Iec 61788 2 2006

untitled NORME INTERNATIONALE CEI IEC INTERNATIONAL STANDARD 61788 2 Deuxième édition Second edition 2006 11 Supraconductivité – Partie 2 Mesure du courant critique – Courant critique continu des supr[.]

Matériau du mandrin de réaction

The reaction chuck must be made from a heat-resistant material, which may or may not have a treated surface Suitable materials for reaction chucks are recommended in section A.3.1, and any of these can be used.

Construction du mandrin de réaction

Il est recommandé que la forme d'ensemble du mandrin de réaction corresponde à celle du mandrin de mesurage sur lequel le spécimen individuel est à transférer

Le diamètre du mandrin de réaction doit être suffisamment grand pour que la déformation de flexion du spécimen, qui est introduite dans le spécimen pendant l'enroulage, soit inférieure à

Le mandrin doit comporter un sillon hélicọdal autour duquel le spécimen doit être enroulé

L'angle de pas du sillon doit être inférieur à 7° La profondeur du sillon doit être au moins égale à la moitié du diamètre du fil

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The goal of this method is to achieve a target precision with a coefficient of variation of less than 3% for critical current measurements conducted at 12 T and approximately 4.2 K.

The use of a common current transfer correction is excluded from this test method

Furthermore, if a current transfer signature is pronounced in the measurement, then the measurement shall be considered invalid

It is the responsibility of the user of this standard to consult and establish appropriate safety and health practices, and determine the applicability of regulatory limitations prior to use

Specific precautionary statements are given below

Measuring very large direct currents at low voltages can pose hazards, particularly due to the risk of accidental shorting with other conductors like tools or transfer lines Such short circuits can release substantial energy, leading to dangerous arcs or burns Therefore, it is crucial to isolate and protect current leads to prevent shorting incidents.

Superconducting magnets, which are typically employed to generate the background magnetic field, can store significant energy that may lead to substantial current or voltage pulses This stored energy can also result in the release of large amounts of thermal energy within cryogenic systems, potentially causing rapid boil-off or even explosive scenarios.

Under rapid boil-off conditions, cryogenic liquids can lead to oxygen-deficient environments, necessitating additional ventilation These liquids are crucial for cooling superconductors to achieve their superconducting state Direct skin contact with cold liquid transfer lines, storage dewars, or spilled cryogens can result in immediate freezing Therefore, it is essential to adhere to safety precautions when handling cryogenic liquids.

For the one-mandrel method, continue with Clause D.2

The reaction mandrel must be constructed from heat-resistant materials, which may feature a treated surface Recommended materials for the reaction mandrel can be found in section A.3.1, and any of these options are acceptable for use.

The overall geometry of the reaction mandrel should be matched closely to that of the measurement mandrel to which the individual specimen is to be transferred

The reaction mandrel shall have a diameter large enough that the specimen bending strain, which is introduced into the specimen during winding, is less than 5 %

The mandrel must feature a helical groove designed for winding the specimen, with a pitch angle not exceeding 7° Additionally, the groove's depth should be at least half the diameter of the wire.

Matériaux du mandrin de mesurage

Le mandrin de mesurage doit être constitué d'un matériau isolant ou d'un matériau conducteur non ferromagnétique recouvert ou non d'une couche isolante

The critical current is inevitably influenced by the material of the measurement mandrel due to the stress generated by the differential thermal contraction between the specimen and the measurement mandrel.

The total deformation in the specimen at the measurement temperature must be limited to ±0.03% If the deformation exceeds this limit due to the differential thermal contraction between the specimen and the mandrel, it is essential to record the critical current to be determined in a state of excessive deformation by identifying the material of the mandrel.

Des matériaux appropriés pour les mandrins de mesurage sont recommandés en A.3.3 Il est permis d'utiliser n'importe lequel d'entre eux

When a conductive material lacks an insulating layer, the leakage current in the core must be less than 0.2% of the total current when the specimen is at the critical current level, I_c (refer to section 9.5).

Construction du mandrin de mesurage

Le diamètre du mandrin de mesurage, l'angle de pas du sillon hélicọdal, sa profondeur et sa forme doivent être proches de ceux du mandrin de réaction

L'angle entre l'axe du spécimen (portion entre les prises de tension) et le champ magnétique doit être égal à (90 ± 7)° Cet angle doit être déterminé avec une précision de ±2°

The current contact and the measuring mandrel must form a rigid assembly to prevent any stress concentration in the transition area between the mandrel and the current contact.

Réalisation des mesures

L’appareillage pour mesurer la caractéristique U-I d’un spécimen supraconducteur est constitué d’une sonde, d’un cryostat d’essai, d’un système d’aimant et d’un système de mesure

The probe, which includes a specimen, a measurement mandrel, a support structure, voltage terminals, and current wires, is inserted into a helium-filled test cryostat Typically, the cryostat houses a superconducting solenoid magnet and its support structure to apply a magnetic field to the specimen The U-I measurement system consists of a DC power source, a recorder, and necessary preamplifiers, filters, or voltmeters, or a combination of these components Additionally, a computer-assisted data acquisition system may be utilized.

Pour la méthode à un mandrin, continuer avec l'Article D.4.

Montage du spécimen pour le traitement thermique de réaction

Le spécimen d'essai ne doit pas comporter de jointure ou d'épissure

The measurement mandrel shall be made from an insulating material, or from a conductive non-ferromagnetic material that is either covered or not covered with an insulating layer

The critical current may inevitably depend on the measurement mandrel material due to the strain induced by the differential thermal contraction between the specimen and the measurement mandrel

To ensure accurate measurements, the total strain in the specimen at the measuring temperature must be limited to within ±0.03% In cases where excess strain occurs due to differential thermal contraction between the specimen and the mandrel, it is essential to identify the mandrel material to determine the critical current under these excess strain conditions.

