
c
Table A.1 – Thermal contraction data of superconductor
and sample‑holder materials [1] . 13
Table B.1 – Conductors distributed in the international RRT . 19
Table B.2 – I data for conductor A . 19
c
Table B.3 – I data for conductor B . 20
c
Table B.4 – I data for conductor C . 20
c
Table B.5 – I data for conductor D . 20
c
Table B.6 – Statistics for each conductor . 21
Table B.7 – ANOVA results for each conductor . 21
Table B.8 – Atmospheric pressure from 1 January 2014 to 31 December 2014 . 24
Table B.9 – Intrinsic I non-uniformity evaluated by RTR-SHPM . 24
c
Table B.10 – Budget table of SUs of I measurements for conductor C . 25
c
Table B.11 – Comparison of the relative standard uncertainties for
conductors B, C, and D . 25
– 4 – IEC 61788-26:2020 © IEC 2020
INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
SUPERCONDUCTIVITY –
Part 26: Critical current measurement –
DC critical current of RE-Ba-Cu-O composite superconductors
FOREWORD
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International Standard IEC 61788-26 has been prepared by IEC technical committee
90: Superconductivity.
The text of this standard is based on the following documents:
FDIS Report on voting
90/455/FDIS 90/458/RVD
Full information on the voting for the approval of this standard can be found in the report on
voting indicated in the above table.
This publication has been drafted in accordance with the ISO/IEC Directives, Part 2.
A list of all parts in the IEC 61788 series, published under the general title Superconductivity,
can be found on the IEC website.
The committee has decided that the contents of this publication will remain unchanged until the
stability date indicated on the IEC web site under "http://webstore.iec.ch" in the data related to
the specific publication. At this date, the publication will be
• reconfirmed,
• withdrawn,
• replaced by a revised edition, or
• amended.
– 6 – IEC 61788-26:2020 © IEC 2020
INTRODUCTION
In 1986, superconductivity in some perovskite type materials containing copper oxides at
temperatures far above the critical temperatures of metallic superconductors was discovered.
In 1987, it was discovered that Y-Ba-Cu-O (YBCO) has a critical temperature (T ) of 93 K. After
c
a quarter century, the RE-Ba-Cu-O (REBCO, RE = rare earth) superconductors became
commercially available.
In 2013, VAMAS-TWA 16 started working on the critical current measurement methods in
REBCO superconductors. In 2014, an international round robin test (RRT) on the critical current
measurement method for REBCO superconductors was conducted that was led by VAMAS-
TWA 16. 10 institutions/universities/industries from five countries participated. The pre-
standardization work of VAMAS was taken as a base for this document, on the DC critical
current test method of REBCO composite superconductors.
The test method covered in this document is intended to give an appropriate and accepted
technical base to engineers working in the field of superconductivity technology.
SUPERCONDUCTIVITY –
Part 26: Critical current measurement –
DC critical current of RE-Ba-Cu-O composite superconductors
1 Scope
This part of IEC 61788 specifies a test method for determining the DC critical current of short
RE (rare earth)-Ba-Cu-O (REBCO) composite superconductor specimens that have a shape of
straight flat tape. This document applies to test specimens shorter than 300 mm and having a
2 2
rectangular cross section with an area of 0,03 mm to 7,2 mm , which corresponds to tapes
with width ranging from 1,0 mm to 12,0 mm and thickness from 0,03 mm to 0,6 mm.
This method is intended for use with superconductor specimens that have critical current less
than 300 A and n-values larger than 5 under standard test conditions: the test specimen is
immersed in liquid nitrogen bath at ambient pressure without external magnetic field during the
testing. Deviations from this test method that are allowed for routine tests and other specific
restrictions are given in this document.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies.
For undated references, the latest edition of the referenced document (including any
amendments) applies.
IEC 60050-815, International Electrotechnical Vocabulary (IEV) – Part 815: Superconductivity
3 Terms and definitions
For the purposes of this document, the terms and definitions given in IEC 60050-815 and the
following apply.
