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DEVELOPMENT OF STANDARDS FDR SUPERCONDUCTORS

Annual Report

FY80

F.R. Fickett, LF. Goodrich, and A.F. Clark

Electromagnetic Technology Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

DECEMBER 1980

Work performed under Department of Energy

contract EA-77-A-01-6010 and Massachusetts

Institute of Technology contract POML-162265

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f b~ hoDEVELOPMENT OF STANDARDS FOR SUPERCONDUCTORS

Annual Report

FY 80

F.R. Fickett, LF. Goodrich, and A.F. Clark

Electromagnetic Technology Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

DECEMBER 1980

Work performed under Department of Energy

contract EA-77-A-01-6010 and Massachusetts

Institute of Technology contract POML-162265

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology, and Innovation

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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CONTENTS

Page

Abstract v

I. INTRODUCTION 1

II. EVALUATION OF PRESENT STATUS 4

A. Test Specification Survey 5

B. Round Robin Test 6

C. A Discussion of Current Transfer 9

III. PREPARATION AND DISSEMINATION OF STANDARDS 13

A. Standard for Terminology 13

B. Standard for Critical Current Measurement 14

C. Standard Reference Materials 15

IV. EXPERIMENTAL PROGRAM: CRITICAL CURRENT 17

A. Sample Mounting 17

B. I Criterion 30

c

C. Sample Current, Resistance Ratio, and Self Field 33

D. Field Orientation and Uniformity 40

E. Conductor Parameters 42

V. CONTRACTOR REPORTS 49

A. Airco Superconductors 51

B. Intermagnetics General Corporation 91

C. Magnetic Corporation of America 141

D. Supercon, Inc 185

VI. REFERENCES 203

APPENDICES

A. Publications and Presentations

B. Staff and Contacts

C. Minutes of ASTM Subcommittee B01.08 on Superconductors
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DEVELOPMENT OF STANDARDS FOR SUPERCONDUCTORS

F. R. Fickett, L. F. Goodrich, and A. F. Clark

Electromagnetic Technology Division

National Bureau of Standards

Boulder, Colorado 80303

Modern practical superconductors are complex materials and the determination of their critical parameters is a difficult task. Many approaches are

possible for determining a given parameter and the results often depend on

which one is chosen. The goal of this program, a cooperative venture involving

DoE, NBS, and private industry, is to arrive at a set of useful voluntary

standards for measurements on modern practical superconductors that will be

acceptable to both manufacturers and users. Agreement on a set of standard

definitions for the commonly used terms is also necessary. This report

describes the status of the program at the end of the second year. The work

in FY 80 has concentrated nearly exclusively on the critical current standard.

Experimental determinations of the effect of various parameters on the measurement have been made by NBS and by the wire manufacturers. Significant progress

has been made in the preparation of the actual critical current measurement

standard and the definition standard. Draft copies of both are now ready for

comment

.

Key words; Critical current; electrical property; magnetic property; stability;

standards; superconductor.

Note: Papers by non-NBS authors have not been reviewed or edited by NBS.

Therefore, the National Bureau of Standards accepts no responsibility

for comments or recommendations contained therein.

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I. INTRODUCTION

The goal of the superconductor standards program is the development of standards of definition and measurement for the various critical parameters of

practical superconducting materials* usually in the form of wires or cables.

The production of superconducting materials is a growing industry in this

country and elsewhere. Because of the complexity of a superconducting composite, it is imperative that everyone be agreed as to how its properties are

to be measured. Two perfectly reasonable and justifiable measurements of

critical current, for example, may give values that differ by 30-40%. It was

in an attempt to avoid such problems that this program was conceived. The

superconductor standards program is a cooperative program between NBS and

three divisions of DoE (Fusion Energy, High Energy Physics, and Magnetohydrodynamics through the Francis Bitter National Magnet Laboratory).

As used here, the term "standard" may indicate: standardization of

terminology; a detailed description of a measurement technique; an experimental apparatus; or a reference material. All of these aspects of standardization are being considered by this program. The specific parameters to be

treated by the overall program are: critical current, transient losses,

matrix properties, critical temperature and critical field.

This report describes the work during the second year of the program.

The first year's work is described in detail in an earlier report [1].

During the first year: a great deal of work was done on standardization of

terminology; a preliminary assessment of the current status of superconductor

measurements around the country was made; an ASTM subcommittee on superconductors was formed; preliminary transient loss measurements were made; critical
temperature measurements on practical materials were made and, after evaluation, it was decided that specific standards for this parameter were not

appropriate yet; extensive research on factors that influence the determination of critical current was done by NBS and the four wire manufacturers

.

The second year's work described in this report has concentrated heavily

on the critical current measurement standard. Figure 1 lists the various

aspects of this experimental program. Each of them is treated in detail here.

In addition, the present state of measurement capability was evaluated by

means of a survey that also determined presently used criteria and precision

and accuracy values for critical current measurements. Also, a round robin

test of several superconducting materials was made among the wire manufacturers

and NBS. The last of four papers on definitions of terms for practical superconductors was published [2] and ASTM draft standards for definitions and

critical current measurement were prepared and an initial presentation made to

the committee. A number of publications and presentations have resulted from

this work. They are listed in Appendix A.

Much of the experimental work was performed by the superconducting wire

manufacturers under contract to NBS. Their reports are included here in

Section V and selected data have been used throughout this report. We are

grateful for their help and for their enthusiastic support of the standards

effort in general. A complete list of those involved in this program is given

in Appendix B along with addresses and telephone numbers. The reader with

questions should feel free to contact anyone on the list.

2
Critical Current Studies

(MBS and contractors)

Holder type

Sample mounting

Joints

Current transfer

Strand — cable

Lot /billet /% SC

Field angle

Field homogeneity

Iq criterion

Current supply

Cu /SC ratio

Spool uniformity

Filament nonuniformity

Aspect ratio

Figure 1. Aspects of critical current measurement treated in this report.
II. EVALUATION OF PRESENT STATUS

An important component of a successful standards effort is the assessment

of present practices in the field. A good understanding of these is essential

to the creation of a standard that will be both understandable and useful.

Furthermore, the technique used to assess the present practices allows many

people to have input to the formative stages of the standard - a step that is

very helpful in developing the required concensus. Last year we made a

preliminary survey of methods of measurement. This year we performed the more

detailed survey described below. Another excellent technique for determining

the state of the art for measurement is to send similar materials to various

laboratories and ask them to make the measurement - a round robin test. Our

test for critical current is described in the second subsection here. Finally,

there was some indication throughout our interactions that the concept of

current transfer in multi filamentary superconductors is not generally well

understood. We have attempted to rectify that situation in the final subsection with a brief discussion of the effect, its various sources and

mani festations

.

A general assessment of the present overall situation regarding the

measurement and reporting of critical current data for practical conductors is

as follows: measurements are usually made with 10-15% accuracy, but often

this number is exceeded; improper measurement of I^ nearly always results in a

lower value than the correct one; few laboratories have setups for the routine

determination of I^; seemingly innocuous practices can have a dramatic effect

on the measurement, such as heavily greasing a sample in place or making a holder

from a material with a total thermal contraction that differs significantly

4
from that of the wire to be measured. The need for standard techniques,

devices, and definitions seems clear and imperative to us.

A. Test Specification Survey

A detailed evaluation of presently used critical current test specifications was made by means of a survey of some forty people in industry, government, and university laboratories. Specific values for precision, accuracy

and other properties of pertinent test variables were solicited. The parameters

considered were:

Critical current

Applied magnetic field

Electrical field criterion

Angle between current and field

Test temperature

Sample identification

Strain

In addition, comments were requested on the use of operational checks for

determining the effect on the measurement of:

Quench-protect circuitry

Contact heating

Lorentz force

The response was excellent with many replies providing great detail on the

reason for a particular choice. The results were tabulated and evaluated at

NBS and, finally, presented to the ASTM subcommittee. Briefly, we found.

• Little agreement on any specific values for accuracy and precision.

• Sample mounting is a serious problem and should either be specified

in a standard or appropriate operational checks should be required.

5
• The transfer voltage is not a wel 1 -understood concept and a method

of correcting for it should be specified in the standard.

• The effect of transient spikes and ripple from the sample current

supply is unknown.

• Accurate magnetic field measurement techniques are needed.

• Stress effects on are becoming understood and appreciated, leading

to the use of more conservative bend radii and allowed differential

thermal contraction in test fixture design.

• The use of an electric field criterion for determination of I is

c not universally accepted, many favor a resistivity criterion.

B. Round Robin Tests

The round robin tests were performed with the help of the wire manufacturers. Three different superconductors were sent to each of them for critical current measurement. These materials were chosen to represent a range of

sizes and types. They were;

Multi filamentary NbTi, ^^>1 00 A at 8 T

Mul ti fil amentary Nb^Sn, I '\^100 A at 8 T

Tape Nb^Sn, %170 A at 8 T

The details of the materials are shown in the metallographic photos of Fig. 2.

Measurements of were requested at fields of 6 and 8T for NbTi, and at 8 and

10 T for the Nb^Sn conductors. No other instructions were given. The samples

were also measured at NBS.

The test results are summarized in Fig. 3. There is obviously a very

large spread in the measured values, even for the NbTi wire. There are many valid

reasons why this happened and there is no real point to be served by discussing

6
Round Robin Samples

MultifHamentary Nb3

Sn, 0.7 mm diameter

Tape Nb 3

Sn, 2. 3x0. 2 mm

Figure 2. Samples used for the round robin critical current tests.

7
MAGNETIC FIELD, T

Figure 3. Results of the round robin tests. Open symbols show actual data

points for each material type. Each of the five sets of measure

ments for each material were made by different organizations.
them all; suffice it to say that the plot shows dramatically the need for

everyone to agree on a standard measurement technique and standard values for

the critical parameters in the measurement of

Our plan is to redo the round robin test after the standard is in general

use. This will provide an excellent measure of its success. Also, it is our

intention to include more laboratories in the next round robin.

C. A Discus'sion of Current Transfer

Current transfer is the redistribution of current among the filaments of

a mul ti filamentary superconductor. This change in distribution of the current

requires that some of the current flow through the normal metal matrix, giving

a voltage drop referred to as the current-transfer voltage. The current

distribution is a function of both current and position along the wire near

any of the following: a joint, a change in the local superconducting properties of the filaments (due to a defect, breakage, or local strain), or a

change in the magnitude or relative angle of the external magnetic field. The

resulting current-transfer voltage will be added onto the usual intrinsic

voltage-current relationship and can complicate determination of the intrinsic

critical current.

The theory [3,4,5] and measurement [6] of current transfer in multifilamentary superconductors has been the subject of several papers. It is a

rather complex problem involving current transfer adjacent to an input lead.

This is where the effect is largest and a very useful first order approximation to this effect is given in [4]. That theory starts with all of the

current on the outer of two concentric rings of superconducting filaments at

one position along the wire, say x = 0. Then the theory follows the current

9
redistribution and current-transfer voltage along the wire as a function of

total current. It is assumed that the whole wire can be made up of such

concentric rings and thus the results follow for a whole wire of any size.

Two important results of the theory (within its approximations) are that

the current transfer voltage is linear with total current and that the magnitude of this effective current-transfer resistivity is a simple function of

position, X. The linear relationship between the current-transfer voltage and

the current allows the easy subtraction of the current transfer effect from

the voltage-current characteristic of the superconductor as illustrated by

Fig. 4. This figure is a schematic representation of the voltage-current

characteristic in the intrinsic region and the current-transfer region. The

measurement of the electric field is made relative to the current-transfer

component of the sample voltage. The second result, that the magnitude of the

current-transfer resistivity is a function of position, can be turned around

to calculate a so called current-transfer length, relative to an acceptable

value of the current-transfer resistivity. This can be used to determine the

required spacing between the current and voltage contacts in order that the

current-transfer resistivity be less than a chosen value. Typical currenttransfer lengths for an acceptable value of current-transfer resistivity equal

-1

2

to 10 f2cm would be approximately 7 wire diameters for a NbTi superconducting

wire and about 60 wire diameters for a Nb^Sn superconducting wire. These

theoretical results have been verified experimental ly [6].

The above correction for the current transfer effect is adequate for most

practical applications and is fairly well accepted by the scientific community.

However, when the electric field critical -current criterion is less than the

10
VOLTAGE

(arbitrary

units)

Figure 4. Schematic representation of the composite superconductor ' s V-I

characteristic in two regions: 1) Intrinsic characteristic showing the usual resistive transition as I approaches I and 2) cur- rent-transfer characteristic exhibiting a linear region at low

current.

11
current-transfer electric field, the assumptions and approximations have to be

reconsidered. It was for this reason that the standard test method for measurement of the critical-current (^III B) includes a requirement that the electric

field critical -current criterion be greater than the current-transfer electric

field. Nonlinearity of the current-transfer voltage with current could be

caused by non-symmetric current injection or by nonuniformities in any of the

other current transfer mechanisms. This would result in an incomplete accounting

for the current-transfer voltage and, perhaps, an erroneous critical current

value. Another concern is whether the ful 1 -cross-section is being tested if

the electric field criterion is less than the current-transfer electric field.

An obvious solution to this problem is to change the geometry of the sample

such that the current-transfer voltage is lower; this is not always practical,

however. Some new experimental data on this matter are discussed in the

sample mounting section of this report (fll A). They illustrate the concerns

that arise when the current-transfer electric field is comparable with the

electric field criterion.

12
III. PREPARATION AND DISSEMINATION OF STANDARDS

The first product of this program and the culmination of all the research

efforts will be acceptable voluntary standards which have been adopted by a

recognized standards organization. Early in the program it was concluded that

the most appropriate first steps should be through ASTM and thus a Subcommittee

on Superconductors (B01.08) was formed within the committee on Conductors

(Bl). An organizational meeting was held in June 1979 outlining the tasks to

be done, and several informal sessions have occured since at various scientific

meetings. The second formal meeting of the subcommittee was held September 4-5,

1980 in Santa Fe, New Mexico at the conclusion of the Applied Superconductivity

Conference. The preparations for and actions taken by the subcommittee are

described below by task and summarized in the minutes of the meeting which are

included as Appendix C. Briefly, the meeting consisted of reports of research,

presentation of draft standards for definitions and small conductor critical

current, working task group sessions to modify the drafts, and a concluding

session to point to future needed work. Two specific needs were expressed:

a) a strong recommendation that NBS generate a standard reference material for

critical current, and b) work begin immediately on the problems of ac loss

measurements in superconductors.

A. Standard for Terminology

As mentioned earlier, the fourth and final paper prepared by the NBS

staff proposing definitions of terms related to superconductivity has now been

published [2]. This set of four papers plus comments by many others was used

as the basis for a set of definitions of terms to be used in critical current

13
standards for ASTM. Only those terms that were expected to occur in the

standard for critical current were included and in many cases were shortened

and changed to a simpler language appropriate for everyday use. This draft

set of terms was presented by task group chairman S. J. St. Lorant to the

subcommittee for discussion, and the next day the task group on definitions

modified, deleted, and added to it. The task group then approved the set for

presentation to the subcommittee by mail for a vote of approval. This process

is in progress at the present time.

B. Standard for Critical Current Measurement

In preparation for the ASTM Subcommittee on Superconductors meeting,

three draft measurement standards for critical current were prepared. One for

a straight geometry specimen was prepared by R. Schwall of IGC and R. Scanlan

of ILL, another for a coil geometry by W. Fietz of ORNL and P. Sanger of

AIRCO, and a third "generic" standard by NBS. After discussion, the subcommittee decided that there were enough common elements to warrant only one

standard for all geometries. As long as all the various criteria were met

then any geometry could be used with suggested ones being preferred. The

following day the task group adroitly chaired by R. Schwall went through the

NBS "generic" standard item by item, incorporating parts of the others, modifying or deleting as necessary. When consensus was not achieved it was left

to the NBS staff to determine the alternatives and recommend a choice while

still enni'merating the dissent. In brief outline form the draft standard

covered

:

1 . Scope of the standard

2. Critical current definition

3. Precision and accuracy of the apparatus

14
4. Test specimens

5. Procedure

6. Significance and use

7. Reporting

The results of the meeting and subsequent efforts to resolve some of the still

open questions were combined in a draft standard which was distributed to all

of the attendees accompanied by a discussion of all objections and open

questions. Responses from these Will be combined into a draft standard which

will be submitted to the subcommittee for approval by mail.

The succession of steps through the ASTM process are approval by the

subcommittee, approval by the whole committee on conductors, and finally

approval by the society as a whole. At each step a l

1

conflicts must be resolved so there is necessarily a great deal of work required to obtain this

approval, but the final product should be acceptable to everyone.

The next problem to be addressed for critical current measurements is a

draft standard for larger current conductors, more than 600 amperes.

C. Standard Reference Materials

The ASTM subcommittee strongly recommended at the September meeting that

NBS initiate the development of a standard reference material for critical

current. Exploratory discussions were held with the NBS Office of Standard

Reference Materials and it appears that additional support from NBS may

be made available for this effort. The criteria will be established based on

some of the contractual research and the requirements of the critical current

standard. It appears questionable now whether a standard production run can

produce the homogeneity necessary and further development or pre-production

criteria may have to be set on the fabrication of materials. The present

1 5
thinking is that NBS should procure several kilometers of a common NbTi

multifilamentary conductor and provide it in several meter increments. The

major question at the moment is whether it is more cost efficient to overcharacterize a standard production run or carefully control a special production. Prominent problems are those of maintaining constant copper-tosuperconductor ratio, residual resistivity characterization, assuring filament

continuity, and the uniformity of the final cold-working. A great deal has

yet to be done.

16
IV EXPERIMENTAL PROGRAM: CRITICAL CURRENT

Nearly all of the experimental work performed this year has been directed

toward understanding the various phenomena that affect the measurement of

critical current. As we showed in Fig. 1, there are many of these. Some,

such as sample mounting, field orientation effects, and the choice of criterion

are of prime importance and have been investigated in considerable detail.

Others, such as self field, curre'nt supply ripple, and field uniformity have

turned out to have a relatively minor influence on the determination of I^ and,

thus, they have not been treated as intensively.

In general, the first two subsections here report NBS experimental work

and the last three the work of the contractors. There are exceptions, however, and we have attempted to give proper credit in each case. In any

event, the reader should look at the complete reports of the next section to

get the whole story on the various contractor results reported here.

A. Sample Mounting

The critical current of a sample can be measured in a number of different

mounting geometries. The most common geometries, illustrated in Fig. 5, are:

short straight, hairpin, coil, and long straight. In all of the geometries the

applied magnetic field is essentially perpendicular to the sample axis (between

the voltage taps), which is the orientation that has the lowest critical current and is the limiting situation for most applications. Also, in each

geometry a test fixture can be designed such that the Lorentz force on the

sample is into the fixture thus minimizing the resulting strain on the sample.

There are a number of considerations that determin which mounting geometry

to use. They are: extent of the contact heating, size of the current-transfer

17
Hairpin

Coil

Long Straight

Figure 5. Common sample mounting geometries illustrated with magnet, bus

bar, sample and voltage leads.

18
voltage, detectable level of the electric field, simplicity of the geometry,

and magnetic field geometry. Each of these considerations has been addressed

and Table 1 lists advantages and disadvantages of each geometry.

Sample geometry

Short straight

Long straight

Hairpin

Coil

Table 1. Sample geometry comparison

Advantage Disadvantage

simple geometry

solenoidal magnet

low contact heating

medium electric field criteria

simple geometry

low contact heating

medium electric field criteria

solenoidal magnet

low contact heating

low current transfer

low electric field criteria

solenoidal magnet

high contact heating

high current transfer

high electric field criteria

some current transfer

spl it-pair magnet

some current transfer

moderate geometry

complicated geometry

The extent of the contact heating will determine if the intrinsic critical current of a sample can be measured. If the contact heating is too large

the sample will be at an elevated temperature and an incorrect critical current

measurement will result. It is also possible that the sample will be driven

into the normal state by the propagation of a normal zone from the contact

through the entire sample at a current well below the intrinsic critical

current. The contact heating depends on the contact resistance and the

critical current. This problem was the subject of some recent experimental

measurements [7] of the lap-joint resistance of a mul ti fil amentary NbTi superconducting wire and the critical current of this wire adjacent to the joint.

19
The lap joint gives a symmetric model of contact resistance and allows

for the separation of the total resistance into (1) interface and (2) currenttransfer components. The results of this work indicated that the interface

contribution to the joint resistance can be calculated for any other rectangular

conductor. The current-transfer contribution is conductor dependent, but the

results can be generalized to give an upper limit to this contribution for any

conductor. However, this generalization needs to be tested for the extreme

case of large current-transfer effects in a multifilamentary Nb^Sn wire.

Critical -current measurements made adjacent to the lap joint indicated that,

when the voltage-current characteristic was reversible, the measurement was

within 2% of the intrinsic-critical current of the wire. The intrinsiccritical current was determined by measuring a control sample without a joint.

The cri tical -current measurements also indicated that when the voltage-current

characteristic was i rreversi bl e, the measured current was systematical ly (as a

function of magnetic field) low indicating that joint heating is affecting the

measurement. The onset of irreversibil ity was correlated with a power per

2 unit surface area of the joint perimeter larger than 1 W/cm . This suggests

that there is a limit to the power per unit area than can be dissipated into

the helium bath. The thermal conductivity of the matrix may affect this

result. It should also be tested for the case of mul tifilamentary Nb^Sn

wire.