Suitable measurement mandrel materials are recommended in A.3.3 Any one of these may be used

When using a conductive material without an insulating layer, it is essential that the leakage current through the mandrel remains below 0.2% of the total current when the specimen is at its critical current, I_c (refer to section 9.5).

The mandrel shall have a helical groove in which the specimen shall be wound

The diameter of the measurement mandrel, the pitch angle of the helical groove and its depth and shape shall be close to those of the reaction mandrel

The angle between the specimen axis (portion between the voltage taps) and the magnetic field shall be (90 ± 7)° This angle shall be determined with an accuracy of ±2°

The current contact shall be rigidly fastened to the measurement mandrel to avoid stress concentration in the region of transition between the mandrel and the current contact

The apparatus to measure the U-I characteristic of a superconductor specimen consists of a specimen probe, a test cryostat, a magnet system and a U-I measurement system

The specimen probe, which includes a specimen, measurement mandrel, support structure, voltage taps, and current leads, is placed in a test cryostat filled with liquid helium Typically, this cryostat houses a superconducting solenoid magnet and its support structure to generate a magnetic field for the specimen The U-I measurement system comprises a direct current source, a recorder, and essential preamplifiers, filters, or voltmeters, potentially integrated with a computer-assisted data acquisition system.

For the one-mandrel method, continue with Clause D.4

7.1 Specimen mounting for reaction heat treatment

There shall be no joints or splices in the test specimen

Lorsqu'on utilise des critères de résistivité pour la détermination du courant critique, la surface totale de section S du spécimen doit être déterminée avec une précision de 5 %

L'enroulement du spécimen doit empêcher toute torsade supplémentaire du spécimen

The specimen should be placed in the reaction chuck groove with minimal tension (less than 0.1% tensile deformation) to ensure that its position is maintained and to minimize contact pressure, thereby preventing diffusion bonding.

The specimen wire must be secured to the reaction mandrel by bending the ends through small holes, one at each end of the mandrel, or by using an equivalent method.

Le spécimen doit être nettoyé pour éviter les effets de la contamination.

Traitement thermique de réaction

The thermal treatment of reaction must be conducted according to the manufacturer's specifications, ensuring that error limits are not exceeded Temperature variations within the furnace should be monitored to adhere to these limits.

Montage du spécimen pour la mesure

Après le traitement thermique de réaction, les extrémités du spécimen doivent être coupées pour correspondre au mandrin de mesurage

Le spécimen doit être dévissé du mandrin de réaction en le serrant légèrement et en faisant tourner le mandrin à l'intérieur de celui-ci

The specimen must be immediately secured to the measuring mandrel in the same manner it was removed from the reaction mandrel When mounting the specimen on the measuring mandrel, it should be placed in the groove, with one end welded to the current contact ring The specimen must be fully inserted, starting from the fixed end, ensuring it is firmly positioned in the groove The free end should then be welded to the other contact ring.

The minimum length of the welded section of the current contact must exceed the lesser value between 40 mm and 30 times the wire diameter Additionally, there should be no more than three turns of the welded specimen on each current contact.

La distance la plus courte entre un contact de courant et une prise de tension doit être supérieure à 100 mm

Tension leads must be soldered to the specimen To minimize mutual inductance between the applied current and the area formed by the specimen and the tension leads, the untwisted section of the tension leads should be wrapped in the opposite direction around the specimen, as shown in Figure A.1.

La distance autour du spécimen entre les prises de tension, L, doit être mesurée avec une précision de 5 % La séparation entre les prises de tension doit être supérieure à 150 mm.

Fixation du spécimen

On doit utiliser la tension d'enroulement du spécimen et/ou un adhésif à basse température

Silicone grease in a vacuum or epoxy resin is used to secure the specimen onto the measuring mandrel, minimizing its movement If the specimen's tension is utilized for fixation, this must be done during the specimen's setup for the measurement process (refer to section 7.3).

When using resistivity criteria for the critical current determination, the total cross-sectional area S of the specimen shall be determined to a precision of 5 %

The specimen shall not be wound in a manner that would introduce additional twists into the specimen

The specimen must be positioned in the groove of the reaction mandrel with minimal tension, specifically less than 0.1% tensile strain, to maintain its location and minimize contact pressure, thereby preventing diffusion bonding.

The specimen wire must be secured on the reaction mandrel by bending its ends through small holes located at each end, or by using an equivalent retention method.

The specimen shall be cleaned to avoid effects of contamination

Reaction heat treatment must adhere to the manufacturer's specifications, ensuring that error limits are strictly maintained It is essential to control temperature variations within the furnace to prevent exceeding these specified limits.

After the reaction heat treatment, the ends of the specimen shall be trimmed to suit the measurement mandrel

The specimen shall be unscrewed from the reaction mandrel by lightly restraining it and rotating the mandrel within it

The specimen must be promptly attached to the measurement mandrel in the same orientation as it was taken from the reaction mandrel It should be placed into the groove, with one end soldered to the current contact ring Beginning at the fixed end, the specimen should be stroked along its entire length to ensure a secure fit in the groove, after which the free end is to be soldered to the opposite contact ring.

The soldered length of the current contact must exceed the lesser value of 40 mm or 30 times the wire diameter, and each current contact should have no more than three turns of the specimen soldered to it.

The shortest distance from a current contact to a voltage tap shall be greater than 100 mm

To minimize mutual inductance between the applied current and the area formed by the specimen and voltage taps, the voltage taps should be soldered to the specimen This can be achieved by counterwinding the untwisted section of the voltage taps back along the specimen, as illustrated in Figure A.1.

The distance along the specimen between the voltage taps, L, shall be measured to an accuracy of 5 % This voltage tap separation shall be greater than 150 mm

To minimize specimen motion during measurement, it is essential to use specimen tension or a low-temperature adhesive, such as silicone vacuum grease or epoxy, to bond the specimen to the measurement mandrel If opting for specimen tension, this bonding must be performed during the specimen mounting process.