ISO and IEC maintain terminological databases for use in standardization at the following URLs:
• IEC Electropedia: available at http://www.electropedia.org/
• ISO Online browsing platform: available at http://www.iso.org/obp/
3.1
constant sweep rate method
U-I data acquisition method where a current is swept at a constant rate from zero to a current
above I , and where the U-I data are acquired continuously or frequently
c
3.2
ramp-and-hold method
U-I data acquisition method where a current is swept in stages from zero to a current above I ,
c
where the current is held for an appropriate amount of time at each stage, and where the U-I
data are acquired continuously or frequently
– 8 – IEC 61788-26:2020 © IEC 2020
4 Principle
The critical current of a composite superconductor specimen shall be determined from a
voltage–current (U-I) characteristic measured in a liquid nitrogen bath at ambient pressure. To
get a U-I characteristic, a direct current is applied to the superconductor specimen and the
voltage generated along the specimen is measured. The current is increased from zero and the
U-I characteristic is recorded. The critical current shall be determined as the current at which a
specific electric field strength criterion (electric field criterion) (E ) is reached. For any selected
c
, there shall be a corresponding voltage criterion (U ) for a specified voltage tap separation.
E
c c
5 Apparatus
5.1 General
The apparatus required for the present test method includes the critical current measuring
system. Additional information relating to the apparatus is given in Annex A.
5.2 Critical current measuring system
The apparatus to measure the U-I characteristic should consist of a specimen probe, an open
bath and a U-I measurement system.
The specimen probe, which consists of a specimen and a measurement holder, is inserted in
the open bath filled with liquid nitrogen. The U-I measurement system consists of a DC current
source and necessary data acquisition system, preamplifiers, filters or voltmeters, or a
combination thereof. Suitable measurement holder materials are recommended in A.3.1.
A computer assisted data acquisition system is recommended.
6 Specimen preparation and setup
6.1 Length
An example of a schematic view of measurement setup is shown in Figure 1.
The length (L) of specimen to be measured shall be defined as follows:
L = L + 2 × L + 2 × L + L ≥ 5 × W (1)
1 2 3 4
L , L , L ≥ W (2)
1 2 3
where
L is the distance between the voltage taps;
L is the length of the current contact;
L is the shortest distance from a current contact to the neighbouring voltage tap;
L is the width of a voltage tap.
W is the width of a specimen to be measured.
The larger the current-carrying capacity of the specimen, the larger shall be L . L shall be
2 2
increased for a specimen that has a stainless steel or other high-resistivity material backing or
jacket. For a measurement that needs the higher voltage sensitivity, L shall be increased. For
some practical values for L through L , see A.3.2.
1 4
Figure 1 – Schematic view of measurement setup
6.2 Mounting of the specimen
The specimen shall be mounted to the flat surface of the holder. Both ends shall be fastened
or soldered to the current contact blocks.
The voltage taps shall be placed in the central part with or without solder.
The current contacts and the voltage taps shall be on the superconducting layer side.
Voltage leads shall be twisted as close to the voltage taps as possible.
7 Critical current measurement
The critical current shall be measured while minimizing mechanical strain.
The specimen shall be inserted slowly into the liquid nitrogen bath. The volume of the liquid
nitrogen bath shall be sufficiently larger than the specimen and the measurement holder. The
depth of the bath shall be sufficiently higher than the height of the measurement holder. The
specimen shall be cooled from room temperature to liquid nitrogen temperature until the
specimen and the measurement holder are sufficiently cooled by liquid nitrogen that boils with
microbubbles, i.e. steady state. It takes several tens of seconds.
When using the constant sweep rate method, the sweep rate shall be selected not to influence
the voltage measurement.
When using the ramp-and-hold method, the current sweep rate between stages shall be lower
than the equivalent of ramping from zero current to I in 3 s. Data acquisition at each stage
c
shall be started as soon as the flow or creep voltage generated by the current ramp can be
disregarded. The current drift during each current set point shall be less than 1 % of I .
c
Record the U-I characteristic with increasing current.