These results [7] allow the designer to estimate the joint resistance

and determine if contact heating will affect the critical current measurement.

Contact heating is of the most concern in the short straight geometry since

this is the only geometry were the length of the current contact is severely

20
limited. In other geometries the designer can estimate the joint resistance

and, in most cases, easily keep joint heating from affecting the critical

current measurement.

As mentioned in the discussion of current transfer, when the electric

field meeting the critical -current criterion is less than the current-transfer

electric field, the accuracy of the critical current measurement is questionable because of the assumptions and approximations of the current transfer

correction. When the electric field meeting the criterion is much larger than

the current-transfer electric field the correction works very well. But, a

closer look at the experimentally observed current-transfer voltage indicates

that it is not linear with current, especially at low currents (where the

slope is smaller) and at high currents (where the slope is larger). There is

a fairly linear section in the middle of the voltage-current characteristic,

but the resulting correction is slightly arbitrary and incomplete. This is

illustrated in Fig, 6, which is a plot of the percent difference between the

critical current (at electric fields of 1 , 2, and 10 uV/cm) for mul tifil amentary

Nb^Sn measured in the short-straight geometry and in the long-straight geometry

as a function of magnetic field. It should be noted that the baseline of this

plot is the critical current appropriate to the particular electric field as

measured in the long-straight geometry. (The differences in the critical

current between the baseline electric field criteria was about 4% between 1

and 2 yV/cm and about 9% between 2 and 10 yV/cm.) The current-transfer electric field in the short-straight geometry was approximately 3.5 yV/cm at 4T

(I^ %248A at 1 yV/cm) and 2.0 yV/cm at 7T (I^ 'vlSGA at 1 yV/cm). The first

observation is that with a criterion of 10 yV/cm, which is much larger than

the current-transfer electric field, the critical current data agree to about

21
^

^ r 1

Multifilamentary Nb3Sn

2 — —

0

Long Straight,

E(/xV/cm) = 1,2&10

a

- . S A

Ale,

-2

o

°

o

—

-4 Short Straight,

E(^V/cm)= 10*-^ ^ 2-D

-6 O

^ ^ l_

1-0 ”

I I I I I I I 0 2 4 6 8 10

/i-oH, T

Figure 6. Comparison of short straight and long straight critical current

measurements at various electric fields as a function of magnetic

f i el d

.

22
^% for the entire range of overlap in magnetic field. The 2 yV/cm criterion

data deviate from each other systematical ly and do not agree to 1% until the

current-transfer electric field is about 2 yV/cm also. There is more scatter

in the 1 yV/cm data, but they indicate a similar, only larger, systematic

deviation. These data indicate that the current-transfer effect correction

tends to underestimate the effect and the resulting critical current may be in

error by about 5 % if the current-transfer electric field is three times the

field defining the critical current. It is in agreement to about 1% if the

criterion is equal to or greater than the current-transfer electric field.

The current-transfer effect is largest next to a current contact, so its

worst case is the short straight geometry. The current-transfer effect in the

long straight geometry is, for the most part, due to the change in magnitude

of the external magnetic field and is relatively small. The same is true of

the current-transfer effect in the hairpin geometry, where the main cause is

the change in angle of the external magnetic field. For the coil geometry the

current-transfer effect is easily minimized by placing the voltage taps well

away from the current contacts and avoiding regions of high magnetic field

gradients. As mentioned in the discussion of current transfer, the currenttransfer length is approximately ten times longer in Nb^Sn wires than it is

in NbTi wires. Therefore, it is easy to compare some of the different sample

geometry measurement methods using a NbTi wire. The critical current measured

in the hairpin and long straight geometries are compared to the short straight

geometry in Fig. 7. The agreement is within 1.5% of short straight values for

the entire range of overlap. The electric field criterion used was 2 yV/cm.

Very similar plots would have resulted for other electric field criteria

in the range of overlap.

23
3 1 r

Sample geometry comparison, NbTi

CJP

o Hairpin ^ O O o

o

0

Short Straight

-1

Long Straight

J ^ ^ L 0 2 8 10

T

Figure 7. Sample geometry comparison relative to short straight sample data
The detectable level of the electric field is a function of the following: voltmeter sensitivity, electronic noise level, changes in thermoelectric voltage, changes in the voltage induced by the ramping of the sample

current, voltage tap separation, and level of the current-transfer electric

field. The round robin samples (§IV B) were measured with two types of voltmeters, an analog nanovoltmeter and a digital multimeter with an analog output.

This allowed comparisons between data taken with the highly processed signal

of the digital multimeter and with' an analog device. This comparison was made

using both a 600 ampere SCR regulated power supply and a 600 ampere battery

power supply. In both cases the agreement between the two types of voltmeters

was within 0.5%. A comparison of the two power supplies will be given in a

later section {?IV C). One source of electronic noise is the SCR switching in

SCR regulated power supplies. A digital voltmeter will average out this noise

but an analog device is very sensitive to it. This noise reduced the sensitivity of the analog device to about 100 nV, the same as the sensitivity of

the digital -vol tmeter. However, when the battery power supply was used for

the sample current, the residual noise level was about 2 nV for the analog device.

Another source of electronic noise is from the magnet used to generate

the external magnetic field at the sample. If the field is provided by a

superconducting maget this noise contribution is minimal. However, conventional magnets such as those at the Francis Bitter National Magnet Laboratory

can add significant electronic noise to the sample voltage.

Electronic noise can also arise due to sample motion under the influence

of the Lorentz force. Under most circumstances this motion can be restricted

by the design of the sample fixture, keeping the Lorentz force into the fixture.

25
However, when the magnet is very noisy, or if the fixture cannot be designed

to balance the Lorentz force in all cases, an adhesive, such as silicone

grease or varnish, can be used to restrict the motion of the sample. Adhesives

tend to impede the heat flow, so their use should be conservative.

Changes in thermoelectric voltages can be minimized by using continuous

copper wires from sample to the connection with the voltmeter input and keeping

this connection at a fairly constant temperature. This can keep the changes

in the thermoelectric voltage at the nanovolt level over the time of a voltagecurrent trace.

Changes in the the voltage induced by the ramping of the sample current

can be minimized by using a constant ramp rate or by minimizing the area

enclosed by the voltage taps and sample. This is especially important in the

inductive coil geometry, where the voltage leads should be co-wound with the

sample to minimize this pick-up. Voltage tap separation can limit the detectable

level of the electric field. This is most severe in the case of the shortstraight and hairpin geometries where the voltage tap separation may be a

centimeter or less. In the long straight geometry, the voltage tap separation

can be a few centimeters. The coil geometry allows the most freedom in separation

of the voltage taps, with separations of several meters possible. The currenttransfer voltage can also limit the detectable level of the electric field, as

discussed in the previous paragraph. This is most pronounced in the shortstraight geometry and is of secondary concern in the hairpin and long straight

geometries and only of minor concern in the coil geometry.

Simplicity is another consideration in deciding what mounting geometry to

use. An important concern is the amount the sample will be strained during

mounting, cool-down, and by the Lorentz force. Limits on the bending strain,

to keep the critical current measurement accurate to 2%, are 0.1% for Nb^Sn

26
and 2% for NbTi based superconductors. Most NbTi wires are delivered on

large diameter spools and, from this slight curvature, they can be mounted on

short-straight or long-straight test fixtures without exceeding the strain

limits. They can also be bent onto hairpin and coil test fixtures if the

diameter of the fixture is large enough. Since the Nb^Sn superconductors

require a heat treatment at the end of their processing to form the brittle

Nb^Sn, they can be formed to fit the test fixture before the heat treatment.

The straight geometries are obviously the easiest. The hairpin is a little

more difficult and the coil geometry is quite complicated. Earlier work at

NBS addressed the problem of strain in the sample introduced by the differential

thermal contraction of the sample and sample holder [8]. This work indicated

that suitable materials for the test fixture were NEMA G-10 or G-11 epoxyfiberglass. The strain caused by the Lorentz force can generally be adequately

balanced by the test fixture, if the sample is reasonably well fitted to the

fixture.

The common magnet geometries are either solenoidal or split-pair. The

short-straight, hairpin, and coil sample geometries are particularly suited to

solenoidal magnets. The bore diameter of the magnet determines the overall

length of the short-straight sample and the diameter of the curvature of the

hairpin and coil geometries. The split-pair magnet is required for the longstraight sample geometry. This magnet is not as common and generally has a

lower maximum field.

Two of the round robin samples were rectangular in cross-section. This

introduces the possibility of the critical current variation due to the orientation of the conductor with respect to the perpendicular magnetic field.

27
Figure 8. Angular-dependence of the critical current for a rectangular

NbTi conductor. At 0°, H is parallel to the wide face.

28
Figure 9. Angular-dependence of the critical current of a Nb^Sn tape conductor at 7T. At 0°, H is parallel to the wide face of the tape.

29
Checking this dependence was easily done in the long-straight geometry since

the sample could be rotated in the split-pair magnet. The usual orientation

for measurement would be the one that is expected to limit the performance of

the conductor in its application, that is, the magnetic field parallel to the

wide face of the conductor. The rectangular NbTi conductor (0.53 x 0.68 mm)

was measured with the magnetic field parallel to both the wide face, and the

narrow face of the conductor on the short-straight, hairpin, and long-straight

sample fixtures. The data on Fig. 7 was taken with the magnetic field parallel

to the wide face of the conductor. The data from the other orientation showed

similar agreement among the sample geometries. Critical currents for both the

NbTi wire and the Nb^Sn tape (0.2 x 2.3 mm) were measured as a function of

angle between the wide face and the magnetic field in a split-pair magnet.

The data at 7T are presented in Figs. 8 and 9. It was observed that this

angular-dependence effect was opposite for the two materials. This is believed

to be caused by differences in the flux-pinning mechanisms. The relative size

of the anisotropy was not a strong function of magnetic field in the range of

3 to 7 Tesla.

B. I Criterion

c The term "critical -current criterion" defines the specific value of a

property that is reached at the critical current. The most commonly used

criteria are electric field and resistivity. The criterion is applied to the

vol tage-current characteristic of the superconductor . A typical voltagecurrent characteristic is shown in Fig. 4. The low current portion of the

characteristic shows virtually zero voltage, or perhaps a small current-transfer

voltage. The high current portion shows an onset of flux-flow voltage

30
j which increases sharply with current. The voltage in the flux-flow region is

reversible and constant in time. It can be measured in some superconductors

over many orders of magnitude in voltage. If the sample could be held at a

constant temperature, this flux-flow voltage would increase with current until

the normal state voltage-current characteristic was reached. However, the

power dissipation in the flux-flow region will generally cause an irreversible

transition (thermal runaway) from the flux-flow region into the normal state.

The electric field criterion indicates the voltage drop per unit length

of the superconductor in the flux-flow state at the critical current. Typical

values range from 0.1 to 10 yV/cm for conductors with critical currents of

less than 600 amperes. The resistivity criterion refers to the effective

resistivity of the superconductor in the flux-flow state, that is, the voltage

drop per unit length divided by the current per unit area (p = VA/LI). Typical

values for the resistivity criterion range from 10”^^ to 10"^^ J2cm using the

total cross-sectional area of the conductor. One problem with the resistivity

criterion is deciding what area is to be used to calculate the resistivity.

In the case of a NbTi conductor one of two cross-sectional areas is commonly

used, the total area of the conductor, or just the area of the NbTi. For a

Nb^Sn conductor the cross-sectional area used may be: the total area of the

conductor, the non-copper area (which may include the area of the diffusion

barrier, bronze, Nb, and Nb^Sn), the area of the Nb and Nb^Sn, or the area of

the Nb^Sn alone. The determination of some of these areas involves extensive

metallography and statistical techniques, which means they are difficult and

very time consuming for another investigator to verify. For the round robin

mul tifil amentary Nb^Sn superconductor, the total cross-sectional area was

about 14 times the cross-sectional area of the Nb and Nb^Sn. The resulting

31
ficm and

-1

1

critical current measurement using a resistivity criterion of 10

these two areas gave critical-current values different by about 19% at 7

tesla

.

The choice of the area involves the particular interpretation or use of

the resulting data. For a designer, the resistivity criterion using the total

cross-sectional area of the conductor is most appropriate considering the

helium refrigeration requirements. The manufacturer, however, considers the

use of the other areas appropriate as a figure of merit for a particular

process and considers the use of the total area as a competitive penalty for

highly stabilized conductors. This natural polarity in the choice of the area

seemed to be unresol vabl e, so the electric field criterion was adopted for the

standard test method for measurement of critical current.

The electric field criterion does not penalize the highly stabilized

conductor and can easily be converted into an equivalent resistivity criterion

using the total cross-sectional area of the conductor. One should note that a

given electric field criterion does not correspond to the same resistivity

criterion at all values of magnetic field. At high fields a given corresponds

to a larger value of resistivity than it does at low fields. This could be a

problem very near to the upper critical field, but our standards effort

is specifically restricted to fields less than 0.8 Furthermore, if

desired, the effect can be circumvented by calculating the specified electric

field criterion on the basis of any other criterion, which may depend on

magnetic field and/or current. Under this framework the electric field criterion is considered to be expedient and verifiable.

The criterion dependence of the critical current was measured on each of

the round robin samples. The percentage change in critical current relative

32
to the critical current at 1 uV/cm is given as a function of magnetic field in

Figs. 10, 11, and 12. The critical current (as measured by NBS) of each of

the round robin samples at 4 K and an electric field of 1 yV/cm was: 281A at

4T and lllA at 8T for the NbTi-, 248A at 4T and 114A at 8T for the MF Nb^Sn;

308A at 4T and 177A at 8T for the Nb^Sn tape. At a given magnetic field, the

flux-flow electric field (E), and thus the criterion dependence, can best be

described by the following expression:

’ E a l" (1)

where I is the sample current and n is a real number. In general, n is a weak

function of E and magnetic field. The mul tifil amentary NbTi (n '^^40) and the

multi filamentary Nb^Sn (n '^^20) samples had values of n which were very weak

functions of E and magnetic field for the range tested. The value of n for

the Nb^Sn tape was '^200 at 4T and ^100 at 8T.

C. Sample Current, Resistance Ratio, and Self Field

There is presently no detailed study indicating the effect of current

variations on the critical current measurement process. These variations

occur both as current ripple and, for higher current supplies, SCR spikes.

Two, very preliminary, attempts to look at this problem were made. The first,

illustrated in Fig. 13, compares the values of obtained (by NBS) at various

magnetic fields using a battery to those found using an SCR-regulated supply.

Sample currents were in excess of 400 A at the lower fields. Two different

wires were compared. The results clearly indicate no significant effect.

Measurements were also made on a high-current (^^,7000 A at 6T) conductor by

Airco using varying degrees of filtering of a 12 kA dc power supply. The

critical current was measured in the presence of ripple (120-360 Hz)

33
I

I

/ioH. T

Figure 10. Relative criterion dependence of the critical current of a NbTi

conductor. The base value used is 1 yV/cm.

34
<

Figure 1 1

.

Relative criterion dependence of the critical current of a multifilamentary Nb^Sn conductor. The base value used is 1 yV/cm.

35
t

Figure 12. Relative criterion dependence of the critical current of a Nb^Sn

tape conductor. The base value used is 1 yV/cm.

36
0.5

Ale:

Battery-SCR

SCR

cjR

_p

<

-oNbTi

Nb^Sn Wire

-0.5

8

/^oH, T

Figure 13. Comparison of critical current measurements made using different

sources of sample current. Data for two types of wire are shown.

37
comprising 14, 22 and 110% of the dc current. The quench currents were essentially the same, but they were quenches and not the smooth, reversible behavior

required for a true determination. In summary, it appears that sample

current variations are probably not a serious source of error in critical

current measurement. However, the question is by no means settled and work is

continuing.

The resistivity of the matrix of a practical superconductor is an important parameter in the determination of conductor stability. The effect of

matrix resistivity on the measured critical current is not well known.

Again, some preliminary results related to this question were obtained. The

effect of adding matrix material to a wire was studied by MCA. Results of

their experiment, in which strands of pure copper were cabled with a superconducting wire to effect an increase in copper-to-superconductor ratio, are

shown in Fig. 14. It appears that, as expected, there is a "threshold" amount

of copper required, but that beyond that, additional copper does little to

increase I^. The (tougher) question that remains to be answered is whether

varying the resistivity of a fixed amount of copper will have a similar effect.

Techniques for the reproducible measurement of resistance ratio of the stabilizer

of a practical superconductor were investigated by IGC. Their report describes

a device for making these measurements and gives resistance ratio data for a

number of their conductors. It is worth noting that the measured resistance

ratio for the composite superconductor is not that of the copper alone unless

the superconductor resistivity is quite high and its normal state resistance

ratio is small.

It has been more or less accepted that the self field due to currents in

conductors of the size treated in this program (I^ < 600 A) has a negligible

effect on the critical current measurement. On the other hand, it could be a

38
Figure 14. The effect of added copper on the critical current of a practical

superconductor . Copper strands were added by cabling. Contractor

data (see page 149)

.

39
significant effect in large conductors with high current densities. Both of

these contentions were treated by IGC in their theoretical and experimental

work on self field effects. Their theory indicates that one should expect a

very small effect in practical wires that most likely would be masked by other

conductor variables. However, as expected, the effect will be largest in the

larger conductors. An attempt to see the effect in large conductors was made

using a 1 0 kA conductor with twist pitches varying from infinity to 2.5 cm,

the latter representing five wire diameters. Various experimental difficulties were encountered, but the tentative conclusion was that no effect of

twist pitch could be detected. Measurements on smaller conductors gave somewhat ambiguous results perhaps indicating a decrease in with twisting. It

seems reasonable to make the general conclusion that if twist pitch has little

or not effect then the self field is not a large contributor to uncertainty in

critical current determination.

D. Field Orientation and Uniformity

The effect on the critical current of field orientation relative to the

dimensions of a rectangular conductor has been described above (see Figs. 8

and 9). Large variations are found and their sense depends on the specifics

of the conductor. Those measurements were made with the field always normal

to the conductor axis and, thus, to the current direction. Figure 15 shows a

different aspect of the field-orientation problem. In this experiment by

Airco a round NbTi conductor was used to wind several coils with different

twist pitches so that the effect of field angle with respect to the current

direction could be determined. The important conclusion from the data is that

the critical current measured in a coil sample wound in any reasonably normal

fashion will not be significantly different from the intrinsic value.

40
O

Q

3.0 r

a, degrees

Figure 15. Relative critical current values as a function of angle between the

magnetic field and the current direction in a circular MbTi conductor.

The data represent values averaged over magnetic fields to 9T.

Contractor data (see page 83).

41
Another component of the Airco study dealt with the effect of magnetic

field inhomogeneity on critical current test results. Noni nductively-wound

coil samples were placed in various field gradients with a fixed value of

maximum field and their critical currents measured. The results are shown in

Fig. 16 taken directly form their report. Again, the conclusion is that, with

reasonable care in positioning a sample, no significant critical current error

should be introduced by field gradient effects.

E. Conductor Parameters

Much of the work reported here implies that modern practical superconductors are of very uniform composition. In fact, significant variations may

exist even in the relatively easily produced NbTi conductor. Several experiments

were done to investigate the effect of such variations on the critical current

determination. Also, many large conductors are made up of smaller strands and

we wished to see if this cabling had an effect on the resulting value of I^.

This last question is easily disposed of by considering Table 2, made up from

Airco data. The cables are made up of sets of triple strand multifilamentary

4

Nb^Sn wires. The cable labeled 3 is fully transposed and compacted in a

copper tube. Clearly, the final of a multi-strand cable is just the product

of the value for the basic strand and the number of strands. It is suggested

that this satisfying result may not occur in highly deformed cables such as

the common flat braid.

The remainder of the studies described here were done by Supercon and

involved the measurement of critical current values for nominally similar

NbTi wires from many billets representing several different lots of NbTi.

Nearly all measurements were made in a 6T field. Figure 17 shows the overall

42
(‘I

!l

^co

•X 100

I 00

Figure 16. Critical current variation due to nonuniform applied magnetic

fields. Contractor data (see page 77).

43
Biliet

Number

cr

LU

CQ

S

D

Z

H

o

rc

V ‘iNBUdno nvoiiido

44

Figure

17.

Variation

observed

in

critical

current

of

similar

NbTi

wires

processed

from

different

billets.

Each

lot

number

indicates

different

lot

of

NbTi

alloy.

Contractor

data

(see

page

199).
Table 2. Critical current of cables from c basic strand

Type No. of strands @ 8T, a I (cable)/! (strand)

Single strand 1 125 -

3 strand triplet 3 374 3

2

3 cable 9 1125 9

3^ cable 81 9500 79*

*I = 120 A for the single strand used to make this cable,

c

^

variation observed among the samples. Note that in some cases, more than one

billet was prepared from NbTi of a given lot. Within a lot, a correlation was

observed between the percentage of superconductor in the final wire and the

critical current as shown in Fig. 18. This is not especially surprising, but

note that the lines for different lots are not parallel, probably reflecting

compositional differences in the NbTi. The variation in critical current

observed along the wire from a single billet is shown in Fig. 19 again correlated with the variation in percent of superconductor measured along the

same wire. Finally, the effect of severe deformation of the filaments on the

critical current was investigated by measuring purposely deformed lengths of

conductor. Their cross sections and critical currents are shown in Fig. 20.