When using an adhesive, a minimal amount must be applied in the groove containing the specimen, and any excess should be removed from the outer surface of the specimen after it is mounted.

L'adéquation du montage du spécimen doit être attestée par l'obtention de la répétitivité du courant critique spécifié

Le spécimen ne doit pas être fixé au mandrin par soudage

The specimen must be immersed in liquid helium during the data acquisition phase It is acceptable for the specimen to be slowly cooled in helium vapor or gradually introduced into a liquid helium bath, or initially immersed in liquid nitrogen before transitioning to liquid helium The cooling process should bring the specimen from ambient temperature to the temperature of liquid helium (or liquid nitrogen) within at least 5 minutes.

A cryostat must create the necessary environment for measuring current (I c), and the specimen should be measured while immersed in liquid helium The liquid helium bath should be maintained at a temperature close to its normal boiling point for the typical atmospheric pressure at the testing site.

La température du bain d'hélium liquide doit être mesurée pendant chaque détermination de I c

The specimen's current must be kept at a sufficiently low level to prevent it from entering a normal state, unless a protective switching circuit or a resistive shunt is employed to safeguard the specimen from potential damage.

When employing the constant sweep speed method, the time variation between zero and I_c must exceed 10 seconds In contrast, when using the variation and hold method, the current sweep speed between the setpoint signals must be less than the equivalent speed for a current change from zero to I_c in 3 seconds Additionally, the current drift during each setpoint signal must remain below 1% of I_c.

Le champ magnétique continu doit être appliqué dans la direction de l'axe du mandrin La relation entre le champ magnétique et le courant de l'aimant doit être préalablement mesurée

Le courant de l'aimant doit être mesuré avant chaque détermination de I c

The direction of the current and the applied magnetic field must generate a Lorentz force directed inward along the length of the specimen, at least between the voltage taps.

Enregistrer la caractéristique U-I du spécimen d'essai dans les conditions de l'essai, ainsi que l'augmentation monotone du courant

A valid U-I characteristic must yield a reproducible current \$I_c\$ with an accuracy of 1%, and this characteristic should remain stable over time under voltages equal to or less than the critical current threshold.

Courant critique

La source de courant doit délivrer un courant continu dont les variations périodiques et aléatoires maximales sont inférieures à ±2 % à I c , dans la largeur de bande de 10 Hz à 10 MHz

Une résistance standard à quatre bornes avec une précision au moins égale à 0,5 % doit être utilisée pour déterminer le courant du spécimen

L’enregistrement de la caractéristique U-I doit permettre de déterminer Uavec une justesse de

10 %, le courant correspondant avec une précision de 1 % et une justesse de 1 %.

Température

The specimen's temperature is assumed to be equal to that of the liquid The liquid's temperature must be measured with an accuracy of ±0.02 K using an appropriate pressure sensor or temperature sensor.

La différence entre la température du spécimen et celle du bain doit être minimisée

To convert the pressure observed in the cryostat into a temperature value, the phase diagram of helium must be utilized Accurate pressure measurements are essential to achieve the required precision in temperature measurement When the depth of the liquid helium exceeds 1 meter, it may be necessary to apply corrections to the sensors.

Champ magnétique

A magnetic system must deliver a magnetic field with an accuracy exceeding ±1% and ±0.02 T, along with a precision better than ±0.5% and ±0.02 T, with the highest value being maintained over the length of the specimen between the voltage taps.

Le champ magnétique doit avoir une uniformité meilleure que 0,5 % et 0,02 T, la valeur la plus grande étant retenue, sur la longueur du spécimen entre les prises de tension

Les variations périodiques et aléatoires maximales du champ magnétique doivent être inférieures à la valeur la plus grande de ±1 % et ±0,02 T.

Structure de support du spécimen

The support structure must provide adequate support for the specimen and allow for its orientation relative to the magnetic field It is considered appropriate if it enables additional determinations of the critical current with an accuracy of 1%.

Protection du spécimen

If a resistive shunt or a protective switching circuit is used in parallel with the specimen, the current flowing through the shunt or circuit must be less than 0.2% of the total current.

9 Precision and accuracy of the test method

The current source shall provide a d.c current having a maximum periodic and random deviation of less than ±2 % at I c , within the bandwidth 10 Hz to 10 MHz

A four-terminal standard resistor, with an accuracy of at least 0,5 %, shall be used to determine the specimen current

The record of U-I characteristic shall allow the determination of Uto a precision of 10 %, the corresponding current to an accuracy of 1 % and with a precision of 1 %

The specimen temperature is considered equivalent to the liquid temperature, which must be reported with an accuracy of ±0.02 K This measurement can be obtained using a pressure sensor or a suitable temperature sensor.

The difference between the specimen temperature and the bath temperature shall be minimized

To convert the observed pressure in the cryostat to a temperature value, the phase diagram of helium is utilized Accurate pressure measurements are essential to achieve the desired precision in temperature readings Additionally, for liquid helium depths exceeding 1 meter, a head correction may be required.

A magnetic system must deliver a magnetic field with an accuracy exceeding ±1% or ±0.02 T, whichever is greater, and a precision surpassing ±0.5% or ±0.02 T, whichever is larger, across the length of the specimen between the voltage taps.

The magnetic field shall have a uniformity better than the larger of 0,5 % and 0,02 T over the length of the specimen between the voltage taps

The maximum periodic and random deviation of the magnetic field shall be less than the larger of ±1 % and ±0,02 T

The support structure must ensure proper alignment of the specimen with the magnetic field while providing sufficient support It is considered adequate if it enables precise measurements of critical current with an accuracy of 1%.

When utilizing a resistive shunt or quench protection circuit in parallel with the specimen, it is essential that the current flowing through the shunt or circuit remains below 0.2% of the total current at I_c.

Critères de courant critique

The critical current, I_c, should be determined using either an electric field criterion, E_c, or a resistivity criterion, ρ_c, particularly when the total cross-section S of the composite superconductor is preferred for resistivity estimation (refer to Figures 1 and 2).