After measurement, the specimen shall be warmed up to room temperature.
Additional information relating to the measurement is given in Annex A.
8 Calculation of results
8.1 Critical current criteria
The critical current I shall be determined by using an electric field criterion E .
c c
– 10 – IEC 61788-26:2020 © IEC 2020
I shall be determined at E = 100 μV/m. I determined at E = 10 μV/m is optional.
c c c c
The I shall be determined as the current corresponding to the point on the U-I curve where the
c
voltage U is measured (see Figure 2 and Figure 3):
c
U = L E (3)
c 1 c
where
U is the voltage criterion in microvolts (μV);
c
L is the voltage tap separation in metres (m);
E is the electric field criterion in microvolts per metre (μV/m).
c
U and I are the corresponding voltage and current values at the intersecting point of the
c c
straight lines with the U-I curve as shown in Figure 2.
Figure 2 – Intrinsic U-I characteristic
If the measured U-I curve includes a resistive component, it is recommended to increase L to
minimize the current transfer component voltage.
Figure 3 – U-I curve with a current transfer component
8.2 n-value (optional)
The n-value shall be calculated as the slope of the plot of log U versus log I in the region where
the I is determined. The corresponding electric field region is recommended to be from 10 µV/m
c
to 100 µV/m.
The electric field region used to determine the n-value shall be reported.
Additional information relating to the calculation is given in Annex A.
9 Uncertainty of measurement
Unless otherwise specified, measurements shall be carried out in a liquid nitrogen bath whose
temperature can range from 76,8 K to 77,7 K. A voltmeter having 7,5 digits resolution,
providing 1 nV sensitivity on 10 mV setting shall be used to measure specimen voltage.
According to the international round robin test (see Annex B), the relative standard uncertainty
is less than 3 %. The target measurement uncertainty shall be 6 % with a coverage factor of 2.
10 Test report
10.1 Identification of test specimen
The test specimen shall be identified by the following:
a) name of the manufacturer of the specimen;
b) classification and/or symbol;
c) lot number.
10.2 Reporting of I values
c
The following values shall be reported:
a) I values with their corresponding electric field criteria;
c
b) specimen temperature and/or ambient pressure.
The reporting of n-values is optional.
10.3 Reporting of I test conditions
c
The following test conditions shall be reported:
a) length of specimen (L);
b) width of specimen (W);
c) thickness of specimen;
d) distance between voltage taps (L );
e) shortest distance from a current contact to a voltage tap (L );
f) length of the current contacts (L );
g) sweep rate when using the constant sweep rate method;
h) ramp pitch, ramping time and holding time when using the ramp-and-hold method.
– 12 – IEC 61788-26:2020 © IEC 2020
Annex A
(informative)
Additional information relating to measurement,
apparatus, and calculation
A.1 General information
There are variables that have a significant effect on the measured value of critical current in
REBCO superconductors. Some of them are addressed in Annex A for users’ attention (see
also Annex B).
Special features found in REBCO superconductors may be classified into two groups. The first
group is specific to REBCO multilayer composite superconductors, including mechanical
fragility of delamination, magnetic flux flow and creep, large anisotropy, screening current
caused by magnetic field change, non-uniformity of superconducting properties, etc. The
second group is due to length of the specimen used in this document. A critical current
measurement on such a specimen may easily pick up different voltage signals due to inductive
voltage, thermal noise, current redistribution, etc. Current transfer voltages may be present due
to the short distance from a current contact to a voltage tap.
Superconductor specimens with critical currents above 500 A could be measured with this
present method with an anticipated increase in uncertainty. A superconductor specimen longer
than 300 mm could be measured with this present method. However, care needs to be taken
for the measurement preparation.
This document assumes that measurements are made in a liquid nitrogen bath. The cryogen is
used at a temperature near boiling point for the normal atmospheric pressure of the test site.