When the variation in due to percent superconductor is accounted for, only

the most severly deformed conductor shows any significant variation in critical

current due to the deformation.

45
CRITICAL CURREMT, A

Figure 18. Correlation of critical current with percent superconductor in the

final wire for several lots of NbTi alloy. Contractor data (see

page 1 98)

.

46
%

SUPERCONDUCTOR

CRITICAL CURRENT, A

Figure 19. Variation in critical current observed along a wire from a single billet correlated with the measured percent superconductor. Contractor data (see page 200).

47
#e

0 0

I A A I

9

0 • •

^A A A

® ^ A #

® © ?.» ®

^ ® © 0

>•% # ©•a®

• ••

I^ = 856 A @ 8 T

= 911 A @ 8 T

L = 856 A (3 8 T I = 759 A 0 8 T

c c

Figure 20. Cross sections of deformed MbTi conductors and their measured

critical currents. Contractor data (see page 202).

48
V. CONTRACTOR REPORTS

Many results from the research carried out by the U.S. wire manufacturers

under this program have been presented and discussed above. The complete

contractor program is described in last year's report [1]. The contract

reports as provided to NBS are reproduced here. There has been only minor

editing for format. The content of each report is the responsibility of the

originating company. A list of contacts for each organization is given in

Appendix B.

A. Airco Superconductors

DEVELOPMENT OF TESTING STANDARDS

FOR SUPERCONDUCTORS

JrINAL REPORT FOR WORK DONE UNDER

NATIONAL BUREAU OF STANDARDS

CONTRACT NO. ; NB79RAC90029

Submitted by:

AIRCO SUPERCONDUCTORS

600 Milik Street

Carteretf New Jersey 07008

51
TABLE OF CONTENTS

SECTION

1.0 INTRODUCTION

2.0 EXPERIMENTAL STUDIES

2.1 Description of the Test Facility and Testing

Geometries

2.2 Round Robin Test Series

2.3 Effect of Magnetic Field Inhomogeneity on

Critical Current Measurements

2.4 Effect of Conductor Orientation with Respect

to the Magnetic Field on Critical Current

Meaurement

2.5 Effects of Imperfect Rectification and

Filtering of an SCR Controlled Current Source

2.6 Support for the Validity of Determining

I^ (Cable) from I^ (Strand)

3.0 CONCLUSIONS AND RECOMMENDATIONS

52
W 1.0 INTRODUCTION

This report is an account of the work carried out at

I Airco Superconductors during the period from September 10,

||j 1979 to April, 1980. The purpose of this effort is to assist

ll the National Bureau of Standards in the development of standI

I ards fulfilling the needs of the superconducting industry. In

i the present contract, this assistance has been directed fli.st,

j at participating in all the various group activities being

I pursued to generate these standards, and second, at investigating and measuring several parameters required as a data

base for the establishment of tolerances in the standards.

In the former catergory Airco Superconductors is parti-

;||\ cipating in the workings of ASTM Subcommittee B-1.08 on Superconductors, prepared samples for and completed the round robin

critical current measurements (these results are presented in

this report) , responded to the critical current measurement

questionnaire, and is cooperating with other superconducting

technologists on formulating a draft of testing standards.

The experimental portion of this effort has included

‘ preliminary studies of the variation of critical current due

I to

I 1) the effect of magnetic field inhomogeneity;

' 2) the effect of orientation of sample

I conductor with respect to the magnetic field;

3) the effect of imperfect rectification and

filtering of an SCR controlled current source.

Furthermore, experimental test data is being contributed to the program so that it may be used in the

I formation of a reliable standards data base. In particular,

measurements on both cabled conductors and the individual

strand of the cable have been made and are included in this

report

.

53
2.0

EXPERIMENTAL STUDIES

2.1 DESCRIPTION OF THE TEST FACILITY AND TESTING GEOMETRIES

The first task of the experimental program was

directed at recalibrating and verifying the accuracy of

the superconducting solenoid test magnet as well as the

current shunts and voltmeters.

2.1.1 Test Facility

The test solenoid is dimensionally specified in

Figure 1 and can be used to generate magnetic fields of

up to 9.5 T. Both its transfer constant and field profile were confirmed using a Rawson-Lush rotating coil

probe. The radial and the axial magnetic field components were measured for three radial positions (0.0,

1.6, and 2.2 cm) and 18 axial locations. These

measurements are presented in Table 1 and were used to

determine the absolute magnitude of the magnetic field

at the locations where the sample test fixtures were to

be placed. For example, /H/ is given for r = 2.2 cm as

a function of z in Figure 2. This profile will be used

later in evaluating the test data taken for the noninductively wound long sample test fixture. In

general, the field profiles obtained in this manner

correspond well to the expected behavior of a solenoid.

2.1.2 Test Geometries

It has generally been the rule that the test

methods adopted by a particular organization are

governed not only by the size and shape of the conductor, but also by the available facilities. For this

reason, Airco Superconductors has developed three

54
TABLE 1: Axial (H ) and Radial (H ) Components of Magnetic

Field as a Function of Distance Above Center (z)

at Three Radial Positions (r)

r=0.0cm =1.6 =2.2

H

r H

z Hr H

z H

r Hz

j=0 . 00cm [49989] 50249 .... 50269

1.03 100 49630 - 566 49960 50100

1.67 63 49230 49590 1422 49600

2.30 110 48550 773 48990 1506 48820

2.94 114 47600

N 927 48200 1907 47900

3.57 190 46400 1088 47150 2150 46700

4.21 212 45000 1303 45730 2803 45250

4.84 271 43420 1507 44000 3165 43550

5.48 327 41750 1786 42050 3606 41500

6.11 349 39750 2007 39800 4494 38900

6.75 399 37600 2211 37400 5311 36320

' 7.38 252 34800 2390 34500 6040 33600

8.02 204 31600 2538 31400 6383 31020

8.65 204 27950 2568 28350 6345 28300

9.29 242 23700 2572 24200 25700

9.92 248 — 2436 6053 23020

10.56 2740 5336 20050

11.19 — — 3849 17800

— 4

ALL FIELD UNITS IN 10 TESLA

55
Fiaure 1 Coordinate System and Dimension of the

Test Magnet Utilized in this Program.

56
Z (CM)
types of test fixtures which meet 95% of its testing

needs and are compatible with its facilities. The

three types of samples which can be tested are:

1) noninductively wound long samples;

2) inductively wound short samples and;

3) a hairpin shaped sample.

Specific test fixture parameters are delineated in

Table 2,

The noninductively wound long sample test fixture,

shown in Figure 3, is particularly suitable for testing

small diameter NbTi wire and permits accurate critical

current measurement at very low voltage sensitivities.

However, Nb^Sn superconductor can not be easily tested on this fixture. This fixture was used in the round

robin measurement of the NbTi wire and selected as the

configuration most suitable for the study of field inhomogeneity effects (Section 2.3).

Two variations of the inductively wound cylindrical test fixture are being used and differ only in

the placement of the voltage taps. In the first

variation (designated 2a)

,

the voltage taps measure one

full turn of sample. One voltage lead is co-wound

parallel to the turn of sample conductor being measured

to reduce noise pick-up. The second configuration

(2b), shown in Figure 4, samples only a 2 cm length of

conductor in the central most portion of the sample

coil. Either configuration can be readily used for

both NbTi and Nb^Sn. Both of the Nb^Sn samples

included in the round robin tests were testd on these

test fixtures. The orientation studies (Section 2.4)

were also performed on these fixtures.

58
TABLE 2: TEST FIXTURE GEOMETRIES

Winding

Configuration

Characteristic

Dimensions

Distance

Between

Voltage Taps

Suitabilit;

for

Wire Types

1. Noninductively

wound , cylindrical

5 cm dia.

X 2.1 cm long

40 cm Small NbTi

2a. Inductively 4.16 cm dia 13.7 cm NbTi and

wound , X 2.1 cm long Nb^Sn

cylindrical

2b. Inductively 3.59 cm dia. 2.0 cm NbTi and

wound , X 2.1 cm long Nb^Sn

cylindrical

3. Hairpin 6.9 cm wide 1.9 cm NbTi and

with 3 cm corners Nb^Sn

59
FIGURE 3:

FIGURE

Noninductive wound long sample test fixture

used for small diameter NbTi wire.

: Inductive wound cylindrical test fixture.

60
The third and final type of test fixture (shown in

Figure 5) is the simple hairpin shape which is suitable

for both Nb^Sn and NbTi but is sensitive to field

nonuniformities. This fixture is particularly useful

when aspected conductors, such as tapes have to be

measured with the applied magnetic field perpendicular

to the broad face of the conductor. In both of the

cylindrical fixtures, the field is applied parallel to

the broad face of the conductor. For this reason, the

Nb^Sn tape in the round robin series was also

measured on the hairpin test fixture.

61
FIGURE 5 : Hairpin critical current test fixture.

62
2.2 ROUND ROBIN TEST SERIES

Three different conductors were supplied to all

the superconductor suppliers with the request that they

be measured in the normal manner for each organization. It was recognized that differences between

measurements of the various participants will be attributed not only to the test fixtures but also to the

choice of voltage criteria. It is our experience that

one single criterion can not adequately fulfill the

requirements of the .various types of wire produced by

Airco Superconductors. Our organization therefore

opted to avoid a debate on the merits of a particular

criterion but rather to reduce the data using as many

of the criteria as possible and reasonable including

both of the two most widely used criteria, resistivity

and electric field, in the hopes that comparisons can

be more easily accomplished. The critical current

obtained using these options has been tabulated in

Table 4-7. Finally, for the specific wire type being

measured, the criterion consistent with Airco Superconductors standard practice was used and the resulting

values reported in Table 8.

2.2.1 Critical Current Criterion

The resistivity criterion requires not only a choice of the acceptable resistivity value but also of

the cross-sectional area to be used in determining the

resistance and subsequently the voltage. In the case

of NbTi superconductor, this choice is straight forward

-12

and nominal resistivity levels of 1x10 and

IxlO”^^ ohm'cm were used in the round robin test

series. The choices for Nb^Sn conductors are more

complicated since a simple division between superconducting components and low normal resistivity components is impractical to measure without subscribing to

63
extraordinary means. In this case, choices of several

possible and appropriate cross-sectional areas have

been made. They include the area of Nb^Sn, the area

of Nb + Nb^Sn, and the area of Ta + Bronze + Nb + Nb^Sn (sometimes referred to as the non-copper

area) . Once again nominal resistivity levels of

-11 -12

10 and 10 ohm’cm were used.

Applying the electric field criterion, to these

tests is much simpler and clearer but its utility to a magnet designer can be debated. Sensitivities of 0.25

y V/cm and 1.0 yv/cm were chosen for the round robin

test series.

The test fixture, test conditions and these

various criteria options are presented in detail in

Table 3 for the three conductors measured.

2.2.2 Round Robin Test Results

For the purpose of this report, each conductor was

described by a photomicrograph, a typical V-I curve at

6 T (Figures 6-8) and the critical current determinations for the various criteria feasible (Figures 6-8

and Tables 4-7). The critical currents, as would

normally be defined by Airco Superconductors, are given

for each wire in Table 8 and shown in graph form in

Figure 9. A word of caution against drawing too many

conclusions from Figure 9 is appropriate. The three

different conductors range so widely in design that an

absolute comparison based on current is not valid.

General characteristics of NbTi and Nb^Sn superconductors are illustrated particularly at high fields

where NbTi is approaching its critical field.

Most of the values appear to be slightly less than

the expected values. This apparent discrepancy may

turn out to be associated with the critical current

criteria. The difference between the two measurements

of the Nb^Sn tape can be attributed to the aspected

64
TABLE 3: CRITICAL CURRENT CRITERIA USED IN THE ROUND ROBIN SERIES

MATERIAL CROSS-SECTIONAL AREA TEST FIXTURE

(cm2)

RESISTIVITY criterion'*’

(UV @ 50 A)

electric field’*”*’ (uV)

Sample 1; ^^hTi (1) Noninductively 1.5 0 1 X 10“^^ P'cm 10 0 0.25 uV/cm

NbTi composite 1.33 X 10“^ wound long

sample 15 0 1 X 10“^^ P'cm 40 0 1.0 yV/cm

Sample 2: No^Sn tape(2a) Inductively Using 3.4 0 0.25 yV/cm

wound sample 3 0.6 @ 1.5 X 10“ Q*cm

_3 \b3Sn

^b+Nb^Sn " ^ 2.03 @ 1.5 x 10“^^n*cm

A^b sn

" ^ ^ ^ 3 (3) Hairpin Using A^^+j^^^Sn 0.5 0 0.25 uV/cm sample , 3 ^ 0.1 0 1.5 X 10 1,9 0 1.0 uV/cm

1.0 @ 1.5 X 10“^^fi'cm

\b^Sn

0.28 0 1.5 X 10"^^fi*cm

2.8 ? 1.5 X 10“^^P*cm

Sample 3: Multi filamentary

Nb^Sn

p* * * ~ Ta+Bronze+

Nb+NbjSn

1.41 X 10

A* * = ^b+Nb^Sn

0.28 X 10

(2b) Inductively

wound sample

Using A^Ta+Bronze+Nb+Nb^Sn 2 0 1.0 gV/cm

0.35 @ 1 X 10“^^ n'cm

\b+Nb3Sn

0.18 @ 1 X 10“^^ n'cm

1.8 0 1 X 10“^^ n*cm

* Measure by weight difference assuming

Nb 46.5 w/o Ti.

** Using dimensions taken from

photomicrographs.

*** Using actual wire dimensions after

etching copper away.

+ Total voltage in yV at 50A transport

current for each conductor area and

sample length. This point is used to define a constant resistance line whose

insertion with the sample V-I curve determines the critical current.

.++ Total voltage in yV for each conductor

and the sample length of the fixture

from Table 2.

65
FIGURE 6 a) Photomicrocgraph of NbTi aspected conductor

measured in the Round robin Tests , and

(125x)

FIGURE 6: b) Typical V-I curve for this conductor

66
TABLE 4 TEST RESULTS for the NbTi CONDUCTOR

PROVIDED in the ROUND ROBIN TEST

1

i

^ H

i I I (2)

I ^2)

I (3)

c c c c

: Tesla Ampe res Amperes Amperes Amperes

9.5 32.25 • 36 36 39

1

i 9.0 51.25 54 51.5 56

8.0 88.1 - 99 98

! 7.0 122.8 125.5 130 130

6.0 159.5 163

j 5.0 200 203

A.O 246 249

3.0 306 306

2.0 399 401

1.0 590 590

Ej. [VJV/cm] 0.25 1.0

P [ohm- cm]

1.0 X lO" 12

-11

1.0 X 10 —

\bTi \bXi

67
FIGURE 7 a Nb^Sn tape provided for the Round Robin

test program.

68
TABLE 5: TEST RESULTS FOR THE Nb

^ Sn TAPE PROVIDED IN THE

ROUND ROBIN SERIES MEASURED ON THE INDUCTIVELY

WOUND CYLINDRICAL FIXTURE

H I

'1'

C

I

>2)

C

j

(3)

C

Tesla Amperes Amperes Amperes

9. 5 108 (111) —

9 122 125 124

8 149 155 152

7 183 (186 ) 184

6 212 217 213

5 245 - 245.5

4 274 - 274

3 306 - 306

2 342 - 342

1. 5 370 - 369

1

• o 416 - 415

[pV/cm] — — 0.25

P [oh-Ti-crn] -12

1.5 X 10 1.5 X lo"^^

using ANb3Sn

69
TABLE 6: TEST RESULTS FOR THE Nb^Sn TAPE PROVIDED IN THE

ROUND ROBIN SERIES MEASURED ON THE HAIRPIN FIXTURE

H I

C

I <2)

C

I

C

I

C

,^(S,

Tesla Amperes Amperes Amperes Amperes Amperes

9.5 - - - -

9 116 - 114 116 113

8.5 132 - 130 131 128

8 147 142 144 146 144

7.5 163 158 162 162 160

7 180 162 177 179 175

6.5 202 192 195 197 194

6 214 - 212 213 “

5 243 240 242 243 240

4 278 270 273 274 270

3 307 301 304 303 301

2 344 334 337 337 334

fpV/cm] -- 1.0 0.25

p I ohm- cm) — 11 — 19 — 19

1.5x 10 1.5 X 10 1.5x 10 ^ — —

-—using Nb + Nb^Sn- -using

^Nb^Sn

oniy70
FIGURE 8 a)

I

I'

1

,

Photomicrograph of the multifilamentary

Nb^Sn wire measured in the Round Robin Test.

(160 x)

FIGURE 8: b) Typical V-I curve.

71
TABLE 7 TEST RESULTS for the Nb

^ Sn MULTIFILAMENTARY WIRE

PROVIDED in the ROUND ROBIN SERIES

H j

(l)Ta

c

j (DSC

c

j (2)SC

I (3)

c

Tesia Amperes Amperes Amperes Amperes

9.5 79 83 75 79

9.0 87 93 84 88

8.0 105 110 102 103

7.0 127 137 122 128

6.0 160.5 170 154.5 160

5.0 196 210 185 191

4.0 254 264 249 235

3.0 317 343 302 304

2.0 433 464 408 395

in

•

•

—

i

521 558 511 505

[pV/cm] __ -- 1.0

P [ohn-cml -11

1.0 X 10 l.U X 1.0 X —

using ^.pa+Bronze+Nb+Nb^Sn ““"5 VjSn only

72
TABLE 8 RESULTS of the ROUND ROBIN CRITICAL CURRENT

MEASUREMENTS (currents in Amperes)

Magnetic NbTi Nb^Sn Nb^Sn Multifilamentary

Field (T) Wire (D Tape(2) Wire

Hairpin Cylindrical

2 399 337 433

4 246 273 254

6 159.5 212 217 160.5

8 88.1 144 155 105

CRITERIA

-12

1.

) NbTi wire; 1.0x10 fi.cm and

- 12

2.

) Nb^Sn tape: 1.5x10 SI. cm and A^^j^ .

3.

) NbjSn MF wire: IxlO'^^ fi.cm and ^ Bronze + Nb + Nb

3

Sn

73
(AMPERES)

1000

900

800

FIGURE 9

CRITICAL CURRENT VS APPLIED MAGNETIC FIELD FOR ROUND ROBIN TEST

700 - 600 -

500 -

400 -

300 -

200 -

100 - 90 - 80 - 70 - o H 60 -

50 -

40

30

X

20 -

H (APPLIED MAGNETIC FIELD)

10 J 1 i I I i \ I \ I TESLA

0 I 2-3 4567 89 10

74
configuration. It is well known that the critical

current of highly aspected conductors varies with the

magnetic field orientation with respect to the broad

side of the conductor. The lower critical current when

the field is perpendicular to the broad face is consistent with this effect.

75
2.3 THE EFFECT OF MAGNETIC FIELD INHOMOGENEITY ON CRITICAL

CURRENT MEASUREMENTS

The question of field homogeneity is a recurring

dilemma to the superconductor tester. The problem

arises in defining how good the field uniformity must

be. The series of measurements described in this section attempts to clarify this situation using the

noninductively wound long sample test fixture.

2.3.1 Test Procedure

The noninductively wound test fixture measures a 40 cm long sample in an axial length of 1.9 cm on a coil radius of 2.5 cm. The measurements begin with the

bottom <Df the coil at z=0 and the magnet at 5 T. After

the critical current is measured, the test fixture is

raised about 5 mm, the magnet current increased such

that the magnetic field at the bottom of the coil (in

its new position) is once again at 5 T and the critical

current measured. It is clear from Fig. 2 that this

procedure will keep the maximum magnetic field

(Bmax)^^ the sample the same, but it lowers the

minimum magnetic field that the sample experiences

( AB increases). This procedure was repeated at seven

positions along the axis.

2.3.2 Test Results

The result of these critical current measurements

-12 for a resistivity of 1x10 ohm*cm are shown in

Fig. 10. As one can see the effect is very small, less

than 2%, for a AB of slightly greater than 15%. It is

important to note that the 15% change is spread out

over 20 cm of sample for an effective 0.75%/cm. This

effect on this type of fixture can be partly attributed

to the nonuniformity in resistivity along the sample.

76
^co

X 100

I CO

AB

B

X 100

MAX

FIGURL: 10: Critical Current Variation Due to Nonuniform

Applied Magnetic Fields Along the Sample

77
Thus to reach a certain voltage level, a higher current

is required in the sample as compared to a more uniform

field case where more of the sample length contributes

to the voltage. It is very likely that a AB of 15%

would have a much more significant effect on a hairpin

test fixture, for instance when the sample length is

reduced by an order of magnitude. It appears that for

the type of fixture used (noninductively wound long

samples) , magnetic field inhomogeneities would not be a major source of error.