T ens ion U (unit és a rbi tr air es )

T ens ion U (unit és ar bi tr air es )

Figure 1a) – Application du critère du champ électrique Figure 1b) – Application du critère de résistivité

NOTE L’application du critère du champ électrique (Figure 1a) et du critère de résistivité (Figure 1b) pour déterminer le courant critique est montrée ci-dessus

T en si on U (u ni té s arbi tr ai res ) T en si on U (u ni té s arbi tr ai res )

Ligne de transfert de courant

The application of the electric field criterion and the resistivity criterion in determining the critical current on a U-I characteristic is illustrated above This includes a current transfer component represented as a linear region traversed by a low current.

Figure 2 – Caractéristique U-I avec une composante de transfert de courant

In the case of an electric field criterion, two critical current values, I_c, must be determined for thresholds of 10 V/m and 100 V/m Conversely, for resistivity criteria, two I_c values should be established for resistivity levels of 10^{-14} Ωm and 10^{-13} Ωm.

The critical current, denoted as \$I_c\$, can be assessed using either an electric field criterion, \$E_c\$, or a resistivity criterion, \$\rho_c\$ For estimating resistivity, it is recommended to consider the total cross-sectional area, \$S\$, of the composite superconductor, as illustrated in Figures 1 and 2.

V olt age U (a rbit ra ry uni ts )

Figure 1a) – Application of the electric field criteria Figure 1b) – Application of the resistivity criteria

NOTE The application of the (Figure 1a) electric field and (Figure 1b) resistivity criteria to determine the critical current is shown above

V ol tage U (a rbit rary unit s)

The application of the electric field and resistivity criteria, as illustrated in Figure 2a and Figure 2b, is essential for determining the critical current on a U-I characteristic This characteristic displays a linear region at low current, highlighting the current transfer component.

Figure 2 – U-I characteristic with a current transfer component

For the electric field criterion, two values of \$I_c\$ will be established at electric field strengths of 10 µV/m and 100 µV/m Additionally, two values of \$I_c\$ will be determined based on resistivity criteria.

Lorsqu’il est difficile d'obtenir un mesurage correct de I c pour un critère de 100 μV/m, un critère

E c inférieur à 100 μV/m doit le remplacer Sinon, des mesurages utilisant le critère de résistivité sont recommandés

Le courant I c doit être déterminé comme étant le courant correspondant au point de la courbe

U-I ó la tension est égale à U c mesurée en fonction de la tension de base (voir Figures 1a) et

U c est le critère de tension, en microvolts (μV);

L est la séparation entre prises de tension, en mètres (m);

E c est le critère de champ électrique, en microvolts par mètre (μV/m)

Ou, en utilisant un critère de résistivité:

The equation \$ U_c = I_c \rho_c \frac{L}{S} \$ describes the relationship between voltage (\$U_c\$), current (\$I_c\$), and resistivity (\$\rho_c\$) at the intersection of a straight line with the U-I curve, as illustrated in Figures 1b) and 2b) Here, \$L\$ represents the distance between voltage measurement points in meters, and \$S\$ denotes the total cross-sectional area in square meters.

Une ligne droite doit être tracée de la tension de base à la tension moyenne proche de 0,7 I c

Figures 1 and 2 illustrate that the finite positive slope of the line may be attributed to current transfer For a valid determination of \$I_c\$, the slope must be less than \$0.3 \cdot \frac{U_c}{I_c}\$ when \$U_c\$ and \$I_c\$ are measured using a criterion of \$10 \, \mu V/m\$ or \$10^{-14} \, \Omega m\$.

Valeur n (calcul facultatif, se reporter à A.7.2)

The value $ n $ should be calculated as the slope of the log $ U $ versus log $ I $ plot in the region where $ I $ is determined, or it can be calculated using two specific values of $ I $ identified in section 10.1 with two different criteria.

L'étendue des critères utilisés pour déterminer n doit être mentionnée

Identification du spécimen d'essai

The test specimen should be identified, if possible, by the following elements: a) the manufacturer's name; b) classification and/or symbol; c) lot number; d) raw materials along with their chemical composition; e) the shape and surface of the wire section, number of filaments, filament diameter, volume fractions of filaments, copper/non-copper ratio, barriers, copper stabilizer, and other wire components, as well as the pitch and direction of twisting; f) manufacturing process technique (such as bronze process, internal diffusion process of tin, etc.).

Compte rendu des valeurs I c

Les valeurs I c et les critères correspondants doivent être mentionnés

When it is difficult to measure the I c properly at a criterion of 100 μV/m, an E c criterion less than 100 μV/m shall be substituted Otherwise, the measurements using the resistivity criterion are recommended

The I c shall be determined as the current corresponding to the point on the U-I curve where the voltage is U c measured relative to the baseline voltage (see Figures 1a) and 2a)):

U c is the voltage criterion, in microvolts (μV);

L is the voltage tap separation, in metres (m);

E c is the electric field criterion, in microvolts/metre (μV/m)

Or, when using a resistivity criterion:

The equation \$U_c = I_c \rho_c \frac{L}{S}\$ describes the relationship between voltage (\$U_c\$), current (\$I_c\$), and resistivity (\$\rho_c\$) at the intersection of a straight line with the U-I curve, as illustrated in Figures 1b) and 2b) In this equation, \$L\$ represents the voltage tap separation in meters, while \$S\$ denotes the total cross-sectional area in square meters.

A straight line shall be drawn from the baseline voltage to the average voltage near 0,7 I c (see

A finite positive slope in the line may indicate current transfer To accurately determine \$I_c\$, the slope must be less than \$0.3 \frac{U_c}{I_c}\$, with \$U_c\$ and \$I_c\$ measured at a criterion of \$10 \, \mu V/m\$ or \$10^{-14} \, \Omega m\$.