This document could be extended to measurements conducted in the cryogen at temperatures
other than near boiling point, i.e. depressurized or pressurized. The measurements in a gas or
a vacuum are not covered by the scope of this document.
A.2 Measurement condition
The minimum total length of the tape specimen is five times the tape width (W) + the voltage
tap width (L ), which represents the sum of the following:
– the minimum voltage tap separation (L ≥ W);
– the length of current contacts (L ≥ W);
– the shortest distance between current and voltage contacts (L ≥ W).
It is expected that the specimen mounting and the specimen cooling procedures in this test
method may be one of the most significant contributors to the overall uncertainty of the critical
current measurement. The value of I is sensitive to strain. Cooling rates influence thermally
c
induced strain due to different thermal time constants and coefficients of thermal expansion
(CTEs) between the sample and mounting materials.
A.3 Apparatus
A.3.1 Measurement holder material
In this method, the specimen strain is controlled to a minimum (less than 0,1 %). A 0,1 %
thermal contraction may result in no appreciable I deviation at 0 T and near 77,3 K.
c
One significant source of strain is the mismatch in thermal contraction rates between the
measurement holder and the specimen when cooled to liquid nitrogen temperature.
Based on the typical thermal contractions shown in Table A.1, the following materials are
suggested for the measurement holder material. For alternate holder materials, a carefully
prepared qualification study should precede the routine tests.
Recommended holder material is glass-fibre epoxy composite, with the specimen lying in the
plane of the fabric warp.
Table A.1 – Thermal contraction data of superconductor
and sample‑holder materials [1]
-6 -1
ΔL/L [%] α [10 K ]
Material
293K-77K 293K
YBCO polycrystal [2] 0,21 11,5
YBCO a,b-plane avg. [2] 0,14 8,5
Ni based alloy (UNS N10276) [3] 0,216 10,9
Silver [4] 0,370 18,5
Copper [5] 0,302 16,7
Glass-fibre epoxy composite, warp [6] [7] 0,21 12,5
Glass-fibre epoxy composite, normal [6] [7] 0,64 41
A.3.2 Measurement holder construction
An example of measurement holder is shown in Figure A.1. Typically, the current contacts are
made from copper blocks, and the thickness of the contact should be determined so that there
is no difference in the level between the holder and the contact surfaces. The contact blocks
should be rigidly affixed to the holder. Solder is often used to make current contacts. However,
the soldering skills depend on the individual. Thus, this document recommends not to use solder
to make current contacts.
Typical L through L values which were used by the participants of the international round
1 4
robin test [8] were as follows: L : 30 mm to 90 mm, L : 25 mm to 40 mm, L : 10 mm to 30 mm,
1 2 3
and L : 1 mm to 10 mm.
Figure A.1 – Illustration of a measurement configuration for
a short specimen of a few hundred amperes class REBCO conductor
– 14 – IEC 61788-26:2020 © IEC 2020
A.4 Specimen preparation
The distance between the voltage taps is defined as the distance between the centres of voltage
contacts, irrespective of their size.
A.5 Measurement procedure
A.5.1 Voltage leads
To reduce thermoelectric voltages on the specimen voltage leads, copper voltage leads are
used which are continuous from the liquid nitrogen bath to room temperature where an
isothermal environment for all room temperature joints or connections is provided. It should be
noted that the joints or connections immersed in cryogen are isothermal.
A.5.2 Cooling process
The specimen cooling rate may affect the measured critical current. The strength of bonding
between the specimen and its holder changes during the cooling process when different thermal
contraction between the specimen and the holder proceeds.
A.5.3 Temperature of liquid nitrogen bath
REBCO critical current depends on temperature (Figure A.2) [9]. The liquid nitrogen
temperature depends on the ambient pressure (Figure A.3) [10]. In addition, oxygen impurities
can change temperature of liquid nitrogen in an open bath. Liquid nitrogen stored in the open
bath for several days will condense enough oxygen impurities to shift the boiling point.