78
2.4 EFFECT OF CONDUCTOR ORIENTATION WITH RESPECT TO THE

MAGNETIC FIELD ON CRITICAL CURRENT MEASUREMENTS

It is well known that the critical current of most

superconductors is greater when the magnetic field is

parallel to the transport current rather than being

perpendicular. The vast majority of superconducting

applications utilize the conductor with the magnetic

field perpendicular to the transport current and for

this reason almost all the testing is performed under

this condition. The tolerance for alignment inaccuracy

will have an impact on both the test fixture design and

the conductor mounting techniques. Obtaining data on

which to base this tolerance is the purpose of this

series of measurements.

2.4.1 Test Procedure

The best test fixture for the measurement of conductor/magnetic field orientation effects would be the

inductively wound cylindrical configuration since it

eliminated, or at least kept constant, the maximum

number of other variables one of which is field

homogeneity. Several samples of NbTi wire were wound

with different pitches on the cylindrical mandrel. The

different spiral pitches produced angles of 30°

(demonstrated in Figure 11) , 60°, 80°, and approximately 90° between the conductor and the magnetic

field. In each case the critical current was measured

-12

at a sensitivity of 1x10 ohm’cm.

Particular care was taken during the sample

mounting to insure that the orientation of the entire

length of sample be uniform, including the portion

soldered to the current leads.
FIGURE 11: INDUCTIVELY WOUND CYLINDRICAL TEST FIXTURE MOUNTED

^th the NbTi SAMPLE at 30° with RESPECT to MAGNETIC

FIELD

80
2.4.2 Test Results

The results of the critical current measurements

are given in Figure 12 as a function of applied

magnetic field for four different angles. The critical

current increase averaged over all the magnetic fields

tested is presented in Figure 13. For a 10° orientation error, a 5.3% current increase is measured.

Most fixture designs can easily maintain less than

5° alignment errors which should yield less than 2%

critical current measurement error from this type of

variation.
amperes

FJC',i:pK 12- Critical Current vs Uayr.etic Field of

a Typical NbTi Conductor for Several

Angles with Respect to the Applied Field

180

160

140

120

100

80

60

40

20

Q = 30’

a = 60

A a - 80

a

“ 90

1 12345678 L- L I I 1 ! L

H Applied rhicjnc-tic Field (Tesla)

82
83
2.5 EFFECTS OF IMPERFECT RECTIFICATION AND FILTERING OF AN

SCR CONTROLLED CURRENT SOURCE

As the size of superconducting magnet conductors

increases, so does their critical current. This

natural progression has required the use of high

current SCR power supplies whose output current usually

contains high frequency spikes and noise to a much

greater degree than the transistor power supplies used

at low currents. The effect of this noise on critical

current measurements is the intended goal of this

section.

2.5.1 Test Procedures

Exploration of high frequency noise effects was

performed on a 12 kA power supply. This power supply

was primarly intended for plating applications. For

the purposes of this test program modifications were

made to the power supply, first, to reduce the noise

level by adding a 0.9 farad capacitor bank across the

terminals and, second, to increase the noise level by

removing the standard filter included in the power

supply. These two cases plus the unmodified configuration produced large changes in the noise level as shown

in Table 9. The critical current measurement was then

made with each configuration.

2.5.2 Results

Measurements were made on a NbTi conductor with an

expected I^ of 7000A at 6T. These tests were limited

by the performance of the test fixture. The current

transfer area was insufficient for the high currents

(approximately 6000A) being used and behavior usually

associated with lead overheating was observed. The

quench currents for Case 2 and 3 were the same (5640A)

while in Case 1 the critical current was slightly

84
I

I

TABLE 9: Description of High Frequency Noise for

Three Filtering Configurations

i|

' Case 1 Case 2 Case 3

Peak to Peak

current ripple

as % of Ip,,

110% 22% 14%

Frequency (hz) 360 360 120

Filter

Configuration

none standard standard

+ 0.9 farad

capacitor banl

85
TABLE 10; Critical Current of Cables Compared with

the Critical Current of the Cable Strand

Number

of

Strands

Critical

Currents

at 8 T

I Cable

I Strand

Single Strand - 125 A 120 A

3 Cable 3 374 A 3

3^ Cable 9 1125 A 9

3^ Cable

w/copper jacket

81 9500 A 79

86
higher (5760A) presumably due to instrumentation filtering saturation at these high AC signals. However,

in all cases no current sharing was observed and the

transition was abrupt and uncontrolled. Modification

of the test fixture and further testing will be

required before any evaluation of these results,

relevant to the effect of noise, can be made.

87
2.6 SUPPORT FOR THE VALIDITY OF DETERMINING I^ (CABLE)

FROM I^ (STRAND)

It was deemed appropriate to the aims of this program to present some Airco Superconductor data which

sheds some light on the validity and/or feasibility of

determining the critical current of a cabled conductor

from a measurement of the critical current of the

single strand which makes up the cable. As part of the

development of the Nb^Sn forced flow conductor,

critical current measurements were made on three cable

configurations using the same strand. Each cable was

measured at 8 T and 4.2 K with a critical current

criterion of 1x10 ohm'cm using:

^Ta + Bronze + Nb + Nb^Sn

The basic strand used in all the cables was similar t^

the wire shown in Figure 8.

The first cable is a simple three strand cable or

triplet having a twist pitch of 25 mm. The second

cable takes three triplets and joins them together on a 37 mm twist pitch. The third conductor is a 3x3x3x3

fully transposed cable with successive cable pitches of

25 mm, 37 mm, 75 mm and 150 mm. This cable was then

compacted in a copper tube. The critical current of

these three cables are given in Table 10.

In general, these measurements support the

hypothesis that the cable current can be predicted from

measurements made on the cable component. It may be

important to note that these cables are round or square

with large radii corners where the strands have not

radically deformed during the cabling process. Measurements on flat cables may yield different results.

88
3.0 CONCLUSIONS AND RECOMMENDATIONS

We believe that the results of these tests will support

the National Bureau of Standards program to develop a set of

standards for superconductors. The round robin test series

have been provided in such a way that they can be used easily

in comparisons.

Both the measurement series on magnetic field nonuniformity and on conductor/magnetic field alignment demonstrated

that they do not place intolerable demands on the test fixture

design. This conclusion is only strictly valid for the types

of fixtures used in each experiment.

The test program exploring the effect of current noise

produced in SCR controlled power supplies should be pursued.

Modifications to the test fixture can be made which will allow

conclusive evidence to be obtained.

B. Intermagnetics General Corporation

THE DEVELOPMENT OF STANDARDS

FOR PRACTICAL SUPERCONDUCTORS

FINAL REPORT

NBS Contract NB79RAC90025

1) Effect of Self-field on Critical Current.

2) Development of a Simple Method for Measuring the

Normal State Resistivity of Composite Conductors.

IGC Report # 10-80-2

ICC Project #9576

R.E. Schwall

W.V. House

R.B. McCown

K.A. Mortensen

91
TABLE OF CONTENTS

List of Figures

List of Tables

1.0 INTRODUCTION

2.0 EFFECT OF SELF-FIELD ON CRITICAL CURRENT

2 o 1 Theory

2.1.1 Prediction of Limiting Cases From

a Simple Model

2.1.2 General Theoretical Behavior

2 .

2

Experiment

2.2.1 High Current Conductors

2.2.2 Low Current Conductors

3.0 A SIMPLE METHOD FOR MEASURING THE NORMAL STATE RESISTIVITY

OF COMPOSITE CONDUCTORS

3.1 Disucssion

3.1.1 Introduction

3.1.2 Measurement Concept

3.1.3 Measurement Procedure

3.1.4 Apparatus

3 . 2 Data

References

92
LIST OF FIGURES

2.1 Illustration of Magnetic Field Geometry in Wire

2.2 CDIF Superconductive Composite

2.3 CDIF Conductor

2.4 Fermi Energy Doubler/Saver Strand

2.5 BNL Isabelle Strand

2.6 Data From Low Current Self-field Experiment

3 . 1 Photo of RRR Apparatus

3.2 Typical V-I Plots from RRR Apparatus

93
LIST OF TABLES

2.1 Self-field Parameter e for a Number of Commercial

Conductors

2.2 Properties of CDIF Superconductive Composite

2.3 Results of High Current Self-field Effect Experiment

2.4 Low Current Self-field Results Fermi Type as Twisted

2.5 Low Current Self-field Results BNL Type as Twisted

2.6 Low Current Self-field Results Fermi Type Drawn After

Twisting

2.7 Low Current Self-field Results BNL Type Drawn After

Twisting

3.1 RRR Data on Various Conductors

3 . 2 RRR vs . Temperature Fermi Conductor

94
1.0 INTRODUCTION

This report is the final report under NBS PO# MB79RAC90025

issued to IGC on July 23, 1979. Under this contract, IGC performed the following tasks:

1. A theoretical analysis of the effect of self-field on

the critical current of short samples of superconductive wire.

2. An experimental evaluation of the effect of self-field

on the critical current of short samples of superconductive wire.

3. The design and construction of a test fixture to measure

the residual resistance ratio of the stabilizer in superconductive

composites

.

4. The measurement of the residual resistance ratio of a

number of composites using this test fixture.

5. Participation in round robin tests of critical current

on superconductive samples provided by NBS

.

6. Participation in the ASTM Subcommittee B1.08, efforts

on Standardization of Superconductors.

7. Participation in NBS surveys concerning the generation

of standards for the measurement of superconducting composites.

The first four tasks are reported in this final report. Interim

reports have covered the participation in round robin tests of

I^ and participation in the ASTM standardization efforts.

The work presented here represents the efforts of a number people

at IGC. The initial work on the matrix residual resistance ratio

measurements was performed by Dr. Mike Walker and Mr. Jack Gramm.

The self-field effect theory presented in Section 2.1.2 was

developed by Dr. Waylon House. The measurements of the self-field

effects and matrix residual resistance ratio were performed by Mr.

Karl Mortensen and Mr. Joe Clements of the IGC Conductor Development

Laboratory. Dr. Robert McCown directed the design of the

95
residual resistance ratio apparatus and provided program

management over much of the duration of the program. Direction

of the experiments reported here and overall program management

were the responsibility of Dr. R. E. Schwall. IGC has been

pleased to participate in this significant standardization effort

and hopes to continue this participation through continued

membership on the AFTM Standardization Subcommittee and future

work with NBS.

96
2.0 EFFECT OF SELF FIELD ON CRITICAL CURRENT

2 . 1 Theory

2.1.1 Prediction of Limiting Cases from a Simple Model

2. 1.1.1 Untwisted Conductor

Consider a cylindrical conductor with uniform current density

J in a transverse magnetic field (Figure 2.1) . At a point at

radius r in the conductor the self-field is:

y Jr

|Bg|= -5- (1)

(MKS units are used throughout this section)

The total field at a point in the wire is the vector sum

of the applied field and the self field.

B^^(r,e) = B^^ + Bg^ - 2 B^ Bg cos (u/2-e)

or

B^^ (r,e) = B^^ +

f \ y Jr

o

- y^Jr B^ sin (0) ( 2 )

The critical current density at a particular point in the wire,

i.e., for a particular filament, is a function of the local field,

hence (2) may be used to calculate the local critical current

density J^ (r , 0)

,

J^ (r,0) = J^ (B^)

If the functional form of J (B^) is known, then the overall

current in the wire can be determined by integration, i.e..

I c

rR rn J^ (r, 0) r d0 dr

o-' -n-'

(4)

97
Figure 2.1 •- Magnetic field geometry is

used in simple model calculation of selffield effect.
!

I!

|i

II'

By assuming a functional form for J (B ) one can thus, in

O J. principle, determine the effect of the self-field directly from

equation 4. There is a proliferation of models for J (B„)

,

however, and one would be hard pressed to experimentally verify

any prediction that was made since changing the wire size to

change the self-field will also change the intrinsic current

density of the superconductor. An order of magnitude estimate

of the effect is, however, quite straightforward. Equation 2 may

be rewritten as

1 -2e sin (0) +

2

£

where e 2B

Jr

A

(5)

( 6 )

In large conductors at low field where is high, e at the wire

surface may be as large as 0.5. In commercial conductors, however,

e ranges from ^0.01 to 0.1 at the rated operating field (see

2 -2 -4 Table 2.1) and the e term will be in the range of 10 to 10

The net effect of the e term will depend on the functional form

2 of (B^) . If (B^) B^ then the integral- over 6 is zero.

For other functional forms, the term is nonzero but of order e.

The net effect of the self— field on an untwisted conductor thus

depends primarily on two factors.

1) The relative magnitude of the self-field and the

applied field.

2) The functional dependence of the critical current on

field

.

99
Conductor I c Diameter

Operating

Field e

( amps) (cm) (Tesla)

CDIF 10583 0.518 7 0.12

GE/LCP 8T 1000 0.187 8 0.027

GE/LCP 6T 1000 0.147 6 0.045

GE/LCP 4T 1000 0.120 4 0.083

GD/LCP-H 580 0.168 8 0.017

GD/LCP-M 900 0.168 6.6 0.033

GD/LCP-L 1250 0.168 5.4 0.055

BNL 58 0.029 5 0.016

FNAL 240 0.067 5 0.029

TABLE 2.1 Self-field parameter e evaluated at the wire surface for

a number of current commercial conductors. Rectangular

conductors were evaluated as rounds of equivalent cross

section. e is defined in equation 6.

TOO
In practical conductors the effect will be small and, in general,

indistinguishable from other factors which affect J such as cold

c work, bend strain, etc. It should be noted however, that with a

detailed knowledge of the function J (B,_) in the superconductor,

O X it is possible to evaluate this effect precisely and compensate

for it. In twisted conductors however, the situation is more

complex

.

2.1.1o2 Twisted Conductor

In the twisted conductor each filament spirals through all possible

values of 9 and hence the field on the filament varies from - Bg

to B^ + Bg. The effect of this on the overall critical current

will depend on the relative size of the current transfer length

and the twist pitch. The current transfer length, in turn, depends

on the matrix resistivity, the wire diameter, the measurement

sensitivity and the nature of the resistive transition of the

superconductive filaments themselves.

From Ekin^ we have

(7)

where X . min = current transfer length

N = exponent describing the resistive transition of

the filaments via the equation p = kJ^

^m

*

P =

= matrix transverse resistivity

equivalent resistivity defining the measurement

sensitivity

D = wire diameter.

Two limiting cases ~ twist pitch) and X. may be evaluated directly.

min < < £p

101
For X . >> ,£p the filaments can be thought of as isolated and min ^ we have simply a weak link problem,

i .e. , + PoJ r

I = 2tt

rR

J

y Jr

+

c

O'' C A 2

* rdr ( 8 )

Such would be the case, for example . in a very tightly twisted

NbTi conductor with a full mixed matrix, i.e. Cu-Ni between each

filament. It should be noted that the current transfer length

X . considered here is not necessarily the same as that which is

involved in introducing current into a wire from an external

source. In the braid used for the Isabelle accelerator magnets,

for example, the wire has an outer shell of Cu-Ni alloy to reduce

current transfer between strands but has a full copper matrix

between the filaments. Thus the value of in equation 7 for

interfilament transfer would be that of the copper matrix while

that for transfer into the strand would include the CuNi shell.

X_ . is therefore shorter for interfilament transfer, min /

Another possible example of the case is a tightly

twisted multifilamentary Nb^Sn conductor with a large amount of

residual tin in the bronze.

The other limiting case of a twisted conductor is X . << Jlp,

i.e., the current transfer length long compared to the twist pitch.

In this case the current can continuously redistribute among the

filaments and the analysis for the untwisted conductor is

applicable. Since twist pitches are usually at least 10 wire

diameters and Ekin"^ has found that the current transfer resistance

is immeasurably small at 10 wire diameters in copper matrix NbTi,

we would expect most copper matrix NbTi materials to fall into

this category. Again, however, this is a function of the particular

geom.etry since a large diameter, high current density tightly

102
twisted conductor measured at a high sensitivity might not be

in this limit.

In the intermediate case, i.e., X . ^ iip the analysis is more

complex and has not been accomplished using this simple model.

2.1.2 General Theoretical Behaviour

2 . 1 . 2 . 1 Approaches

There are two basic theoretical approaches useful for describing

the distribution of current density within composite conductors.

The first, which has been useful in describing A.C. losses, is

to minimize the ohmic power dissipation. For the case of static

conditions, however, this approach results in an integral form

for the equation of continuity subject to various kinds of

(generally) integral constraints.

The second, in one guise or the other, attempts to solve the

potential problem subject to the constraints of continuity in

differential form. The latter approach is more amenable

mathematically and is followed here.

Two essential views can be taken in formulating the potential

problem. The first taken by Ekin^ is to consider the resistivity

p (or conductivity a) a scalar variable dependent on position.

In this formulation, the problem begins with two equations,

V-f = O C9al

=0'!’ = ff" Vf (9t>)

which yield

crV^5 — V?'V^

The overall solution of equation 9 is a very formidable task.

Ekin' s approach is to consider two concentric cylinders of

superconductor in a conducting matrix. He then solves a different equation in J. From this formulation, he is able to

extract a parameter X . which describes the characteristic

length required for the effects of current input/output to vanish.

103
A second approach is to consider the conductivity as a tensor

with a certain spatial dependence. This problem is solvable and

some important conclusions can be drawn.

2 , 1 . 2 . 2 Model

The model proposed is to consider the conductivity as a tensor

• E (9d)

The conducting composite is considered to have identical conductivity cr, in the (rO) or (xy) direction and a much larger

conductivity cr^ in the Z (polar) direction. Further it is

assumed that cr-^ may have (r6) dependence. (The axis of the

conductor will be taken in the Z direction)

.

Then (9e)

cr, = (9f)

2 The off-diagonal elements can be shown to vanish . Clearly the

choice of such a tensor is tantamount to choosing a continum

model with microscopic anisotropy - much as in anisotropic

problems in solid state physics. In addition spatial variation

is allowed in the 3rd dimension.

2. 1.2. 3 Solution for a Straight Composite

Consider first the case for untwisted composite. The equation

for (static) continuity gives (in cylindrical cordinates)

V-T cr, X — r

^ ^

r 5r p r

4. X Ll

V*"*-

CIQI

+ 2 = o

J

104
( 10 )

since <r

^ normal to

(re) i

Z , we

L

s spatially dependent only on the coordinates

find

1 + S Co 0) o

where CO C is a measure of the ratio of longitudinal to transverse conductivity.

Equation 10 is separable with respect to the Z-coordinates

,

- - ( 11 )

2 Where + k is the separation constant and k can be chosen positive

without loss of generality. Choosing positive sign in the constant,

we obtain

II

<3(f06))

O

H? ^ iCiTjO) ^C<rj&J

(12a)

(12b)

Choosing the negative sign, we obtain

r - k^-f = o (13a)

[i 2.

L V* 3r

(13b)

Examination of 12b and 13b show that in both cases the equation

for gCr0) appears as in an eigenvalue equation.

In point of fact, both these equations can be viewed as

2-dimensional Schrodinger equations and can be solved exactly for £

• 3

independent of 9 in Laquerre Polynomials.

105
Instead, however, consider 6 (re) to be a constant S where (re)

dependence of S(re) can be considered later as a perturbation.

4 Then both 12b and 13b are separable in re. It is easy to show

that with this approximation, the radial equation for 12b is the

modified Bessel equation and that for 13b is the Bessel equation.

The radial equation for equation 12 b has solutions of form

R = h. I (r) m

h-K (r)

2 ra

and equation 13b of form

R = h^J (r) + h. Y (r)

3 n 4 n

Applying the condition of finality (R(r) finite at zero) eliminates

both K and Y functions, and requiring that e be continuous and

of 2tt period forces n and m to be integer.

With the assumption that the potential be finite for r < ro, and

continuous in 6, the general solutions for 12 and 13 are

(14a)

/ \kvi© — ^ p-7 \

yy)zo

(14b)

•f <12. V< j 2_-.U,„e + yX(R\ls''J

yi z o

(14c)

1 = 0

xHo

\X^

(solution for K = 0)

106
Of course k may have a continuous or discrete spectra depending

on the additional boundary conditions.

2. 1.2. 3.1 Radial Boundary Conditions

It is assumed that there is no current flow radially out of the

composite conductor, i.e.,

XI = o

^ \ Y -z fo

This is equivalent to the requirement that

- O

Imposing this condition on equations 14 yields

(15)

4 ( = (a u f b)+

^^^ ry\i.p

where X is the mth root of

mn

J C XJ ^ 0 TV”

2. 1.2. 3. 2 End Boundary Conditions

The remaining constants in equation 15 can be determined by the

end boundary conditions. These can be specified, for example,

as the potential distribution at +Zo and - Zo, (or its Z-derivative

there) . A quite general result is obtainable using the Fourier-

. . . 5 » 6 Bessel and Dim series.

107
( 16 )

The 6 dependence can be dropped since it does not add any

qualitatively different results to the solution. Assuming

cylindrical symmetry, the solution by this means becomes

Although appearing formidable, this result is quite easily

understood and significant. The term A corresponds to the mean

value of the potential at Z=0 due to the imposed potentials at

-Zo, +Zo. The term B corresponds to the difference between the

r-averaged imposed potentials at -Zo, +Zo. Note that these terms

are uniform over the radius r and are independent of S .