10.2 n -value (optional calculation, refer to A.7.2)

The n-value is determined by calculating the slope of the log U versus log I plot in the region where the critical current (I c) is identified, or by using two I c values obtained under different criteria as specified in section 10.1.

The range of the criteria used to determine n shall be reported

The test specimen should be identified by several key factors, including the manufacturer's name, classification or symbol, lot number, and the raw materials along with their chemical composition Additionally, important specifications such as the shape and cross-sectional area of the wire, the number and diameter of filaments, volume fractions, copper/non-copper ratio, barriers, copper stabilizer, and other components must be documented Finally, the manufacturing process technique, such as bronze or internal tin diffusion, should also be noted.

The I c values, along with their corresponding criteria, shall be reported

Reaction mandrel material

The reaction mandrel must be constructed from heat-resistant materials, which may feature a treated surface Recommended materials for the reaction mandrel can be found in section A.3.1, and any of these options are acceptable for use.

Reaction mandrel construction

The overall geometry of the reaction mandrel should be matched closely to that of the measurement mandrel to which the individual specimen is to be transferred

The reaction mandrel shall have a diameter large enough that the specimen bending strain, which is introduced into the specimen during winding, is less than 5 %

The mandrel must feature a helical groove designed for winding the specimen, with a pitch angle not exceeding 7° Additionally, the groove's depth should be at least half the diameter of the wire.

6.3 Matériaux du mandrin de mesurage

Le mandrin de mesurage doit être constitué d'un matériau isolant ou d'un matériau conducteur non ferromagnétique recouvert ou non d'une couche isolante

The critical current is inevitably influenced by the material of the measurement mandrel due to the stress generated by the differential thermal contraction between the specimen and the measurement mandrel.

The total deformation in the specimen at the measurement temperature must be limited to ±0.03% If the deformation exceeds this limit due to the differential thermal contraction between the specimen and the mandrel, it is essential to record the critical current to be determined in a state of excessive deformation by identifying the material of the mandrel.

Des matériaux appropriés pour les mandrins de mesurage sont recommandés en A.3.3 Il est permis d'utiliser n'importe lequel d'entre eux

When a conductive material lacks an insulating layer, the leakage current in the core must be less than 0.2% of the total current when the specimen is at the critical current level, I_c (refer to section 9.5).

6.4 Construction du mandrin de mesurage

Le diamètre du mandrin de mesurage, l'angle de pas du sillon hélicọdal, sa profondeur et sa forme doivent être proches de ceux du mandrin de réaction

L'angle entre l'axe du spécimen (portion entre les prises de tension) et le champ magnétique doit être égal à (90 ± 7)° Cet angle doit être déterminé avec une précision de ±2°

The current contact and the measuring mandrel must create a rigid assembly to prevent any stress concentration in the transition area between the mandrel and the current contact.

L’appareillage pour mesurer la caractéristique U-I d’un spécimen supraconducteur est constitué d’une sonde, d’un cryostat d’essai, d’un système d’aimant et d’un système de mesure

The probe, which includes a specimen, a measurement mandrel, a support structure, voltage terminals, and current wires, is inserted into a helium-filled test cryostat Typically, the cryostat houses a superconducting solenoid magnet and its support structure to apply a magnetic field to the specimen The U-I measurement system consists of a DC power source, a recorder, necessary preamplifiers, filters or voltmeters, or a combination of these components Additionally, a computer-assisted data acquisition system may also be utilized.

Pour la méthode à un mandrin, continuer avec l'Article D.4

7.1 Montage du spécimen pour le traitement thermique de réaction

Le spécimen d'essai ne doit pas comporter de jointure ou d'épissure

Measurement mandrel material

The measurement mandrel shall be made from an insulating material, or from a conductive non-ferromagnetic material that is either covered or not covered with an insulating layer

The critical current may inevitably depend on the measurement mandrel material due to the strain induced by the differential thermal contraction between the specimen and the measurement mandrel

To ensure accurate measurements, the total strain in the specimen at the measuring temperature must be limited to within ±0.03% If excess strain occurs due to the differential thermal contraction between the specimen and the mandrel, the critical current should be assessed under this excess strain condition by identifying the mandrel material.

Suitable measurement mandrel materials are recommended in A.3.3 Any one of these may be used

When using a conductive material without an insulating layer, it is essential that the leakage current through the mandrel remains below 0.2% of the total current at the critical current level, I_c (refer to section 9.5).

Measurement mandrel construction

The mandrel shall have a helical groove in which the specimen shall be wound

The diameter of the measurement mandrel, the pitch angle of the helical groove and its depth and shape shall be close to those of the reaction mandrel

The angle between the specimen axis (portion between the voltage taps) and the magnetic field shall be (90 ± 7)° This angle shall be determined with an accuracy of ±2°

The current contact shall be rigidly fastened to the measurement mandrel to avoid stress concentration in the region of transition between the mandrel and the current contact.

Measurement set up

The apparatus to measure the U-I characteristic of a superconductor specimen consists of a specimen probe, a test cryostat, a magnet system and a U-I measurement system

The specimen probe, which includes a specimen, measurement mandrel, support structure, voltage taps, and current leads, is placed in a test cryostat filled with liquid helium Typically, this cryostat houses a superconducting solenoid magnet and its support structure to generate a magnetic field for the specimen The U-I measurement system comprises a direct current source, a recorder, and essential preamplifiers, filters, or voltmeters, potentially integrated with a computer-assisted data acquisition system.

For the one-mandrel method, continue with Clause D.4.

Specimen mounting for reaction heat treatment

There shall be no joints or splices in the test specimen

Lorsqu'on utilise des critères de résistivité pour la détermination du courant critique, la surface totale de section S du spécimen doit être déterminée avec une précision de 5 %

L'enroulement du spécimen doit empêcher toute torsade supplémentaire du spécimen

The specimen should be placed in the reaction chuck groove with minimal tension (less than 0.1% tensile deformation) to ensure that its position is maintained and to minimize contact pressure, thereby preventing diffusion bonding.