To reduce the uncertainty caused by the temperature, the specimen temperature (temperature
of the specimen surface) would be measured using appropriate thermometer(s) shown in [1].
Ambient pressure would be atmospheric pressure (950 ≤ P ≤ 1 050 hPa, corresponding to
76,8 K ≤ T ≤ 77,7 K).
Figure A.2 – Temperature dependence of I for
c
commercial REBCO superconductors (data from [9])
Figure A.3 – Pressure dependence of boiling temperature of liquid nitrogen
A.5.4 System noise and other contributions to the measured voltage
If the system noise is significant compared to the prescribed value of voltage, i.e. U , it is
c
desirable to increase the time for the ramp from zero current to I to more than 30 s. In this
c
case, care should be taken to increase the heat capacity and/or cooling surface of the current
contacts enough to suppress the influence of heat generation due to the longer time required
for the measurement. It should be noted that the ramp-and-hold method allows for averaging
data that can be appropriately distributed along the U-I characteristic.
Ramping the current can induce a positive or negative voltage on the voltage taps. This source
of interfering voltage during the ramp can be identified by its proportional dependence on ramp
rate. If this voltage is significant compared to U , then decrease the ramp rate (increase the
c
ramp time from zero current to I ), decrease the area of the loop formed by the voltage taps
c
and the specimen between them, or else use the ramp-and-hold method.
The baseline voltage may include thermoelectric, off-set, ground-loop and common-mode
voltages. It is assumed that these voltages remain relatively constant for the time it takes to
record each U-I characteristic. Small changes in thermoelectric and off-set voltages can be
approximately removed by measuring the baseline voltage before and after the U-I curve
measurement and assuming a linear change with time. If the change in the baseline voltage is
significant compared to U , then corrective action to the experimental configuration should be
c
taken.
A larger separation between a current contact and a voltage tap may be necessary if a
significant current transfer voltage exists relative to the criteria.
– 16 – IEC 61788-26:2020 © IEC 2020
A.6 Calculation of n-value
The U-I characteristic curve of a superconducting tape near the I can usually be approximated
c
by the empirical power-law equation:
n
I
UU= (A.1)
c
I
c
where
U is the specimen voltage in microvolts (μV);
U is the critical current criterion voltage in microvolts (μV);
c
I is the specimen current in amperes (A);
I is the critical current in amperes (A).
c
The n-value (no units) reflects the general shape of the curve near I .
c
A plot of log U versus log I is not always linear, even in the current range near the critical
current criteria (E ) of 10 µV/m and 100 µV/m; thus, the range of the criteria used to determine
c
the n-value needs to be reported.
Annex B
(informative)
Evaluation of combined standard uncertainty
for REBCO I measurement [8]
c
B.1 Practical critical current measurement
A superconductor in a superconducting state, which has no resistance, transitions to a normal
state when a transport current exceeds a certain threshold value. The threshold current value
is called the critical current (I ). There are several methods to measure I . A four-probe method,
c c
which is the most popular and practical, is introduced in Annex B.
The four-probe I measurement is described using a circuit shown in Figure B.1. The transport
c
current (I) is supplied by a DC current supply. The voltage drop (U) along the specimen length
is measured. Typical U-I characteristic is shown in Figure B.2. The U-I characteristic is
nonlinear. The transport current value that corresponds to the threshold voltage U is
c
determined to be I .
c
Figure B.1 – Typical circuit to measure I
c
– 18 – IEC 61788-26:2020 © IEC 2020
The current corresponding to the threshold voltage (U ) is determined to be I .
c c
Figure B.2 – Typical voltage–current (U-I) characteristic of a superconductor
B.2 Model equation
The U-I characteristic of a practical superconductor is well approximated by an empirical power
law:
n
I
UU= (B.1)
c
I
c
where the index n is called the n-value. U is described using L , which is a distance between
c 1
the pair of voltage taps:
U = LE (B.2)
c 1c
where
E is an electric field criterion to determine I .
c c
The model equation can be described as follows considering Formulas (B.1) and (B.2):
LE
n
c
I= Ig++T ε (B.3)
( )
c
Temp NU
U
where g (T) and ε are terms coming from temperature and non-uniformity of I along the
Temp NU c
length of the conductor, respectively.