M z I where

a

B I o o

^ '{V to

o

and where J* 0 defines X.m

108
The term is the coefficient of the radial variation of

the potential as a function of Z. The functions J (r /r ) o xm^ o

form a complete set covering well-behaved functions of r.

Consequently, describes how the radial variation of the

potential due to the electrodes (or fixture) dies out in the

axial direction.

As Ekin^ has pointed out, the exact end conditions depend on the

details of the fixture. The equation for C (Z) or C (Z,0) in

the extended case enables an exact calculation for this effect.

In addition, this enables us to write the worst case decay

constant since X, <^

2

’ X - = \IT

X| 3.7/

where the radial potential decays as,

Clearly, 2Zo, the separation of the fixture should be '^^lOO times

the radius r^ to prevent interference with the measurement. (Of

course, placing the voltage measuring taps equidistant from the

wire midpoint can diminish these effects significantly, at least

when the fixture is symmetric.)

2. 1.2. 3. 2 Current Distribution

At a sufficient distance from the fixture, then the surfaces of

equi-potential are flat planes normal to Z. Consequently the

current density in this region is

Ti - T^Crjs)'^ ~ A.
The r,0 dependence of cT

^

t>e re-introduced for it can be

seen that the perturbation in S in equation 13b changes only

the decay constants in . In this case then the total current

is

r<, 2/T = J J

Ti i-JrJ© =

O o 2^

2ir (17)

0^

r JrJ(9 .

2. 1.2. 4 Solutions for Twisted Wire

The case of a twisted composite can be treated in a way analogous

to the straight composite. Consider equations 9e, 9f again,

this time replacing 0"

2 by a substantially larger conductivity

^2)

* 1^ fact (T 2

be allowed to have an r-dependence

.

Equation 10 is then modified to

\ "9 r

=0 do'

where S(r6) is now a measure of the ratio of longitudinal to

radial conductivity and ^ (r0) is a measure of 0-angular conductivity to radial conductivity. (Note that Z separation

proceeds as in the untwisted case.)

So long as the equation 10 ' remains an elliptical differential

equation (insured by S > > j ), the qualitative form of the

solution remains the same. The effect of t (r) on the equation

for g(r0) influences the decay constant through the boundary

conditions on Jn.

no
The details of the actual solution are unimportant, however,

since it is only the limiting case (after fixture effects have

died out) which is of physical interest. In this limit

*3"

i da

/ 'Sj

And the total current is (see eq. 17)

I ^ ^ ^ ^

(17' )

In this, the (T^ conductivity has been primed to indicate that

it is a different value from the untwisted composite. The

assumption is made that the superconductor to normal conductor

ratio, X , is the same (by volume) in twisted and untwisted cases.

With this notation, the current for given potential in the twisted

and untwisted cases should have the ratio

stej)

08 )

where n is the number of turns in length L. This results arises

simply from the difference in aspect ratio of the two cases with

respect to the z-axis, i.e.

Ill
2. 1.2. 5 Self-field and Critical Current

A truly accurate evaluation of the effects of an applied field

and a self field requires a very detailed evaluation of the

specific conductor configuration. However, the simple assumption

that critical field effects can be described by a thermodynamic

argument leads to the approximation that ratios of critical

parameters can be treated on the basis of an integrated volume.

Consider equation 17 as either the current or self or applied

field increases. At some point the conductivity at r,0 reaches

a value corresponding to J^(r0). Further increasing current or

field causes additional regions to reach their and so on. The

details of this process may be quite obscure and in any case an

ensemble approach is indicated by the long-range nature of

superconductive interactions.

Thus whenever the integral in equation 17 reaches "criticality"

for an untwisted sample, the integral in 17' for a twisted sample

will also reach "criticality". The ratio between the two cases is

given in equation 18.

For normally encountered twist pitches, this factor is ~ 5% and

so may well be obscured by other effects such as the detailed

structure of the composite.
2 . 2 Self-Field Effect; Experiments

2.2.1 High Current Conductors

As seen in Section 2.1, the self-field effect is expected to be

largest in large diameter high current density conductors. In an

attempt to observe the effect in such conductors, a number of

tests were made using the superconducting composite from the

CDIF conductor. This composite, (shown in Figure 2.2) is normally

laminated into a copper core and then fabricated into a cable

with extended cooling surface (Figure 2.3). For this test, however,

it was used as an unstabilized composite with the characteristics

shown in Table 2.2.

In view of the high cost of test fixtures for such high current

tests, we chose to use an existing test fixture at the Francis

Bitter National Magnet Laboratory (FBNML) to perform our tests.

The fixture, which was built to perform 12 simultaneous short

sample tests, consists of 4 circular copper plates each 3.2 cm

thick separated by phenolic insulators.

Each plate holds 3 samples and the apparatus is

assembled so that the samples are electrically in series. The

normal short sample test is performed by placing two plates

symmetrically around the midplane of a Bitter solenoid and

measuring the voltage across all 6 samples simultaneously. The

voltage taps on the samples are then 1.2 cm apart giving a sensitivity of '^^2 X 10~^^ S7-cm at 1 yv sample voltage and 8 kA current.

113
Figure 2.2 - CDIF superconductive

COMPOSITE USED IN HIGH CURRENT SELFFIELD EXPERIMENT.

114
Figure 2.3 - CDIF conductor incorporating

THE COMPOSITE OF FIGURE 2.2.

5 »

I fI

t .

I 115
Composite Diameter

Cu:Sc Ratio

Nb-Ti Filament Number

Nb-Ti Filament Diameter

Critical Current

0.518 cm

1:1

198

24 0 ym

10583 A 0 7T

Table 2.2 Characteristics of conductor used in

high current self-field experiment.

Actual conductor used had slightly

lower I due to lack of final size

heat treatment.

116
For the self-field experiment/ one 60 cm long sample was placed

in each plate. Three sets of voltage taps spaced at 1.1 cm,

3.9 cm and 42 cm were installed in the copper near the sample

using existing holes. The samples were soldered to the copper

plate along their entire length using pure indium.

The 4 samples tested were produced by twisting adjacent pieces of

CDIF composite with twist pitches of 2.5 cm, 5.0 cm and 10.0 cm.

The 4th sample was untwisted. These twist pitches represent 5,

10 and 20 wire diameters.

Two trips were made to the Magnet Lab to run the experiment. On

the first trip the SCR power supply used to supply current to the

samples failed and no data was obtained. On the second trip,

critical current data was obtained at field of 7.46 and 7.01 T

on all four samples. A total of 16 runs were made with 3 sets of

voltage taps monitored on each run.

Data was recorded using the MIT data acquisition system that is

normally used for the CDIF short sample tests. In this system,

three voltage signals are fed through 10 Hz bandwidth amplifiers

with a gain of 1000 to a Biomation 4 channel transient recorder.

The 4th channel is used to record sample current. All signals

are recorded as a function of time as the sample current is

ramped linearly from zero with the background magnetic field held

constant. The current is dropped to zero after the sample

critical current is reached and the data stored in the Biomation.

Memory is read out to an X-Y recorder as 3 voltage vs. current

traces

.

The quality of data obtained in this experiment was variable.

Noise on the various voltage channels ranged from 2 yv p-p to

^ 20 yv p-p. All channels were susceptible

117
to random noise spikes and occasional large amplitude long time

constant surges. The combined effect of these was to render some

of the data useless and to reduce the overall sensitivity of the

experiment to an equivalent resistivity of 2 x 10 fi-cm. All

the data obtained from the voltage taps spaced 42 cm apart showed

a large resistive component indicating incomplete current transfer

and thus was not used in the analysis.

A summary of the data obtained using the 3.9 cm voltage tap

separation is given in Table 2.3. Although there appears to be a

systematic variation of critical current with twist pitch, this

was found to be due to variations in the magnetic field at the

assumed equivalent sample locations. In the final two runs of

this experiment, the untwisted and 2.5 cm twist pitch samples

were both run with the sample located on the magnet midplane and

the currents were identical to within the resolution afforded by

the system noise.

Subsequent examination of the Bitter magnet by FBNML personnel

indicated that the coil was shorted between plates above the

midplane and was producing a non-homogeneous field.

We thus conclude that for a short sample test of a copper matrix

NbTi sample where the sample is imbedded in a large area of

stabilizer, the current redistribution through the sample-stabilizer

assembly is such that there is no appreciable effect of

pitch on the critical current measured at a sensitivity

fi-cm.

twist

V ,.-11

^ 10

118
H = 7.46 Tesla

Twist Pitch

(cm) fi-cm

I

c

Quench

Untwisted 7650 amps 7700 amps

7600 7700

2 . 5 cm 7880 8080

7900 8100

5 . 0 cm 7850 7980

7880 7950

10.0 cm 8200 8280

8250 8300

H = 7.0 Tesla

Untwisted 8700 8700

8750 8750

2 . 5 cm 9080 9180

5 . 0 cm 8750 9000

10.0 cm 9300 9300

H = 7.0 Tesla Sample on Magnet Midplane

Untwisted 8800 8850

2.5 cm 8750 8890

Table 2.3 “ Results of High Current Self-field Effect

Experiment. Each Twisted Sample was Run Twice at 7.46 T

and Once at 7.0 T.
2.2.2 Low Current Conductors

Following the essentially negative result of the high current

measurements a series of high sensitivity measurements were made

on long samples of low current wire. The samples were fabricated

of conductor currently in production at IGC for the Fermi Energy

Doubler/Saver Accelerator (Figure 2.4) and for the Isabelle

Accelerator at BNL (Figure 2.5). A section of each conductor was

removed from the production cycle prior to the final twisting

operation and cut into three lengths, each ^ 80 cm long. One

length of each sample was measured untwisted and the other two

were uwisted by hand to varying twist pitches and then measured.

The test sample in each case was a 5 turn single layer spiral

wound on a phenolic holder. The sample was potted in wax and

measured in the bore of a 10 T Nb^Sn tape solenoid. Current was

supplied by two IGC 180M power supplies operated in parallel and

voltage was measured by a micro-voltmeter and recorded versus

current on an X-Y recorder. The active sample length between

voltage taps was 'r 70 cm.

Data quality on this experiment was quite good (see Figure 2,6)

with peak co peak noise usually about 500 nV. Data was evaluated

~ 1 9 -IT

at 10 "" f2-cm for fields from 1 to 8 T and at 10 r2-cm from

1 to 4 T on the BNL wire. The Fermi data extends from 4T to 8T

reflecting the maximum available current of 360 amps. (Tables 2.4 & 2.5)

It is seen that there is a definite decrease in critical current

when the conductor is twisted and that this effect is larger in the

Fermi me terial than in the BNL material, as would be expected by

the relative values of e (see Table 2.1). The decrease in

critical current does not, however, show the expected progression

wit! magnetic field, i.e., the effect does not grow larger as the

field is rediiced. This indicates that the critical current change

is perhaps caused by some effect other than self-field. To eliminate

the possibility of dimensional changes which could have occurred

during the twisting operation, the previously tested samples were

120
^^mm^simissm i

Figure 2.4 - FNAL energy doubler/saver

TYPE STRAND USED IN THE LOW CURRENT

SELF-FIELD EXPERIMENTS.

121
Figure 2.5 - BNL Isabelle type strand

USED IN THE LOW CURRENT SELF-FIELD

EXPERIMENTS.

122
Figure

2.6

-

Data

from

low

current

self-field

experiment.

123
SENSITIVITY 10 f2-cm

-12

H

(Tesla)

Untwisted

I

(am^s)

0 . 32cm

I

(aSps)

Twist

AI

(%?

8 115.5 98.3 14.9

7 168 143.3 14.7

6 219 187.5 14.4

5 277.5 235.5 15.1

4 339 289.5 14.6

TABLE 2.4 Critical current of FERMI type conductor as twisted.

AI is I change upon twisting,

c c
i

. . . -12 Sensitivity: 10 fi-cm

H Untwisted 1 cm Twist 0.16 cm Twist

(Tesla)

I c

( Araps)

I c (Amps)AI

c

(%)

I c (Amps)

AI

c

(%)

8 27.8 26.6 4.3 24.8 10.8

7 41.6 39 .

8

4.3 38.3 7.9

6 56.3 54.8 2.6 52.5 6.8

5 72.4 70 .9 2.1 67.5 6.8

4 91.5 89.3 2.4 89.5 6.1

3 116.3 113.3 2.6 108.8 6.4

2 154.5 144.8 6.3 138.8 10.2

1 225 211.5 6.0 207.8 7.6

Sensitivity ; 10“^^ J^-cm

1 85.6 84 1.8 80.3 6.2

2 112.5 106 5.8 100.5 10.7

3 146 135 7.5 129 11.6

4 210 199 5.2 194 7.6

Table 2.5 Critical Current of BNL Type Conductor as Twisted For

Different Twist Pitches. AI is I Change Upon Twisting.

c c

125
drawn through the dies which are normally used after the production

twisting operation to insure a uniform cross section. The samples

were remeasured and the results are shown in Tables 2.6 & 2.7. Again

there is a definite reduction in the critical current upon twisting

and the effect becomes larger as the wire is twisted more tightly

and as the field is lowered. It scales, however, much more slowly

than e indicating that if a self-field effect is present, it

is not adequately described by the simplistic model used in Section

2.1.1. It is difficult, however, to postulate a mechinism which

would explain the observed behaviour. Most phenomonen which degrade

critical current such as non-uniform reduction in filaments or nonuniform strain in filaments, have an effect which is predominate at

high fields, and in this data the effect is larger at the low fields.

At this point, we would therefore say that there does exist a

degradation of the critical field in NbTi superconductor wires upon

twisting which can tentatively be ascribed to self-field effects in

the absence of a more satisfactory explanation. It is obvious,

however, that considerably more experimental and theoretical work

v.ou_d be necessary to unambigously establish this effect and to

-^uantify it in such a manner that it could be properly taken into

account in the design of short sample tests.

126
SENSITIVITY 10"^^ i^.-cm

H

isla)

Untwisted

I c (Amps)

0 . 5 cm

I c(amps)

Twist

AI

c

(%)

0.3 cm

(amps)

Twist

AI

c

(%)

8 87 72.8 16.3 72.8 16.3

7 123 108 12.4 105 14.8

6 160.8 141.8 11.8 134.3 16.5

5 198 127 10.6 165 16.7

4 241 202 16.0 200 16.9

3 296 252 15.0 245 17.1

TABLE 2.6 Critical current of FERMI type conductor drawn after

twisting. AI is I change upon twisting,

c c

127
SENSITIVITY lO"^^ ^^-cm

Untwisted 1 cm Twist 0.16 cm Twist

H I c

I cAt

c

I c AI

c (Tesla) (amps) (amps) (%) (amps) (%)

8 23.7 23.3 1.7 22.0 7.2

8 35.8 35.3 1.4 32.8 8.4

6 48.4 47.3 2.3 44.6 7.9

5 61.9 60.8 1.8 57.2 7.6

4 78.0 76.5 1.9 71.3 8.6

3 97.7 85.3 2.5 89.6 8.3

2 128 124.5 2.7 116.7 8.8

1 184.4 176.3 4.4 168.3 8.7

SENSITIVITY

-13

10 fi-cm

4 72.8 69.9 4.0 66.2 9.1

3 90.7 88.5 2.4 83.9 7.5

2 118.5 115.5 2.5 105 11.4

1 170.6 165 3.3 154.6 9.4

TABLE 2.7 Critical current of BNL type conductor drawn after

twisting AI vs I change upon twisting,

c c

128
3.0 A SIMPLE METHOD FOR MEASURING THE NORI'IAL STATE RESISTIVITY

OF COMPOSITE CONDUCTORS

3 . 1 Discussion

3.1.1 Introduction

Measurement of the resistivity ratio of the stabilizer in composite superconductors, although simple in concept, can be

difficult or complicated in' practice. The problem is associated

with the ability to fix the conductor temperature within reasonable limits at some low level above its transition temperature.

Immersion in liquid hydrogen is ideally suited to this purpose

for most practical superconductors, but liquid hydrogen is not

always available and the safe handling of it is a serious problem.

Dangling the conductor in a helium-filled dewar at a sufficient

height above the helium level to insure that the superconductor

is normal can work, but the temperature of a long length of

conductor may be uncertain.

3.1.2 Measurement Concept

The temperature is stabilized by "pinning" the conductor between

liquid helium as a thermal sink and current leads as a thermal

source, while the voltage drop across a short section of it is

measured using relatively high current for adequate sensitivity.

The temperature range within the measured section is monitored

using gold-iron and chromel thermocouples spaced above and below

the measured section.

3.1.3 Procedure

Although the procedure described below has been empirically

derived, it seems to have a wide range of applicability. It has

been used to measure the resistivity ratio of the copper component

129
of multi filamentary NbTi-copper superconductors, and is should

be readily applicable to other types of superconductors as well.

3. 1.3.1 Mounting the Sample

The conductor is mounted on a holder which hangs vertically in a

helium dewar and is immersed at its lower end in liquid helium.

The top end of the conductor is soldered to a terminal capable

of carrying 50 Amperes at room temperature. The total conductor

length should be long when mounted on the holder shown in

Figure 3.1. The circuit is completed by soldering the conductor

to a second terminal at the lower end.

Voltage taps from twisted-pair leads are soldered to the conductor

using No. 36 wire at the center of the conductor and separated

by one inch. This spread is precisely measured. Five mil diameter

gold-iron and chromel thermocouples are soldered to the sample at

points h" above and below the voltage taps, with particular care

to insure that they are thermally grounded by the solder to the

sample. Cold reference junctions are located at the bottom of

the probe, which will always be in liquid helium for the measurement, The thermocouple leads are taken directly from the probe to

differential floating input terminals without plugs or connectors

to minimize extraneous thermal EMF's.

3.1. 3.2 Instrumentation

The instrumentation consists of three microvoltmeters, an x - y

recorder, and a DC current source. Two of the meters are used to

monitor the thermocouple EMF's. The third meter must have a chart

recorded output voltage and is used to record the voltage drop

across the conductor test length. V is plotted vs. I on the

X - y recorder using the chart recorder voltage output from the

microvcitmeter to drive the "y" input and the voltage drop across

an appropriate current shunt to drive the "x" input.

130
Figure 3,1a - Lower end of RRR apparatus.

Thermocouple reference junctions are to right

OF PICTURE,

131
Figure 3.1b- Details of voltage taps and

THERMOCOUPLE ATTACHMENT TO SAMPLE.

132
3. 1.3. 3 Measurement of Resistance Near Room Temperature

Immerse the sample in a stirred alcohol bath which is held at

0°C by a surrounding ice-water bath. Record the bath temperature.

Record voltage vs. current with I varying from 1=0 to I=^-25

Amperes for .049" diameter conductor, and smaller maximum current

for smaller wire. The measurement should be repeated using

different ramp rates for the currents. The data should be logged,

noting any non linearities and hysteresis in the traces.

3 . 1 . 3 . 4 Measurement of Resistance Near 10 °K

(1) Immerse the probe in helium until the thermocouple EMF's are

constant and approximately zero, then zero both of the thermocouple microvoltmeters. Mark the helium level by the lack of

change in the thermocouples as the sample is moved vertically.

(2) Lift the sample until the lower thermocouple indicates

approximately 10 °K. Verify that the upper thermocouple temperature

is less than 15°K. Be sure that the cold junctions of the thermocouples remain in the liquid helium. Record the helium level from

the probe end. Record both thermocouple readings.

(3) Record voltage vs. current from I = 0 to I = 25 Amp (or less)

.

Hold the current at maximum I and verify that the thermocouple

temperatures are less than 15 °K. Vary the I sweep rate and repeat

the above measurement. The temperature is expected to shift as

a function of I, If this shift causes an appreciable change in the

chart recorder slope, then the measurement of R can be taken

point by point as a function of average temperature between the

two thermocouples. In general the resistance measured at the

lowest temperature that is still above the superconductor Tc will

be most relevant.

133
3. 1.3. 5 Resistance and Resistivity Ratios

(1) RRR' (Tj^/ : The ratio of the resistance measured at

T and T gives directly the Resistance Ratio.

(2) RRR' (T, : To convert the measured ratio to represent

the ratio for some standard temperature near room temperature,

the Gruneisen relation is used;

p

cc TG(e/T)

where

G(e/T)=(e/T)

-4

' Q/T S^ds

o^ (e®-l) d-e"®)

with 0 = 330K for copper for the most common conversion, from

273K to 300K we have RRR' (273, TL) = 0.899 RRR' (300K, Tl) .

(3)

Both of the above are measures of resistance ratio. To

determine the resistivity ratio for the stabilizer component of

the superconductor wire, the room temperature resistivity of the

superconducting alloy or compound may have to be taken into

account and the fractions of each component must be known.

RRR (T, T^ ) = RRR^ . (T, T^ ) - cu ' L tot ' L

R (T) cu

R (T^

)

sc L

Where; RRR„ (T, T^. ) is the ratio of the copper resistance at

CU. J-i T to that at Tt

.

1j

'^RR^^^ (T, T^) is the ratio of the composite resistance

at T to that at Tj^.