The specimen wire must be secured to the reaction mandrel by bending the ends through small holes, one at each end of the mandrel, or by using an equivalent method.

Le spécimen doit être nettoyé pour éviter les effets de la contamination

The thermal treatment of reaction must be conducted according to the manufacturer's specifications, ensuring that error limits are not exceeded Temperature variations within the furnace should be monitored to adhere to these limits.

7.3 Montage du spécimen pour la mesure

Après le traitement thermique de réaction, les extrémités du spécimen doivent être coupées pour correspondre au mandrin de mesurage

Le spécimen doit être dévissé du mandrin de réaction en le serrant légèrement et en faisant tourner le mandrin à l'intérieur de celui-ci

The specimen must be immediately secured to the measuring mandrel in the same manner it was removed from the reaction mandrel When mounting the specimen on the measuring mandrel, it should be placed in the groove, with one end welded to the current contact ring The specimen must be fully inserted, starting from the fixed end, ensuring it is firmly positioned in the groove The free end should then be welded to the other contact ring.

The minimum length of the welded section of the current contact must exceed the lesser value between 40 mm and 30 times the wire diameter Additionally, there should not be more than three turns of the welded specimen on each current contact.

La distance la plus courte entre un contact de courant et une prise de tension doit être supérieure à 100 mm

Tension leads must be soldered to the specimen To minimize mutual inductance between the applied current and the area formed by the specimen and the tension leads, the untwisted section of the tension leads should be wrapped in the opposite direction around the specimen, as shown in Figure A.1.

La distance autour du spécimen entre les prises de tension, L, doit être mesurée avec une précision de 5 % La séparation entre les prises de tension doit être supérieure à 150 mm

On doit utiliser la tension d'enroulement du spécimen et/ou un adhésif à basse température

Silicone grease in a vacuum or epoxy resin is used to secure the specimen onto the measuring mandrel, minimizing its movement If the specimen's tension is employed for fixation, this must be done during the specimen's setup for the measurement process (refer to section 7.3).

When using resistivity criteria for the critical current determination, the total cross-sectional area S of the specimen shall be determined to a precision of 5 %

The specimen shall not be wound in a manner that would introduce additional twists into the specimen

The specimen must be positioned in the groove of the reaction mandrel with minimal tension, specifically less than 0.1% tensile strain, to maintain its location and minimize contact pressure, thereby preventing diffusion bonding.

The specimen wire must be secured on the reaction mandrel by bending its ends through small holes located at each end, or by using an equivalent retention method.

The specimen shall be cleaned to avoid effects of contamination.

R eaction heat treatment

Reaction heat treatment must adhere to the manufacturer's specifications, ensuring that error limits are strictly maintained It is essential to control temperature variations within the furnace to prevent exceeding these specified limits.

Specimen mounting for measurement

After the reaction heat treatment, the ends of the specimen shall be trimmed to suit the measurement mandrel

The specimen shall be unscrewed from the reaction mandrel by lightly restraining it and rotating the mandrel within it

The specimen must be promptly attached to the measurement mandrel in the same orientation as it was taken from the reaction mandrel It should be placed into the groove, with one end soldered to the current contact ring Beginning at the fixed end, the specimen should be stroked along its full length to ensure a secure fit in the groove, after which the free end is soldered to the opposite contact ring.

The soldered length of the current contact must exceed the lesser of 40 mm or 30 times the wire diameter, and each current contact should have no more than three turns of the specimen soldered to it.

The shortest distance from a current contact to a voltage tap shall be greater than 100 mm

To minimize mutual inductance between the applied current and the area formed by the specimen and voltage taps, solder the voltage taps to the specimen and counterwind the untwisted section of the voltage taps back along the specimen, as illustrated in Figure A.1.

The distance along the specimen between the voltage taps, L, shall be measured to an accuracy of 5 % This voltage tap separation shall be greater than 150 mm.

Specimen bonding

To minimize specimen motion during measurement, it is essential to use specimen tension or a low-temperature adhesive, such as silicone vacuum grease or epoxy, to securely bond the specimen to the measurement mandrel If opting for specimen tension, this should be applied during the mounting process for accurate measurements.

When using an adhesive, a minimal amount must be applied in the groove containing the specimen, and any excess should be removed from the outer surface of the specimen after it has been mounted.

L'adéquation du montage du spécimen doit être attestée par l'obtention de la répétitivité du courant critique spécifié

Le spécimen ne doit pas être fixé au mandrin par soudage

The specimen must be immersed in liquid helium during the data acquisition phase It is acceptable for the specimen to be slowly cooled in helium vapor or gradually introduced into a liquid helium bath, or initially immersed in liquid nitrogen before transitioning to liquid helium The cooling process should bring the specimen from ambient temperature to the temperature of liquid helium (or liquid nitrogen) within at least 5 minutes.

A cryostat must create the necessary environment for measuring current (I c), and the specimen should be measured while immersed in liquid helium The liquid helium bath should be maintained at a temperature close to its normal boiling point for the typical atmospheric pressure at the testing site.

La température du bain d'hélium liquide doit être mesurée pendant chaque détermination de I c

The specimen's current must be kept at a sufficiently low level to prevent it from entering a normal state, unless a protective switching circuit or a resistive shunt is employed to safeguard the specimen from potential damage.

When employing the constant sweep speed method, the time variation between zero and I c must exceed 10 seconds In contrast, when using the variation and hold method, the current sweep speed between the setpoint signals must be less than the equivalent speed for a current change from zero to I c in 3 seconds Additionally, the current drift during each setpoint signal must remain below 1% of I c.