B.3 I measurement results
c
An international round robin test (RRT) on I measurement of REBCO superconductors was
c
conducted. Four kinds of REBCO conductors were distributed to 10 participating
institutions/universities/industries. Each participant measured five specimens for each
conductor. Table B.1 shows the specifications of distributed conductors.
Table B.1 – Conductors distributed in the international RRT
Manufacturer A B C D
Rare earth elements Y Gd Y and Gd Gd
Deposition processes RABiTS/MOD IBAD/RCE-DR IBAD/MOCVD IBAD/PLD
Tape width [mm] 4,4 4,1 4 5
Tape thickness [mm] 0,4 0,1 0,095 0,16
Superconductor thickness [µm] 1 1,0 to 1,5 no information no information
Substrate Ni-5W Ni based alloy Ni based alloy Ni based alloy
Substrate thickness [µm] 50 to 75 60 50 75
Lamination Brass n/a n/a n/a
Lamination thickness [µm] 150 n/a n/a n/a
Copper stabilizer n/a Both sides Both sides Superconductor side
Copper thickness [µm] n/a no information 20 × 2 75
n/a = not applicable
Table B.2, Table B.3, Table B.4, and Table B.5 show I data reported from participants P1 to
c
P10 for conductors A, B, C, and D. Since some data were lacking for P9, the P9 column was
not used for analysis for conductors B and D.
Table B.2 – I data for conductor A
c
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10
1 104,898 102,89 97,802 97,73 104,0 106,95 104,3 104,05 103,190 105,54
2 106,819 102,93 98,834 100,86 103,8 108,20 102,0 104,69 100,755 106,10
3 108,932 102,49 98,731 103,38 102,8 104,87 103,6 104,25 113,625 105,35
4 103,792 101,22 99,062 98,89 101,2 105,07 101,4 103,35 110,202 105,77
5 104,538 102,32 98,608 99,55 100,60 104,09 103,80 102,70 104,338 105,98
I [A]
105,796 102,37 98,607 100,082 102,48 105,836 103,02 103,808 106,422 105,748
c,avg
X [A]
SD 2,079 0,693 4 0,480 2 2,163 1,527 1,688 1,250 0,785 7 5,317 0,308 2
X [A]
SU 0,929 7 0,310 1 0,214 7 0,9674 0,682 9 0,754 9 0,558 9 0,351 4 2,378 0,137 8
X [%]
0,879 0,303 0,218 0,967 0,666 0,713 0,543 0,338 2,234 0,130
RSU
– 20 – IEC 61788-26:2020 © IEC 2020
Table B.3 – I data for conductor B
c
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10
1 187,837 197,180 189,935 196,920 189,600 198,020 191,000 187,350 191,440 200,140
2 183,258 189,390 184,803 191,290 191,400 198,990 190,800 192,570 181,650 197,050
3 188,917 193,150 191,041 192,630 193,000 193,910 197,000 198,360 195,870
4 192,467 194,320 188,539 194,210 191,600 193,100 195,600 197,920 192,160
5 187,803 195,510 192,863 190,540 187,600 194,680 177,600 193,320 196,920
I [A]
c,avg 188,056 193,910 189,436 193,118 190,640 195,740 190,400 193,904 186,545 196,428
X [A]
SD 3,291 2,934 3,035 2,543 2,085 2,608 7,664 4,502 6,923 2,869
X [A]
SU 1,472 1,312 1,357 1,137 0,933 1,166 3,428 2,013 4,895 1,283
X [%]
0,783 0,677 0,716 0,589 0
...








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