Rcu (T) is the resistance of the copper at T

Rsc (T

2

) is the resistance of the superconductor at T^^

We assume T > T_ so that the superconductor is in the normal

J-j u state. We also assume that R (T) >> R (T)

.

sc cu

134
3.1.4 Apparatus

Th© basic test apparatus is illustrated in the detailed

construction blueprints included in this report as Attachment

A*. It consists of an epoxy glass or phenolic sample holder with

two high conductivity copper current contacts mounted on the end

of a 0.5" diameter stainless steel tube. Leads for sample current,

sample voltage and thermocouple voltage are routed through the

tube. The phenolic holder is slotted to contain the sample and all

leads within a 0.5" diameter circle. This allows the entire

apparatus to be introduced into a helium storage dewar via an

0 ring sealed "quick connect" fitting without venting the helium

to air.

The thermocouple junctions themselves are potted in epoxy in

holes cut in the phenolic and thermal contact to the samples is

made via copper foil tapes which are soldered to the sample and

to the junctions. This arrangement provides protection for the

junctions and still yields good thermal contact to the wire. It

was found that a solder bond of a thermocouple to the sample was

essential for accurate temperature measurement. Other methods of

attaching the thermocouple, such as clamping or spring-loaded

pressure contacts resulted in measurement of a temperature more

characteristic of the surrounding helium than of the sample itself.

The apparatus described here represents a third generation in the

evolution of this measurement technique at IGC. Two previous

pieces of equipment were built and used for varying lengths of

time, and experience with them contributed to the design of the

present facility. The current design can be, we believe, easily

duplicated in any low temperature laboratory, and, if sufficient

interest exists, can be offered by IGC as a commercial product.

* Editor's note - The blueprints are not included in this NBSIR. Interested

persons should contact the authors.

135
3 . 2 Data

The apparatus was tested by measuring a variety of wires and by

measuring RRR of a single wire at several temperatures by

changing the position of the holder in the helium dewar. A

typical set of V-I plots obtained on the apparatus is shown

in Figure 3.2.

Data on 4 different wires ranging in RRR from %1 . 2 to 113 are

presented in Table 3.1. The results compare quite well with

measurements from other sources.

In Table 3.2, data on a second sample of FNAL is presented as a

function of temperature. It appears that the resistivity is

slightly temperature dependent in the 11® to 17 °K range as would

be expected from data on pure copper.

136
/y

c>3

l,WrU>^

137

Figure

3.2

-

Data

from

RRR

Apparatus
Dia

.

Conductor (inches) TL

(K)

BNL Isabelle ,0117 15

Full Cu-Ni

Matrix .010 . 14

FNAL " as

twisted .027 14

FNAL #1

final product .027 14

I max

(300K)

(A)

Imax

(TL)

(A)

RRR

1.5 3.4 53.6

1.2 1.2 1.19

3.4 12 36.6

4 12 113

TABLE 3.1 - RRR Data Obtained with NBS Test Fixture
TL

(K)

RRR

9.5 superconducting

11 120

12 120

1

—

t

- 118

17 115

TABLE 3.2 - RRR data on FNAL #2 final product

for different temperatures TL.

139
REFERENCES

1) J.W. Ekin, J Appl Phys ^ 3406 (1978, J Appl Phys ^ 3410 (1978).

2) J.C. Maxwell, A Treatise on Electricity and Magnetism , 3rd

Ed. Dauer 1954 p. 4T5

.

3) J. W. Huang, A. Kozycki, Am. Jour. Phys. #11, p. 1005,

4) N. N. Lebedev, Special Functions and Their Applications , Dover 1972, p. 98. '

5) G. P. Tolstov, Fourier Series , Prentice Hall 1962, p, 197.

6) G. N. Watson, A Treatise on the Theory of Bessel Functions , Cambridge Univ. Press, London 1962.

140
C. Magnetic Corporation of America

DEVELOPMENT OF CRITICAL . CURRENT

MEASUREMENT STANDARDS

FINAL REPORT

Prepared for

U.S. Department of Commerce

NATIONAL BUREAU OF STANDARDS

Boulder, Colorado

Under Contract No. NB79RAC90026

Prepared by

MAGNETIC CORPORATION OF AMERICA

179 Bear Hill Road

Waltham, Massachusetts 02154

Principal Investigator:

Z. J. J. Stekly

Investigators:

H. R. Segal

K. F. Hwang

NBS-02

141
LIST OF FIGURES

2.2- Figure Number

1 Straight sample holder. 2.2-

2 Noninductive sample holder.

2.2-

3 U-shaped sample holder.

2.3-

1 Variation in critical current as a function of electric field

sensitivity.

2.3-

2 Variation in critical current change as a function of heat flux.

Results obtained using voltage/length criterion.

2.3-

3 Variation in critical current change as a function of heat flux.

Results obtained using equivalent resistivity criterion.

2.3-

4 Critical current as a function of measurement criterion.

2.3-

5 Short sample performance of round-robin NbTi at 1 mv/cm.

2.3-

6 Short sample performance of round-robin Nb^Sn tape at 1 mv/cm.

2.3-

7 Short sample performance of round-robin multifilamentary Nb^Sn

at 1 mv/cm.

3.3-

1 Current transfer measurements. Effect of removing some copper from

current contacts.

3.3-

2 Current transfer into CuNi matrix cable.

142
LIST OF TABLES

Table Number 2.1-

2.1- 1 Group 1 samples.

2 Group 2 samples (cable).

2.1-

3 Group 3 samples (round robin).

2.3-

1 Critical currents of Group 2 samples.

2.3-

2 Conductor performance as a function of sample holder.

2.3-

3 Short sample performance 'of round robin NbTi.

2.3-

4 Short sample performance of round robin Nb^Sn tape.

2.3-

5 Short sample performance of round robin mul tifilamentary Nb^Sn.

3.1-

1 Current transfer samples.

143
ABSTRACT

This report on U. S. Department of Commerce Contract Number NB79RAC90026

deals with the development of standards for critical current measurements.

The two tasks investigated were: (1) The Determination of Critical Current

of Short Samples as a Function of Transition Criterion, and (2) Analysis of

Current Transfer from Sample Holder to Sample. The samples used in the

critical current measurements included both NbTi and Nb^Sn. Critical currents

were measured using the equivalent resistivity criterion with sensitivities

-7 -1

2

ranging from 10 S7-cm to 10 f^-cm and using the electric field criterion

with sensitivities of 1 mV/cm to 100 nV/cm. Current transfer measurements

. were performed on monolithic conductors with critical currents greater than

1,000 amps and on a CuNi-matrix cable. The results of the program are that

no single measurement standard and no single test holder are suitable for all

types of critical current measurements, and that sample holders must be

designed with sufficiently large copper current contacts in order to minimize

current transfer effects.

144
I.O INTRODUCTION

Although superconductivity was discovered almost seventy years ago

and although applied superconductivity is approximately twenty years old,

at the present time there are still no defined standards for the basic

superconductivity parameters (critical field, critical temperature, and

critical current) . There can easily be a 50% difference in the critical

current of a sample depending upon the measuring technique. In addition,

in most reports on critical current measurements, the evaluation criterion

is not mentioned. In order to assist the National Bureau of Standards (NBS)

in the development of standards for superconductivity parameters the

Magnetic Corporation of America (MCA) has undertaken a program to investigate

critical current measurements. Testing was performed on approximately

twenty samples using three types of test fixtures. Critical current measurements were made using two evaluation criteria (electric field and

resistivity) and various sensitivities.

With the results of the tests on those samples, including three

round-robin conductors supplied by NBS to MCA and the other contractors,

recommendations are made on the establishment of evaluation criteria and

standardized sample holders. As an additional guide in the design of test

fixtures, testing was performed to determine current transfer properties

from the sample holder into the superconductor. Recommendations are made

on means of improving the current transfer characteristics. In the following section the results of the short sample tests are discussed. Descriptions of the experimental equipment including the various test fixtures

are included. In Section 3 the current transfer tests are described. The

effect of modifying the amount of copper on the current contacts is shown.

In Section 4 the conclusions of the program and recommendations for the

establishment of tests standards are made.

145
2.0 Short Sample Measurements

The majority of the work performed during this program involved the

measurement of the critical current of approximately twenty samples. The

samples varied in their diameters, copper-to-superconductor ratios, and

superconducting material. The measurements were made usir.g three different

sample holders, each sample holder using a different length conductor in a

different configuration. The tests were made at various magnitudes of

external magnetic field and at various sensitivities. The critical current

was determined in terms of electric field and equivalent resistivity.

2.1 Description of Samples

Three groups of samples have been tested. The first group consisted

of 15 samples of multifilamentary, copper stabilized NbTi. The wire diameter varied from .020 cm to .109 cm and the copper-to-superconductor ratio

ranged from 1.25 to 5.5. The specification of the samples in that group

are listed in Table 2.1-1. These samples were chosen to demonstrate the

influence, if any, of copper current density, matrix resistance, heat flux,

etc., on the critical current of superconductors. It was hoped that by

careful analysis of the critical current at different measurement criteria

fo»" the various samples, a single fundamental measuring technique might

be formulated for all short sample testing. In order for that to be possible the relationship between the critical current and the other sample

parameters must be understood. For example, suppose short sample critical

current measurements are made using a criterion of 10 ^]-cm

equivalent resistivity. The resistivity of the copper stabilizer in a "8

typical conductor in an external field of 7 tesla is approximately 5 x 10

-1

2

^2-cm. Therefore, for typical samples the resistivity measured at 10 fl-cm

is due almost exclusively to the superconductor. It is thus conceivable

146
TABLE 2.1-1 GROUP 1 SAMPLES

DIAMETER

(cm)

.020

.028

.041

.064

Cu/SC NO. OF FILAMENTS

1.25 367

1.25 367

1.25 367

1.25 367

.020 1.6 180

.051 1.6 180

.028 1.8 2178

.064 1.8 2200

.020 3.0

.028 3.0

.051 3.0

.061 3.0

.086 3.0

.109 4.0

.100 5.5

121

361

121

121

2772

84

114

147
that the critical current measurements could be independent of the amount

of copper in the conductor. This hypothesis could be tested by determining

the critical current of samples with identical amounts of NbTi but with

varying amounts of copper. It is for such reasons that the chief variables

of the Group 1 samples are copper-to-superconductor ratio and wire diameter.

With the samples chosen in Group 1 it is not possible to hold all the

variables constant while varying only the amount of copper. This is due

to the fact that the critical current density varies with the amount of

cold work reduction. As the diameter of a given type of wire increases,

its critical current density decreases. In order to have a few conductors

with a fixed amount of superconductor which would behave identically in

each of the samples while having a variable amount of copper, a second

group of samples was made. The three samples listed in Table 2.1-2 each

consist of a strand of identical multifilamentary NbTi. In the second

sample of the group the superconductor is cabled with a single strand of

copper wire, and in the third sample the superconductor is cabled with two

strands of copper wire. In this way the superconductor of all three samples

will be identical and only the amount of copper will vary.

Finally, Group 3 consists of samples sent to us by NBS to be evaluated

in round-robin testing. The three samples consist of multifilamentary NbTi,

multi filamentary Nb^Sn, and Nb^Sn tape. A description of each sample is

listed in Table 2.1-3.

2.2 Description o ^ E quipment

Samples were tested on three sample holders. Since part of the goal

of th 33 program is to aid in the establishment of a standard test fixture

it was hoped that a comparison of the results obtained from different sample

holders might lead to a preference in geometry.

148
TABLE 2.1-2 GROUP 2 SAMPLES (CABLE)

SUPERCONDUCTOR COPPER OVERALL Cu/SC

Sample

Number

Number Of

Strands

Strand Dia.

__ (cm) Cu/SC

Number of

Strands

Strand Dia.

(cm)

Cl 1 .028 1.25 0 1.25

C2 1 .028 1.25 1 .018 3.06

C3 1 .028 1.25 2 .018 4.90

TABLE 2.1-3 GROUP 3 SAMPLES

(ROUND ROBIN SAMPLES)

MATERIAL TYPE CROSS SECTION

Mul tifil amentary NbTi 0.53 X 0 .68mm

Nb^Sn Tape

i 2.3 X 0.2mm

(

Mul tifil amentary Nb^Sn

i

i

\

0.7mm diameter 1

1

j

1

149
The first sample holder accommodates four straight samples each up

to 3.5 cm long. A photograph of the sample holder is shown in Figure 2.2-1.

This sample holder was originally built to test reacted Nb^Sn samples. The

straight sample shape permits the Nb^Sn to be reacted in the simplest geometry and mounted with a minimum amount of handling. This sample holder was

designed for use in a dewar with an inner diameter of less than 4 cm. Because of the short sample length this holder is suitable only for conductors

with very short current transfer lengths. In addition, the current through

the sample should be limited to less than lOOA in order to minimize the

joule heating at the current contacts. This point is discussed further in

the next section of this report.

For systems with a larger magnet bore, a similar sample holder could

be built to handle longer and higher current samples. With the present

system a distance between voltage taps of 1 cm is about the largest reliable

length. In order to ensure that each sample is placed in the central field

region the samples are attached to a phenolic support tube which may be raised

or lowered through a quick connect in the top plate of the holder. The

sample holder is made out of phenolic. Small grooves are machined into the

sample holder to help in the alignment of the samples. The samples are held

rigidly in place during testing by a coating of vacuum grease. Because of

the simple geometry the mounting of samples is extremely fast and convenient.

With this sample holder, as well as the other two to be described, one current

le=>d is common to all the samples. The total number of current leads is therefore N+1 , where N is the number of samples in a sample holder.

A second sample holder designed for use in a small bore magnet is

shown in Figure 2.2-2. Three noninductively wound samples can be mounted

on each sample holder. The length of each sample is approximately 75 cm and

150
straight Sample Holder

Figure 2.2-1

FA 5241

151
Non-inductive Sample Holder i

L

Figure 2.2-2 !

I

ii

FA 5242

152
a typical distance between voltage taps is 40 cm. Grooves are machined

in the phenolic sample holders to accommodate samples up to .150 cm in

diameter. Each sample is held in place with two to three pieces of lacing

cord. The samples are prevented from moving during testing by a coating

of vacuum grease. Just as for the straight sample holder, each sample can

be located in the central field by sliding the support tube through a quick

connect on the top plate. Because of the limited helium capacity of the

dewar, sample current is restricted to lOOA.

The third sample holder is shown in Figure 2.2-3. The samples are

U-shaped and approximately 35 cm long. Three samples can be mounted to

the holder. The maximum current that can be carried is 850A. As with the

other sample holders, conductor motion is prevented by coating the samples

with vacuum grease. This sample holder is designed to fit into a magnet

with a bore of 7.6 cm. Because of the curvature of the bottom of the

sample holder, only a very small portion of the sample is perpendicular to

the magnetic field. Because of the variation in sample orientation with

respect to field direction, this sample holder is most suited for less

sensitive measurements such as quench currents, rather than for measurements

in which there is significant current sharing between the superconductor

and the copper stabilizer. The current contact region is 8 cm long on each

end of the sample.

Terminal voltage versus current (V-I) characteristics were obtained

for all samples. The current was generally supplied by a lOOA lOV Hewlett

Packard power supply. For samples that carried more than lOOA, a 500A lOV

supply was used. The current was measured using an external shunt. The

output of the voltage taps was fed into a Keithley microvol tmerer. The

amplified output of the microvoltmeter was the input to the X-axis of an

153
U-shaped Short Sample Holder

Figure 2.2-3

^ i,

FA 5240

154
X-Y recorder, and the potential difference across the shunt was the input

to the Y-axis. With this experimental setup it was possible to measure

sample voltages as low as 0.1 yV. Critical current measurements were made

at MCA using a 7.5 cm diameter, 7 tesla, superconducting magnet and at the

Francis Bitter National Magnet Laboratory at MIT. The magnetic field was

supplied by a 15 tesla, 5.4 cm bore, water-cooled Bitter coil.

2.3 Results and Analysis

The V-I characteristics of the three groups of samples described in

Section 2.1 have been measured as a function of applied field and voltage

sensitivity. In addition to measuring the quench current of each sample

the critical current was measured using electric field and equivalent resistivity criteria. With electric field used as the evaluation condition

critical currents were determined for a range of sensitivity from 1 mV/cm.

Maximum sensitivity was between 1 yV/cm and 0.1 yV/cm, depending upon the

particular sample and sample holder. When resistivity was used as the

evaluation criterion, measurement sensitivity ranged from 10~^ S7-cm to

10 si-cm or 10"^^ S7-cm.

It was originally planned to test the samples in Group 1 at fields

of 3 tesla to 7 tesla. However, it was observed that at low fields there

was little variation in critical current as a function of the measurement

standard. This can be seen in Figure 2.3-1 for a sample with a copper-tosuperconductor ratio of 1.25. In that figure for fields less than 7 tesla

there is less than a 10% reduction in critical current as the measurement

criterion is varied from 1 mV/cm to 0.1 yV/cm. For samples with higher

copper-to-superconductor ratios the reduction is somewhat larger. However,

for a sample with a wire diameter of 0.06 cm and a copper-to-superconductor

ratio of three, the decrease in critical current at 7 tesla is only 11%

155
80 70 60 50 40

(%) WO/AWI iV

Q3ynsv3w iNHiiano IVOIilHO 30 59ViN33'd3d

156

FAS 178

ELECTRIC

FIELD

SENSITIVITY
as the measurement criterion is increased four orders of magnitude from

1 mV/cm to 0.1 yV/cm. In order to maximize the difference in critical

current with sensitivity it was decided to vary the magnetic field between

7 tesla and 10.5 tesla instead of between 3 tesla and 7 tesla. It should

be pointed out, however, that the small variation in critical current with

sensitivity up to 7 tesla implies that there is a good deal of freedom in

the definition of critical current in that range. Although it is not

common to measure critical currents in NbTi superconductors at 10.5 tesla

at a temperature of 4.2K, this is in many ways equivalent to measuring the

critical current at a lower field of a sample with a high copper-tosuperconductor ratio. At least some of the variation of critical current

with measurement standard can be related to the joule heating in the conductor. Low critical currents at high fields result in joule heating that

is comparable to that of low field high current conductor having a high

copper-to-superconductor ratio. For example, a typical critical current

4 2 density at 10.5 tesla is 1 x 10 A/cm . If all of the current would

transfer to the stabilizer in a conductor with a copper-to-superconductor

2 ratio of 1.8, the copper current density would be 5,500 A/cm .

On the other hand, at 7 tesla a typical superconductor current density

5 2

of 1 X 10 A/cm would require a copper-to-superconductor ratio of 18 in

order to have the same stabilizer current density. Therefore, testing

samples at high field values seems to be a reasonable method of simulating

results for high copper-to-superconductor ratio conductors.

The change in critical current with measuring sensitivity varied

significantly as the sample, magnetic field, copper-to-superconductor ratio,

and wire size were varied. For example, a sample with a 0.0635 cm diameter

and a copper-to-superconductor ratio of 1.25 exhibited only a 3.8% decrease

in critical current as the sensitivity was varied from 1 mV/cm to 0.2 yV/cm

157
at a field of 7 tesla. On the other hand, there was a 54% decrease in

critical current in a 0.020 cm diameter wire with a copper-to-superconductor

ratio of 1.6 when the sensitivity was varied from 1 mV/cm to 0.5 yV/cm

when the external field was 10 tesla.

The critical current data obtained using an electric field standard

were analyzed in order to understand the variation in performance with

measuring sensitivity. For example, it would be advantageous to be able

to predict the performance of a conductor at a high measuring sensitivity

based on the quench current results. Attempts were made to find a good

correlation of the data with one of the significant parameters of the

experiment. The best fit of the data occurred when the decrease in critical

current with sensitivity was plotted as a function of heat flux. In Figure

2.3-2 the percentage decrease in critical current from 1 mV/cm to 0.1 yV/cm

sensitivity is plotted as a function of heat flux at 1 mV/cm sensitivity.

NbTi samples from all three groups and at various magnetic field are included in the data. The solid lines represent an envelope of the data

points. The heat flux is calculated assuming 100% wetted surface area.

In fact, the samples were coated with a thin layer of vacuum grease to

prevent motion. The influence of the grease on the heat flux will account

for some of the scatter in the data. For the conductors tested in the

straight sample holder, conduction cooling through the ends will also cause

scatter in the data. In view of these considerations the data points tend to be

situated on a common curve. It is thus possible to estimate the performance

of a sample at 0.1 yV/cm sensitivity from the short sample data at 1 mV/cm

sensitivity.

A similar study was performed on results using equivalent resistivity

as a criterion. It was hoped that resistivity might be a more fundamental

158
.01 .1 1 2

Heat Flux at 1 mV/cm Sensitivity [W/cm )

Fig. 2.3-2 Variation in Critical Current Change as a Function of

Heat Flux. Results obtained using Voltage/Length

Criterion

FA 5227

159
standard than electric field. For example, consider a conductor with a

copper-to-superconductor ratio of 1.25, a copper residual resistance ratio

of 100, and an applied magnetic field of 7 tesla. At an equivalent resis-

-1

1

tivity of 10 fi-cm, the resistivity of the superconductor is 17,000 times

smaller than that of the copper. Since almost all of the current will flow

through the superconductor one might expect that the results are independent

of copper-to-superconductor ratio and are, therefore, intrinsic to the

superconductor. Even at an equivalent resistivity of 10"^^ fi-cm the total

resistance of the copper is 1,400 times greater than that of the superconductor. The experimental results shown in Figure 2.3-3 are very similar

to those for electric field. In that figure the decrease in critical

current with a four order of magnitude increase in sensitivity is plotted

-8

along the ordinate and the heat flux at 10" f^-cm sensitivity is plotted

along the abscissa. The spread of data is approximately the same for the

two cases.