Le champ magnétique continu doit être appliqué dans la direction de l'axe du mandrin La relation entre le champ magnétique et le courant de l'aimant doit être préalablement mesurée

Le courant de l'aimant doit être mesuré avant chaque détermination de I c

The direction of the current and the applied magnetic field must generate a Lorentz force directed inward along the length of the specimen, at least between the voltage taps.

Enregistrer la caractéristique U-I du spécimen d'essai dans les conditions de l'essai, ainsi que l'augmentation monotone du courant

A valid U-I characteristic must yield a reproducible current \$I_c\$ with an accuracy of 1%, and this characteristic should remain stable over time under voltages equal to or less than the critical current threshold.

The base voltage of the U-I characteristic should be regarded as the voltage recorded at zero current using the variation and current maintenance method, or as the average voltage at approximately 0.1 I c using the constant sweep speed method.

When applying an adhesive, it is essential to use only a minimal amount within the groove that holds the specimen After mounting the specimen, any excess adhesive should be carefully removed from its outer surface.

The adequacy of specimen bonding shall be demonstrated by a successful completion of the specified critical current repeatability

Solder shall not be used to bond the specimen to the mandrel

During the data acquisition phase, the specimen must be immersed in liquid helium It can be cooled gradually in helium vapor before entering the liquid helium bath, directly inserted into the liquid helium, or initially cooled in liquid nitrogen before transitioning to liquid helium The cooling process should take at least 5 minutes to lower the specimen's temperature from room temperature to that of liquid helium or liquid nitrogen.

The cryostat will create the ideal conditions for measuring critical current (I c), with the specimen submerged in liquid helium The liquid helium bath will be maintained at a temperature close to its normal boiling point, tailored to the typical atmospheric pressure at the testing location.

The temperature of the liquid helium bath shall be measured during each determination of I c

To prevent damage to the specimen, the current must be maintained at a low level, ensuring it does not reach the normal state unless a quench protection circuit or resistive shunt is employed for safety.

When employing the constant sweep rate method, the ramp time from zero current to I_c should exceed 10 seconds In contrast, the ramp-and-hold method requires that the current sweep rate between set points remains lower than the equivalent rate for ramping from zero current.

I c in 3 s The current drift during each current set point shall be less than 1 % of I c

The d.c magnetic field will be oriented along the mandrel axis Prior measurements will establish the relationship between the magnetic field and the magnet current Additionally, the magnet current must be recorded before each measurement of the critical current, I_c.

The direction of the current and the applied magnetic field shall result in an inward Lorentz force over the length of the specimen at least between the voltage taps

Record the U-I characteristic of the test specimen under test conditions and monotonically increasing current

A valid U-I characteristic shall give a repeatable I c to a precision of 1 % and the characteristic shall be stable with time for voltages at or below the critical current criterion

Critical current

The current source shall provide a d.c current having a maximum periodic and random deviation of less than ±2 % at I c , within the bandwidth 10 Hz to 10 MHz

A four-terminal standard resistor, with an accuracy of at least 0,5 %, shall be used to determine the specimen current

The record of U-I characteristic shall allow the determination of Uto a precision of 10 %, the corresponding current to an accuracy of 1 % and with a precision of 1 %.

Temperature

The specimen temperature is considered equivalent to the liquid temperature, which must be reported with an accuracy of ±0.02 K This measurement can be obtained using a pressure sensor or a suitable temperature sensor.

The difference between the specimen temperature and the bath temperature shall be minimized

To convert the observed pressure in the cryostat to a temperature value, the phase diagram of helium is utilized Accurate pressure measurements are essential to achieve the desired precision in temperature readings Additionally, for liquid helium depths exceeding 1 meter, a head correction may be required.

Magnetic field

A magnetic system must deliver a magnetic field with an accuracy exceeding ±1% or ±0.02 T, whichever is greater, and a precision surpassing ±0.5% or ±0.02 T, also whichever is greater, across the length of the specimen between the voltage taps.

The magnetic field shall have a uniformity better than the larger of 0,5 % and 0,02 T over the length of the specimen between the voltage taps

The maximum periodic and random deviation of the magnetic field shall be less than the larger of ±1 % and ±0,02 T.

Specimen support structure

The support structure must ensure proper alignment of the specimen with the magnetic field while providing sufficient support It is considered adequate if it enables precise measurements of critical current with an accuracy of 1%.

Specimen protection

When utilizing a resistive shunt or quench protection circuit in parallel with the specimen, it is essential that the current flowing through the shunt or circuit remains below 0.2% of the total current at I_c.

The critical current, I_c, should be determined using either an electric field criterion, E_c, or a resistivity criterion, ρ_c, particularly when the total cross-section S of the composite superconductor is preferred for resistivity estimation (refer to Figures 1 and 2).

T ens ion U (unit és a rbi tr air es )

T ens ion U (unit és ar bi tr air es )

NOTE L’application du critère du champ électrique (Figure 1a) et du critère de résistivité (Figure 1b) pour déterminer le courant critique est montrée ci-dessus

T en si on U (u ni té s arbi tr ai res ) T en si on U (u ni té s arbi tr ai res )

Ligne de transfert de courant

The application of the electric field criterion and the resistivity criterion in determining the critical current on a U-I characteristic is illustrated above, with a current transfer component represented as a linear region traversed by a low current.

Figure 2 – Caractéristique U-I avec une composante de transfert de courant

In the case of an electric field criterion, two values of $ I_c $ must be determined for criteria of 10 V/m and 100 V/m Conversely, for resistivity criteria, two values of $ I_c $ should be established for resistivities of $ 10^{-14} \, \Omega \cdot m $ and $ 10^{-13} \, \Omega \cdot m $.

Critical current criteria

The critical current, denoted as \$I_c\$, can be evaluated using either an electric field criterion, \$E_c\$, or a resistivity criterion, \$\rho_c\$ For estimating resistivity, it is recommended to consider the total cross-sectional area, \$S\$, of the composite superconductor, as illustrated in Figures 1 and 2.