It is clear, based on the results of Figure 2.3-2 and Figure 2.3-3,

that the change in critical current with sensitivity is inversely related

to the heat flux. This is true even when only a small fraction of

the transport current is flowing through the copper stabilizer. In order

to verify that the critical current at all measuring sensitivities is dependent on the amount of copper stabilizer and the size of the conductor,

the samples in Group 2 were tested. These samples have identical amounts

of superconductor and cold work reduction. The amount of copper and the

wetted surface area are the only variables. In Table 2.3-1 the critical

currents of the samples are listed for various magnetic fields, evaluation

criteria, and sensitivities. From these results it can be seen that the

critical current increases as the copper-to-superconductor ratio increases.

In other words, the amount of copper and the amount of cooling are important

influences on the critical current. For the criteria used, the critical

i

current is not a function only of the amount of superconductor.

160
Decrease

in

Critical

Current

from

10~°fi-cm

to

10"^^i^-cm

Sensitivity

100 r

-8 2

Heat Flux at 10’ s^-cm Sensitivity (W/cm \

Fig. 2.3-3 Variation in Critical Current Change as a Function of

Heat Flux. Results obtained using Equivalent Resistivity

Criterion.

FA 5228

161
1

TABLE 2.3-1 CRITICAL CURRENTS OF GROUP 2 SAMPLES

Sample

Number Cu/SC Sensi tivity

Critica

(/>

1 Curren

imps)

t

7T 9T lOT 10. 5T

Cl 1.25 lOOyv/cm 33.2 16.6 7.9 4.4

. lyv/cm 31.2 14.7 5.6 2.1

10 ^fi-cm 33.4 16.8 8.3 4.4

10-llfi-cm 31.6 15.4 5.7 2.0

C2 3.06 lOOyv/ cm 36.2 18.9 10.4 6.2

. lyv/cm 32.0 15,0 6.1 2.5

10~®fi-cm 36.4 18.0 10.0 5.2

10“llj2-cm 33.0 14.0 6.1 2.0

C3 4.90 lOOyv/cm 36.6 19.9 12.2 4.2

. lyv/cm 32.0 15.2 6.8 2.7

10~^S7-cm 37.5 19.9 11.0 3.9

10"lln-cm 33.6 15.2 6.6 2.4

162
In Figure 2.3-3 only the change in critical current between 10 ^ ^2-cm

and 10 J^-cm is plotted. In Figure 2.3-4 the critical currents at intermediate sensitivities are shown for a sample with a wire diameter of 0.041 cm

and a copper-to-superconductor ratio of 1.25. For comparison the critical

current measured at 10 ^ V/cm and 10 ^ V/cm is also presented. It can be

seen that at 7 tesla and at 9 tesla the critical current is almost constant

between 10 f^-cm and 10 S7-cm sensitivity. Reductions in critical current

begin to become significant only at 10”^^ fi-cm. For many applications (e.g.,

most epoxy-filled intrinsically stable magnets) it is not necessary to know

the critical current at the high sensitivities. On the other hand, for some

magnets, such as for NMR applications where low level losses become important,

the critical current must generally be known at 10~^^ J7-cm to 10~^^ ^-cm

sensitivity. To a certain extent it is possible to extrapolate short sample

curves like these in Figure 2.3-4. However, particularly at the higher

fields the variation in critical current is very rapid as a function of

sensitivity, and it would be difficult to obtain a reliable extrapolation.

On the other hand, because of difficulties in measuring voltages lower

than 0.1 yV it is not practical to increase the sensitivity of the measurement

when testing very short samples. The best solution would be to use a sample

holder consisting of a small spool of noninductively wound wire. For example, with a measuring sensitivity of 1 yV one can detect a signal of 1 nV/cm

across a 10 meter long sample. While such a sample holder is not convenient

for a typical short sample test it would be extremely useful for certain

applications where high measuring sensitivity is required.

An important consideration in measuring critical currents is the consistency of measurements made with different sample holders. In order to

163
Resistivity

(fi-cm)

Fig. 2.3-4 Critical Current as a Function of

Measurement Criterion

FA 5207

164
study this effect two approaches were used: (1) samples were tested using

three different sample holders available at MCA, and (2) three round-robin

samples supplied by NBS were tested. The three sample holders have been

described in Section 2,2. The two most significant differences among

the sample holders are the sample geometries and lengths. Sample

shapes are straight, U-shaped, and noninductively wound spiral. Sample

lengths vary from 3.5 cm to 1 meter. The straight sample holder

and the noninductive sample holders were designed for use below lOOA. For

the noninductive sample holder the voltage drop across the current leads

limits the current to 100 amps when used with a 10 volt power supply.

Although larger currents can be passed through the straight sample holder

the results above lOOA tend to be unreliable. Therefore, in order to make

a good comparison among the various sample holders, critical currents were

generally limited to lOOA or less. Since the U-shaped sample holder is

designed for use in a magnet with a maximum central field of 7 tesla, the

comparison measurements were made at low fields only. In general, the

agreement in critical currents as measured in the three sample holders was

quite good. Typical results are presented in Table 2.3-2. The maximum

variation between any two measurements is 1 %. Similar tests made with only

the U-shaped and straight sample holders at higher fields yielded similar

results

.

It was possible to make a partial comparison of sample holder performance with one of the round-robin samples. In Figure 2.3-5 and Table 2.3-3

the short sample performance of the multifilamentary NbTi sample is presented.

At 9 tesla the noninductive and straight sample results varied by 7% from one

another. Although it was possible to obtain results from the straight sample

holder at currents above lOOA, they were not expected to be reliable. In the

figure the large difference between the U-shaped and straight samples can be seen.

165
TABLE 2.3-2 CONDUCTOR PERFORMANCE AS A FUNCTION

OF SAMPLE HOLDER

Critical Currents @7 Tesla, 4.2K Measured At

Imv/cm Sensitivity

Sample Description Cr itical Curren t (Amps)

Wire Diameter

(cm) Cu/SC

U-Shaped

Sample

Straight

Sampl e Non-InductiveSampl e

.0508 3.0 54 55 55

.0508

j 1.6 104 99.5 --

.041 1.25 54 50.4 52.5

166
Critical

Current

at1

mV/cm

(Amps)

01234567&9

Magnetic Field (tesla)

Fig. 2.3-5 Short Samole Performance of Round Robin NbTi

FA 5229

167
All of the samples in Groups 1 and 2 were round. In Group 3 two of

the samples are rectangular. Consequently the mounting orientation of

those samples is an additional parameter in the round-robin measurements.

For the NbTi sample the aspect ratio is 1.28. However, even for such a

low aspect ratio there is a 5% to 6% difference in critical current between

the two measurements. It is extremely important, therefore, that the orientation of samples be reported for all rectangular short sample measurements.

A list of the critical currents of the NbTi sample for various sensitivities

and sample holders is presented in Table 2.3-3.

Sample 2 in the round-robin series is a Nb^Sn tape. Again, the orientation of the sample is important. For fields up to 7 tesla, measurements

were made using the U-shaped sample holder. When mounted in that sample

holder the wide face of the tape is perpendicular to the field in the region

in which the conductor voltage is measured. At fields above 7 tesla the

straight sample holder is used, and the face of the tape is parallel to the

magnetic field. In Figure 2.3-6 the short sample results measured at 1 mV/cm

are shown. It can again be seen that at currents above 100 amps the straight

sample holder is unreliable. In the case of this sample at 8 tesla the

current may be underestimated because of current transfer problems as well

as because of joule heating at the contact points. A complete listing of

short sample performance of the Nb^Sn tape is given in Table 2.3-4.

The final round-robin sample was multifilamentary Nb^Sn. Because the

sample was heat treated in a straight length it could be tested only in the

straight sample holder. Critical currents are shown in Figure 2.3-7 for fields

from 8 tesla to 12 tesla at 1 mV/cm sensitivity. The critical currents at

168
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iq. 2.3-6 Short Sample Performance of Round

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170
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171

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Robin Multifilamentary Nb^Sn

FA 5231

172
other sensitivities are listed in Table 2.3-5. It can be seen from that

table that the decrease in critical current with increasing measuring

sensitivity is greater for this sample than it is for the NbTi samples

discussed earlier in this section. For example, at 10 tesla and 10~^ fi-cm

resistivity the heat flux of a 0.7 mm conductor is 0.075 W/cm^ for a current

of 80 amps. Based on the results in Figure 2.3-3 for NbTi, the decrease in

critical current from 10 ^ J^-cm to 10 fi-cm sensitivity is between 8% and 18%.

However, for the Nb^Sn sample the decrease in critical current when

the sensitivity is increased from 10"^ ^^-cm to 10"^^ ^^-cm is 32%. It thus

appears that the curves generated for NbTi are not applicable to Nb^Sn.

It would be useful if attempts were made to develop similar curves for Nb^Sn.

3. Current Transfer Measurements

The second task of this program was to study current transfer between

the sample holder and the test conductor. The importance of this task is

apparent from some of the measurements reported in the previous section.

The straight sample holder was designed to use very short samples at low currents.

When currents greater than 100 amps were put through a sample, the critical

current measurements were frequently underestimated. This was undoubtedly due

to joule heating at the current contacts and current transfer problems.

Within the scope of this program the important questions in studying

current transfer are: (1) what length of conductor is necessary to give

reliable data, and (2) what are the requirements of the current contacts on

a sample holder?

3.1 Description of Samples

Six samples were tested in this program phase. A description of the

conductors are given in Table 3.1-1. With the exception of the cabled conductor and the .081 cm x .163 cm conductor, all the samples were capable

173
CRITICAL

CURRENT

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SAMPLE

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(MULTIFILAMENTARY

Nb^Sn)

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174

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TABLE 3.1-1 CURRENT TRANSFER SAMPLES

Dimensions Cu/SC

Number of

Fil aments

Twist Pitch

(cm)

.157 cm X .315 cm 5 672 2.5

.210 cm diameter 1.25 361 2.5

.318 cm X .210 cm 1.8 180 2.5

. 183 cm X . 183 cm 2.6 132 2.5

.081 cm X . 163 cm 5 672 2.5

7 Strand Cable

.035 cm dia. strand * 54/strand 0.5

*CuNi matrix. CuNi/SC = 2.5

175
of carrying currents of at least 1,000A. Those monolithic samples had

copper-to-superconductor ratios ranging from 1.25 to 5. The cabled

conductor was composed of seven strands. It was chosen for these tests

because the matrix was made of CuNi instead of copper. Previously published

experimental results^ have indicated that current transfer lengths in copperstabilized NbTi are extremely small and difficult to detect. The CuNi matrix

material would be expected to have a much larger current transfer length

than a similar conductor with copper. In fact, current transfer problems

in some other CuNi matrix superconductors at MCA have been solved only by

soldering high purity copper to the test conductor.

3.2 Description of Equipment

Two sample holders were used for these tests. One was the U-shaped

sample holder described in Section 2.2. The other was a U-shaped sample

holder used specifically for high current samples. The sample holder has

been used to measure critical currents up to 5,000A. The sample length

is approximately 45 cm long. The ends of the samples are soldered into

13 cm long OFHC channels which are soldered to 1.27 cm diameter OFHC copper

rods. The rods are connected to vapor-cooled leads. The advantage of

soldering the sample into a channel instead of directly to the copper rod

is that the extra copper cross section and cooling surface of the channel

aids in the current transfer. The sample holder is designed to fit into

the bore of a 7.6 cm diameter superconducting magnet. The sample is held

in place with stainless steel ties, vacuum grease, and a two-piece phenolic

jacket that fits around the sample. Each sample holder was fitted with five

pairs of voltage taps to be attached to the sample. Two or three pairs of

voltage taps were attached to the section of the conductor in contact with

^See, for example, J.W. Ekin and A.F. Clark, "Current Transfer in

Multifilamentary Superconductors. 1 1. Experimental Results",

J. Appl . Phys. Vol 49, p 3410 (1978).

176
the sample holder. The remaining leads were distributed along the test

portion of the short sample. The voltage signals were detected with a nanovoltmeter and X-Y recorder. Two power supplies were available for use

in testing. One was a 10,000A 10-volt Saban power supply, and the other

was a 500A 10-volt Electronic Measurements supply.

3.3 Results and Analysis

Current transfer measurements were performed on the six samples

previously described. Because’of the low copper-to-superconductor ratio

of most of the samples and because of the high matrix resistance of the

cabled sample, the test currents were kept below the quench values in

order to eliminate sample burnout. In addition, because of excessive noise

pickup in the nanovoltmeter from the 10,000A supply it was decided that the

maximum sensitivity would be achieved through the use of the 500A supply.

The accuracy of the experiment was not hampered in any way by the limitation

in current since flux flow resistivity predominates over the current

transfer effects near the critical current. In general, there was

no detectable signal along the test length (the length between the

current contacts) of any of the NbTi samples mounted as described in the

previous section. It was possible to measure resistivities to 10'^^ ^2-cm

-12 or 10 J^-cm. In every case a pair of voltage taps was positioned one

centimeter apart and directly adjacent to the current contacts. This was

the case for samples mounted in either sample holder. Signals were, however,

occasionally detectable along the current contact regions. For example,

when the .152 cm x .315 cm sample was mounted in the high current

sample holder there was an equivalent resistivity of 3.2 x 10 S7-cm in

the first centimeter of conductor adjacent to the current contacts. In the

-1

2

next 12 cm the average resistivity was 8.0 x 10 $^-cm, and in the last

-1

2

centimeter of contact the resistivity dropped to approximately 1.6 x 10 fi-cm.

177
In order to estimate the effect of the sample holder on the measurements the same sample was remounted on the sample holder without the copper

channels. The sample was soldered directly to the 1.27 cm diameter copper

rods. The result was that the removal of some copper greatly increased the

current transfer effects. In the first centimeter of the contact area the

-10

resistivity was 1.9 x 10 fi-cm, and at the end of the contact area the

resistivity is 5 x 10"^^ fi-cm. In Figure 3.3-1 a comparison is made of the

current transfer resistivity along the sample with and without the copper

channel. It can be seen that at all points along the conductor for which

a voltage was detectable the current transfer resistivity is approximately

an order of magnitude higher for the case in which the copper channel was

removed from the sample holder. The results shown in Figure 3.3-1 were

obtained in an external magnetic field of 5 tesla. The measurements obtained at 3 tesla and at 7 tesla were identical within the experimental

uncertainty.

The one conductor that is not copper stabilized is the seven strand

cable with a CuNi matrix. Each cable strand has a diameter of .035 cm.

The critical current of each strand is 42 amps at 3 tesla. If such a small

conductor were copper stabilized one would not expect to detect current

transfer resistance. Any effects are due to the high resistance matrix.

The sample was mounted in the lower current U-shaped sample holder. The

results which are again independent of external field are shown in Figure

3.3-2. It can be seen that the current transfer region extends past the end

of the current contacts and is still measurable in the middle of the sample.

It is clear that the short sample characteristics of this sample cannot be

measured accurately with this sample holder and mounting procedure. In the

past it has proven very effective to solder a copper strip to the conductor

to shorten the current transfer region in CuNi matrix conductors.

178
Resistivity

(f2-cm)

Fig. 3.3-1 Current Transfer Measurements. Effect of Removing

Some Copper from Current Contacts

FA 5260

179
Resistivity

(fl-cm)

Fig. 3.3-2 Current Transfer into CuNi -Matrix Cable

I

I FA 5259

180
4. Conclusions and Recommendations

It was originally hoped that on the basis of this program a single

measuring procedure and sample holder could be recommended for adoption

as a test standard. After the completion of this work it becomes clear

that no single procedure or test apparatus is suited for all types of

samples. The sample holder and measurement standard that are most suited

for a conductor such as that used for the Fermilab Doubler Magnets is not

necessarily practical for measuring the critical currents of a high resistivity matrix superconductor or of a conductor requiring very low losses.

For many applications such as intrinsically stable magnets not run

in a persistent mode the quench current is a satisfactory measurement of

the critical current. These measurements are easy to perform with a minimum

of instrumentation. Many different configurations of sample holder can be

used. The samples can be mounted very quickly and multiple sample test

fixtures are very practical. It is also straightforward to estimate the

critical current at a higher sensitivity if that should be of interest.

Although it would be worthwhile to have a standard established for this type

of measurement, that standard need not be very rigorous. An uncertainty in

measurement of at least 5% should be acceptable for this type of test.

On the other hand, if the same conductor is to be used in a coil

with a persistent switch and if the magnet decay rate is extremely low, then

it is essential to define the critical current at a very low resistivity

or electric field. Depending upon the details of the magnet, critical

-12 -14

currents might need to be defined in the 10 S7-cm to 10 F2-cm range.

In order to measure such low values it is necessary to use a very long

sample. For example, a small, noninductively wound coil with up to 10 meters

of test conductor might be needed. Because of the extra equipment (e.g..

181
a microvoltmeter or nanovoltmeter) that is needed for the measurement, and

because the mounting and the testing of the samples will be slower than

those of a quench measurement, it is recommended that this type of measurement be made only when high sensitivity results are needed. It should not

be adopted as the standard for routine measurements.

Sample holders must be designed to assure that all the current has

transferred into the sample, outside of the region in which the test signals

are detected. Although it was observed that current transfer can be improved

by soldering additional copper to the sample for testing, this is not as

satisfactory a solution as having a test holder with a very long current

transfer region. This is due to the fact that the amount of copper in a

conductor can affect its critical current. It is possible to design a sample

holder with a sufficiently large sample contact area to ensure reliable measurements, The improvement in current transfer measurements has been

noticed when extra copper was added to the current contact areas.

Basec on all of these measurements it seems clear that two or three

types of sample holders are needed in order to test all types of conductors.

A similar number of measuring standards are needed as well. It is hoped that

the results of this program will contribute to the development of those

standards

.

182
ACKNOWLEDGMENTS

Most of the high field critical current measurements were made by

the authors at the Francis Bitter National Magnet Laboratory at Massachusetts Institute of Technology. We would like to thank the Magnet Laboratory

staff for their assistance in our effort.

We would like to thank Joseph Pileeki, Sileshi Woldemariam, and Rene

Chouinard for help in performing short sample tests.

We would also like to acknowledge many helpful discussions with Dr.

F. R. Fickett at the National Bureau of Standards, Boulder, Colorado.

4

183
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Supercon, Inc.

9 Erie Drive

Natick MA 01760

185
Introduction

Towards the effort by the National Bureau of Standards to

standardize measurement practices for practical superconductors,

Supercon, Inc. has accomplished the following:

1. A determination of the variations in critical current,

I^j from composite superconducting wire that is similarly processed.

2. A determination of the relative stabilities of superconducting wires.

3. A determination of the effect of filament uniformity

on the I^ and stability of superconducting wire.

4. Participation in NBS and ASTM on-going activities.

1 Powell and Clark provide a workable definition of critical

current as the "electrical current below which an ideal superconductor may exist in the superconducting state at a specified temperature, magnetic field strength, and other specified external conditions".

The four terminal electrical resistance method generates a current

versus voltage function which can be interpreted in a variety of ways

to determine the value of the critical current. The most common

criteria are based on voltage, power or resistivity; these are also

2

described oy Powell and Clark .

186
Experimental Work

Testing by the four terminal electrical resistance method

is fairly straightforward. Minimum component requirements are a

DC power supply with variable output and a known volts/amp outlet

for monitoring; a calibrated electromagnet capable of accepting a

sample and its cryogenic envelope through its bore; a recording

device capable of plotting current versus resulting voltage.

Standard practice includes the calibration of the recording device

with a voltmeter, and a test run using a sample of known critical

current.

Many test configurations are currently in use for superconducting wire. The easiest tests, and those requiring the least

amount of superconductor, are the straight sample and hairpin tests.

We have found these tests most useful in surveying large numbers of

samples, comparing samples of a broad range experiment to narrow the

field of variables, and the testing of A15 and other brittle superconductors requiring reaction in the geometrical form of the test to

reduce strain of handling. Hairpin and straight samples lend themselves particularly well to the design of multiple sample probes;

see Figure 1.

Longer samples of wire are usually bifilar wound to cancel

out the self field of the sample and inductance from the magnet. The

samples are either wound as a solenoid or a pancake, the solenoid being
preferred for round wire and any test in a small bored magnet, and

the pancake for conductors that are either very bulky or have a

high aspect ratio, and in facilities where very large bored magnets

are available. See Figure 2,

A number of production variables affect the correlation

between short (< 10 cm) and long (>1 M) sample test results. We use

this difference and consider it along with the value of the critical

current. The amount of degradation from a short to a long sample

corresponds to relative filament integrity, most useful in the

examination of multifilamentary wire for assessment of the severity

of its processing. This kind of evaluation is based primarily on

engineering experience and would be difficult to quantify. In general,

short samples are for screening, either for production uniformity or

production variable testing, and long samples are used to better

project end use performance.

There are prevailing conditions at the Francis Bitter National

Magnet Laboratory which limit the precision of data collection. This

is a large facility with water cooled copper magnets capable of serving

up to four experiments simultaneously. Some magnet noise is always

picked up by the voltage taps, but noise can increase substantially with

the field changes of other investigators, A six pole bessle filter on

the voltage taps is used to reduce the low frequency noise which, on a

188
bad day can amount to as much as 200 u V, but on a good day may be

less than 10 u v. Considering these limitations, we have confidence

in measurements of voltage changes greater than 20 u V and interpret

our data accordingly. Practical sample sizes, equipment precision,

and power supply noise also limit the sensitivity of the I-V plots.

-9

A voltage of 100 u V is an ef-fective resistivity of 2 x 10

(ohm cm) for a .5mm diameter short sample carrying 100 amps. A three

meter sample of the same material will have an effective resistivity

f “12

or b X iU (ohm cm). We have chosen 10 (ohm cm) resistance as

the criterion for critical current for these long samples and 10

(ohm/cm) the criterion for the short samples.

•8

Many factors influence the current carrying capacity of a

superconductor. The amount of superconductor, the number, size,

and shape of the filaments, the reduction schedule and heat treatments,

and the chemical composition of the alloy. This last variable is

controlled by the manufacturer's specification to the producer; if

the specifications are too tight, the cost is increased. The chemistry

of the superconductor, therefore, varies from lot to lot. We have

received more than one billet from a lot and in surveying a large

amount of Iq data have found that current density measurements from

the billets of one lot vary consistently with those of billets from

a different lot. See Figure 3. The effect of specific elements is

beyond the scope of this study.

189
With any composite extrusion there are areas of nonuniformity at the nose and tail of the resulting bar due to "end

effects". With single core composites of copper around niobium

titanium, the superconductor can take on a "dog-bone" shape which,

if drawn to wire, will have varying ratios of copper to superconductor,

see Figure 4. A judicious cropping of the extruded rod eliminates

gross irregularities, but slight variations along the length of the

wire will remain. Two simple methods for determining ratio of

copper to superconductor are: measure the diameter before and after

a nitric acid etch and take a ratio of the areas, or weigh a length

of composite wire before and after etching and calculate the ratio

while factoring in the difference in densities.

Short samples from six consecutive pieces of Cu-NbTi wire

approxinately 30,000 ft long were tested for critical current and

subsequently weighed and etched to find the volume percent of superconductor in each. The results are plotted in Figure 5; the relation

is linear, as would be expected.

A survey of I-H tests from 26 billets processed similarly

shows the variations from billet to billet due to differences in

chemistry as explained above, minor changes in ratio, and improvements

in quality control. See Figure 6.

190
There are as many definitions of the stability of a superconductor as there are uses for them. Most of them depend considerably

on design parameters of the device such as electrical, thermal, and

magnetic insulation, and fluid dynamics, which cannot be controlled

by the wire manufacturer. But there is a need to be able to compare

wires and therefore to define relative stability.

In the current versus voltage curve of a multifilamentary

wire, there is a region of current sharing. This means not all of

the current is passing through a superconductor. The onset of this

phenomena is defined as the critical current; the voltage will rise

as more current is passed through the wire until the voltage "takes

off" and displays resistance comparable to a normal conductor. The

detectable voltage found in this current sharing region can be useful

in monitoring the performance of a device as a warning signal that

the conductor is nearing its limit.

Some ways of comparing wire have been suggested: reporting

-12 _ii

currents at two resistance levels, i.e., 10 ohm cm and 10 ohm cm,

-7 -6 or two voltage levels, 10 and 10 V/cm. For this study, a similar

approach was taken. The definition combines two previously defined parts

3

of the I-V curve , 1^, (as defined by the resistivity criterion of

10“^^ ohm cm) and the (the "take off" current), by finding their

difference as a ratio to the critical current, The result

could be reported with the critical current as a per cent current

sharing margin, and as such could be compared with similar conductors.

191
This analysis was done for some multifilamentary superconducting wires of varying copper to superconductor ratios and

number of filaments. The results can be found in Table 1. It

should be noted that the conductors have different current densities due to difference in reduction schedules and heat treatments;

an attempt to keep all parameters constant would be very time

consuming and expensive.

The per cent current sharing margin increases with increasing

copper content (see Figure 7), with increasing numbers of filaments

(see Figure 8), and with decreasing filament size (see Figure 9).

This is as would be expected, for all of these functions either

increase the surface area of the filaments or the amount of copper

around them, both of which improve the heat transfer characteristics

of the composite. All results are from tests at 8 Tesla.

The method of comparing the current sharing characteristics

just described is easily adapted to normal I-H testing procedures.

The reproducibility of the result is limited by that of the take-off

current measurement.

In the extrusion of a multifilamentary composite just as

with a monofilament composite, there are regions of non-uniform crosssection. In multifilament wire, many more types of non-uniformity

are possible. Examples of non-uniform filament patterns are: out of

192
round filaments, over-sized center filaments, (typical of the nose

of an extrusion), and undersized center filaments (typical of the

tail of an extrusion).

Six non-uniform wires were processed and tested for critical

current and per cent current sharing, and were weighed and etched to

determine copper content, see Table 2. Their cross sections were

examined and are found in Figure 10. Since all samples were processed

identically, comparison of their current densities is important to

distinguish differences due to changes in the ratio of copper to

superconductor from any effects of non-uniformity. None of the

mildly distorted wire produced significant changes in the current

density; their differences in critical current are proportional to

their differences in superconductor content. A slight difference

can be seen in the current density of the highly distorted sample.

Number 6. The per cent current sharing margin is not affected.
References

1. R. L. Powell and A. F. Clark; "Definitions of terms for

practical superconductors 2, Critical parameters".

Cryogenics 19 3 (1979) p 140,

2. ibid.

3. D. T. Read, J. W. Ekin, R. L. Powell, and A. F. Clark;

"Definitions of terms for practical superconductors 3.

Fabrication, stabilization, and transient losses";

Cryogenics 19 j6 (1979) pp 327-332,

194
List of Figures

Figure 1 Short sample multi pie test probe

Figure 2 Long sample test probes

Figure 3 vs per cent superconductor for different lots

Figure 4 Typical composite extrusion shape

Figure 5 vs per cent superconductor for six consecutive lengths

Figure 6 vs billet at two fields

Figure 7 Per cent current sharing vs copper content

Figure 8 Per cent current sharing vs number of filaments

Figure 9 Per cent current sharing vs filament size

Figure 10 Non-uniform cross sections of 54 filament wire

List of Tables

Table 1 Current sharing of multifilament wire

Table 2 Current capacity of non-uniform wires

195
Table 1

(Mils)

I.D. No.

Volume 7o S. C.No. of Size of

Filaments Filaments

7/o Current Sharing

Margin at 8 T.

2770 51.5 517 1-0 2

2791 37.4 54 1.0 12

2620 26.7 54 1.0 33

2260 42.0 294 1.0 24

2720 28.8 48 4.8 19

2792 34.6 54 1.6 11

2793 34.9 54 1.2 11

2794 35.5 54 1.9 10

2795 35.4 54 2.4 5

Table 2

Volume 7o Current Density/7o Current Sharing Margin

I.D. No. S.C. 9T 8T 7T

2951 36.3 557 5 856 5 1182 2

2952 36.3 533 4 911 3 1223 2

2953 38.2 542 7 788 10 1098 5

2954 40.8 520 7 786 6 1052 3

2955 41.5 535 11 856 4 1106 5

2956 36.4 488 6 759 2 1030 3

196
figure 1

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197
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199
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VI. REFERENCES

[1 ] F. R. Fickett and A. F. Clark, "Development of Standards for Superconductors, Annual Report FY 79," NBSIR 80-1629 {December 1979).

[2] F. R. Fickett, S. B. Kaplan, R. L. Powell, R. Radebaugh, and A. F. Clark,

"Definitions of Terms for Practical Superconductors: 4. Josephson

Phenomena," Cryogenics^, 31 9-325 (1 980).

[3] M. N. Wilson, Rutherford Lab. Report SMR/1 , Chilton, Oxfordshire, England,

1 977 (unpublished).

[4] J. W. Ekin, "Critical Transfer in Multifilamentary Superconductors.

I. Theory," J. Appl . Phys. 49, 3406-3409 (1978).

[5] L. Dresner, "Distribution of Current Among the Filaments of a Multifilamentary Superconductor Close to the Input Leads," Cryogenics 1_8, 285-288

(1 978).

[6] J. W. Ekin, A. F. Clark, and J. C. Ho, "Current Transfer in Multifilamentary Superconductors. II. Experimental Results," J. Appl. Phys. 4^,

341 0-3412 (1 978).

[7] L. F. Goodrich and J. W. Ekin, "Lap Joint Resistance and Intrinsic Critical

Current Measurements on a NbTi Superconducting Wire," Proc. 1980 Applied

Superconductivity Conference, IEEE Trans, on Mag. (to be published).

[8] G. Fujii, J. W. Ekin, R. Radebaugh, and A. F. Clark, "Effect of Thermal

Contraction of Sample Holder Material on Critical Current," Adv. in

Cryog. Eng. Plenum Press, New York (1980) p. 589.

203
APPENDIX A

PUBLICATIONS AND PRESENTATIONS

Major publications and presentations resulting from the research performed under this program during FY 80 are listed here. Copies are available

from NBS.

F. R. Fickett, S. B. Kaplan, R. L. Powell, R. Radebaugh, and A. F. Clark,

"Definitions of Terms for Practical Superconductors: 4. Josephson

Phenomena," Cryogenics^, 31 9-325 (1 980).

F. R. Fickett and A. F. Clark, "Development of Standards for Superconductors," Proc. 8th Int. Cryo. Eng. Conf. (ICEC8), IPC Science and Technology

Press (1980) pp. 494-498.

L. F. Goodrich and J. W. Ekin, "Lap Joint Resistance and Intrinsic

Critical Current Measurements on a NbTi Superconducting Wire," Proc. 1980

Applied Superconductivity Conference, IEEE Trans. Mag. (to be published).

G. Fujii, "Present Practices in Japan for the Measurement and Definition

of Various Superconducting Parameters," Tech. Report of ISSP, Ser. A, No.

1 063 (July 1980).

G. Fujii, J, W. Ekin, R. Radebaugh, and A. F. Clark, "Effect of Thermal

Contraction of Sample-Holder Material on Critical Current," Adv. Cryo.

Eng. Plenum Press, New York (1980) p. 589.

A-1
R. Radebaugh, G. Fujii, D. T. Read, and A. F. Clark, "A Standards Program

for AC Losses in Superconductors," Proc. XVth International Congress of

Refrigeration (1980).

H. R. Segal, Z. J. J. Stekley, and T. A. DeWinter, "Development of Critical

Current Measurement Standards," Proc. 1980 Applied Superconductivity

Conference, IEEE Trans. Mag. (to be published).

F. R. Fickett and A. F. Clark, "Standards for Superconductors," Proc.

1979 Mech. and Mag. Energy Storage Contractors' Review Meeting, Conf790854 (December 1 979).

F. R. Fickett and L. F. Goodrich, "NBS Superconductor Standardization

Program," Proc. 7th Int. Conf. on MHD Electrical Power Generation (June

1980) (to be published).

G. Fujii, M. A. Ranney, and A. F. Clark, "Thermal Expansion of Nb^Sn and

V^Ga Multifilamentary Superconducting Cables, Fiberglass-epoxy and

Cotton-phenolic Composite Materials," Jap. J. Appl . Phys. (to be published).

G. Fujii and J. W. Ekin, "Effect of Compressive Strain on the Critical

Current of Mul ti fil amentary Nb^Sn and V^Ga," (in preparation).
APPENDIX B

STAFF AND CONTACTS

A significant amount of the work on this program was done under subcontract to NBS. We list here both the NBS staff and the technical contacts for

the various contractors.

National Bureau of Standards* Electromagnetic Technology Division,

Boulder, CO 80303. Ph. (303) 497+EXT, FTS 320+EXT

F. R. Fickett (PI) x3785

A. F. Clark (PI) X3253

L. F. Goodrich x3143

Airco Superconductors, 600 Milik Street, Carteret, NJ 07008. Ph. (201)

541-1300.

P. Sanger

C. Rosen

Intermagnetics General Corporation, P. 0. Box 566, Guilderland, NY 12084.

Ph. (518) 456-5456.

R. Schwall

R. McCown

Magnetic Corporation of America, 179 Bear Hill Road, Waltham, MA 02154.

Ph. (617) 890-4242.

H. Segal

B. Strauss

Supercon Inc., 9 Erie Drive, Natick, MA 01760. Ph. (617) 655-0500.

W. Larson

K. Stohlman

B-1
APPENDIX C

MINUTES

ASTM SUBCOMMITTEE B01.08 ON SUPERCONDUCTORS

Held October 2-3, 1980

La Posada Inn, Santa Fe, New Mexico

(In conjunction with the 1980 Applied Superconductivity Conference)

SUMMARY

The meeting was called to order at 5:00 pm October 2, 1980 by the chairman,

A1 Clark, who outlined the tasks to be accomplished at the meeting to the 33

attendees (list attached). These were: 1) a presentation and discussion of

the results of a survey of test methods and a round robin test of superconductor critical current, 2) presentation of draft standards for definitions and

three critical current tests, and 3) the majority of the time to be spent by

the task groups modifiying the draft standards into working standards to be

submitted to the subcommittee for approval. All the tasks were accomplished

with the exception that the critical current test standard needs further modification as directed by the subcommittee. The subcommittee also strongly

recommended that a standard reference material for superconductor tests be

generated and that work begin Immediately on the problems of ac loss measurements in superconductors.

SURVEY AND ROUND ROBIN RESULTS

The results of a mail survey of test methods and specifications and of a series

of round robin tests were presented by Fred Fickett of NBS. The survey

indicated that more understanding is needed of transfer voltage, stress, and

power supply effects on critical current measurements and that it is necessary

to specify sample mounting techniques and to develop accurate magnetic field

measurement. In general, specific values for various criteria, sensitivity

limits, and most other aspects of the measurement were not agreed upon. The

survey served well as the basis for the draft standards preparation.

The round robin tests were performed by the four superconducting wire manufacturers on identical sets of three different conductors: a NbTi multifilamentary wire, a Nb3 Sn multifilamentary wire, and a Nb3 Sn tape. A "critical

current" value at several magnetic fields was requested, but no other instructions were provided. Variations on the order of 30% were found for all materials with no consistency. The subcommittee felt this was cause enough to proceed with vigor!

For information Fred Fickett also presented a list of 16 areas in which

research has been done by the wire manufacturers and the National Bureau of

Standards (sponsored principally by the Department of Energy) on parameters

that can effect a critical current measurement. This information was used as a resource by the task groups in development of the draft standards.

C-1
PRESENTATION OF DRAFT STANDARDS

A draft set of definitions of terms related to standards for practical superconductors was presented by Steve St. Lorant who had created the draft based

upon four articles published by NBS in Cryogenics , the Compilation of ASTM

Standard Definitions, and his own input and that from several of his colleagues. The subcommittee decided that these definitions should only include

terms usable in the critical current standard with others to be added as needed

.

Three separate draft standards for critical current were presented by Bob

Schwall, Bill Fietz, and Loren Goodrich. The subcommittee decided to combine

the measurement standards for the various geometries (e.g. straight, hair-pin,

and coil) into one test with three variations and use the most generic of the

drafts as a basis for discussion and modification.

The meeting was adjourned at 10:00 pm to reconvene at 8:30 am on October 3,

1980 to work in task groups on the drafts and incorporate the modifications

from the evenings discussions.

TASK GROUP MODIFICATIONS

The two task groups met the following morning, the one on definitions chaired

by Steve St. Lorant and the one on critical current chaired by Bob Schwall.

The set of definitions was cut and edited, added to and clarified until a workable set of definitions was agreed to by the task group. These will be retyped

and submitted to the subcommittee for approval by mail.

The task group on critical current measurements was faced with an almost impossible job of going through the more than 50 detailed parts of the draft standard, but did remarkably well. Those areas where consensus was not achieved in

short order were left to be resolved later. These were assigned to the NBS

staff for further evaluation. The next version of the draft standard is to be

circulated by mail for comment in late October. A discussion of the open

questions will accompany the draft as will comments relating to specific

objections

.

After a joint discussion of the results the meeting adjourned about 11:30 am.

C-2

J
A1 Clark

Electromagnetic Technology Div.

National Bureau of Standards

Boulder, CO 80303

Bob Wolf

CERN

Geneva, Switzerland

K. J. Best

Vacuums chmelze GMBH

Postfach 109

D-6450 Hanau 1 West Germany

J. D. Thompson

Los Alamos Scientific Lab.

P-10, MS-764

Los Alamos, NM 87545

Harvey Segal

Magnetic Corporation of America

179 Bear Hill Road

Waltham, MA 02154

Kate Stohlman

Supercon, Inc.

9 Erie Drive

Natick, MA 01760

M. J. Superczynski

Naval Ship R&D Center

Annapolis, MD 21402

Don Waltman

Naval Ship R&D Center

Annapolis, MD 21402

F. McDonald

Naval Ship R&D Center

Annapolis, MD 21402

B. Zeitlin

Intermagnetic General Corp.

P. 0. Box 566

Guilderland, NY 12084

L. F. Goodrich

Electromagnetic Technology Div.

National Bureau of Standards

Boulder, CO 80303

C. E. Oberly

Air Force AFAPL/POD-1

Wright-Patterson AFB, OH 45433

H. Riemersma

Westlnghouse Electric Corp.

Churchill Boro

Pittsburgh, PA 15235

Max Swerdlow

AFOSR/NE

Bldg. 410, Rm. C213

Bolling AFB

Washington, DC 20332

Jack Ekin

Electromagnetic Technology Div.

National Bureau of Standards

Boulder, CO 80303

Thomas Luhman

Brookhaven National Lab.

Upton, NY 11973

Don Beard

Office of Fusion Energy

Department of Energy

Washington, DC 20545

Bill Fletz

Oak Ridge National Lab.

P. 0. Box Y

Bldg. 9204-1, MS-14

Oak Ridge, TN 37830

Phil Sanger

Alrco Superconductors

600 Milik Street

Carteret, NJ 07008

Moyses Kuchnir

FERMILAB

P. 0. Box 500

Batavia, IL 60510

R. N. Randall

Supercon, Inc.

9 Erie Drive

Natick, MA 01760

C-3
Bruce Strauss

Magnetic Corporation of America

179 Bear Hill Road

Waltham, MA 02154

Bob Schwall

Intermagnetics General Corp.

P. 0. Box 566

Guilderland, NY 12084

Jim Ho

Physics Department

Wichita State University

Wichita, KS 67208

Steve St. Lorant

Stanford Linear Accelerator Center

P. 0. Box 4349

Stanford, CA 94305

Bill McDonald

Wah Chang Corporation

Albany, OR 97321

Dave Sutter

High Energy Physics

Department of Energy

Washington, DC 20545

Eric Gregory

Airco Superconductors

600 Milik Street

Carteret, NJ 07008

Meyer Garber

Brookhaven National Laboratory

Upton, NY 11973

Dave Larbalestier

University of Wisconsin

1500 Johnson Drive

Madison, WI 53706

K. Hemachalam

Magnetic Corporation of America

179 Bear Hill Road

Waltham, MA 02154

F. Fickett

Electromagnetic Technology Div.

National Bureau of Standards

Boulder, CO 80303

R. Boom

University of Wisconsin

1500 Johnson Drive

Madison, WI 53706

14 Users

11 Producers

8 Researchers

C-4
U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publication Date BIBLIOGRAPHIC DATA

REPORT NO.

December 1980 SHEET (See instructions) NBSIR 80-1642

4. TITLE AND SUBTITLE

Development of Standards for Superconductors

5. AUTHOR(S)

F. R« Flckett, L. F. Goodrich, and A. F, Clark

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s)

national bureau of STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bl iography or literature survey, mention it here)

Modern practical superconductors are complex materials and the determination of their critical parameters is a difficult task. Many approaches are possible for determining a given parameter and the results often depend on which

one is chosen. The goal of this program, a cooperative venture involving DoE,

NBS, and private industry, is to arrive at a set of useful voluntary standards

for measurements on modern practical superconductors that will be acceptable to

both manufacturers and users. Agreement on a set of standard definitions for

the commonly used terms is also necessary. This report describes the status of

the program at the end of the second year. The work in FY 80 has concentrated

nearly exclusively on the critical current standard. Experimental determinations

of the effect of various parameters on the measurement have been made by NBS and

by the wire manufacturers. Significant progress has been made in the preparation of the actual critical current measurement standard and the definition

standard. Draft copies of both are now ready for comment.

12. KEY WORDS fS/x to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Critical current; electrical property; magnetic property; stability; standards;

superconductor

13. AVAILABILITY

I X| Unlimited

I I For Official Distribution. Do Not Release to NTIS

I I Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO, OF

PRINTED PAGES

220

15. Price

$13,00

USCOMM-DC 6043-P80
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