V olt age U (a rbit ra ry uni ts )

NOTE The application of the (Figure 1a) electric field and (Figure 1b) resistivity criteria to determine the critical current is shown above

V ol tage U (a rbit rary unit s)

The application of the electric field and resistivity criteria, as illustrated in Figure 2a and Figure 2b, is essential for determining the critical current on a U-I characteristic This characteristic displays a linear region at low current, highlighting the current transfer component.

Figure 2 – U-I characteristic with a current transfer component

For the electric field criterion, two values of \$I_c\$ will be established at electric field strengths of 10 àV/m and 100 àV/m Additionally, two values of \$I_c\$ will be determined based on resistivity criteria.

Lorsqu’il est difficile d'obtenir un mesurage correct de I c pour un critère de 100 μV/m, un critère

E c inférieur à 100 μV/m doit le remplacer Sinon, des mesurages utilisant le critère de résistivité sont recommandés

Le courant I c doit être déterminé comme étant le courant correspondant au point de la courbe

U-I ó la tension est égale à U c mesurée en fonction de la tension de base (voir Figures 1a) et

U c est le critère de tension, en microvolts (μV);

L est la séparation entre prises de tension, en mètres (m);

E c est le critère de champ électrique, en microvolts par mètre (μV/m)

Ou, en utilisant un critère de résistivité:

The equation \$U_c = I_c \rho_c \frac{L}{S}\$ describes the relationship between voltage (\$U_c\$), current (\$I_c\$), and resistivity (\$\rho_c\$) at the intersection of a straight line with the U-I curve, as illustrated in Figures 1b) and 2b) Here, \$L\$ represents the distance between voltage measurement points in meters, while \$S\$ denotes the total cross-sectional area in square meters.

Une ligne droite doit être tracée de la tension de base à la tension moyenne proche de 0,7 I c

Figures 1 and 2 illustrate that the finite positive slope of this line may be attributed to current transfer For a valid determination of \$I_c\$, the slope must be less than \$0.3 \cdot \frac{U_c}{I_c}\$ when \$U_c\$ and \$I_c\$ are measured using a criterion of \$10 \, \mu V/m\$ or \$10^{-14} \, \Omega m\$.

10.2 Valeur n (calcul facultatif, se reporter à A.7.2)

The value $ n $ should be calculated as the slope of the log $ U $ versus log $ I $ plot in the region where $ I $ is determined, or it can be calculated using two specific values of $ I $ identified in section 10.1 with two different criteria.

L'étendue des critères utilisés pour déterminer n doit être mentionnée

The test specimen should be identified, if possible, by the following elements: a) the manufacturer's name; b) classification and/or symbol; c) lot number; d) raw materials along with their chemical composition; e) the shape and surface of the wire section, number of filaments, filament diameter, volume fractions of filaments, copper/non-copper ratio, barriers, copper stabilizer, and other wire components, as well as the pitch and direction of twist; f) the manufacturing process technique (such as bronze process, internal tin diffusion process, etc.).

Les valeurs I c et les critères correspondants doivent être mentionnés

When it is difficult to measure the I c properly at a criterion of 100 μV/m, an E c criterion less than 100 μV/m shall be substituted Otherwise, the measurements using the resistivity criterion are recommended

The I c shall be determined as the current corresponding to the point on the U-I curve where the voltage is U c measured relative to the baseline voltage (see Figures 1a) and 2a)):

U c is the voltage criterion, in microvolts (μV);

L is the voltage tap separation, in metres (m);

E c is the electric field criterion, in microvolts/metre (μV/m)

Or, when using a resistivity criterion:

The equation \$U_c = I_c \rho_c \frac{L}{S}\$ describes the relationship between voltage (\$U_c\$), current (\$I_c\$), and resistivity (\$\rho_c\$) at the intersection of a straight line with the U-I curve, as illustrated in Figures 1b) and 2b) In this equation, \$L\$ represents the voltage tap separation in meters, while \$S\$ denotes the total cross-sectional area in square meters.

A straight line shall be drawn from the baseline voltage to the average voltage near 0,7 I c (see

A finite positive slope in the line may indicate current transfer To accurately determine \$I_c\$, the slope must be less than \$0.3 \frac{U_c}{I_c}\$, with \$U_c\$ and \$I_c\$ measured at a criterion of \$10 \, \mu V/m\$ or \$10^{-14} \, \Omega m\$.

n-value (optional calculation, refer to A.7.2)

The n-value is determined by calculating the slope of the log U versus log I plot in the region where the critical current (I c) is identified, or by using two I c values obtained under different criteria as specified in section 10.1.

The range of the criteria used to determine n shall be reported

Identification of test specimen

The test specimen should be identified by several key factors, including the manufacturer's name, classification or symbol, lot number, and the raw materials along with their chemical composition Additionally, important specifications such as the shape and cross-sectional area of the wire, the number and diameter of filaments, volume fractions, copper/non-copper ratio, barriers, copper stabilizer, and other components must be noted Finally, the manufacturing process technique, such as bronze or internal tin diffusion, should also be documented.

Report of I c values

The I c values, along with their corresponding criteria, shall be reported

11.3 Compte rendu des conditions d'essai

The following testing conditions must be specified: a) the magnetic field strength, along with its uniformity and accuracy; b) the testing temperature and its precision; c) the number of turns in the coil used for testing; d) the distance between voltage taps and the total length of the specimen; e) the shortest distance from a current contact to a voltage tap; f) the minimum distance between current contacts; g) the length of the welds for current contacts; h) the method of securing the specimen, including the identification of the fastening material; i) the materials used for the reaction and measurement mandrels; j) the diameters of the reaction and measurement mandrels; k) the depth, shape, pitch, and angle of the grooves; l) the thermal treatment conditions for the reaction.

Tiêu đề	Critical Current Measurement of Nb3Sn Superconductors
Trường học	Unknown University
Chuyên ngành	Superconductivity
Thể loại	Standard
Năm xuất bản	2006

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