LHC IR QUAD Magnet Inner and Outer Cable

Manufacturing Specification

1 SCOPE [2](#scope)

1.1 Cable definition [2](#cable-definition)

2 REFERENCE DOCUMENTS [2](#reference-documents)

3 REQUIREMENTS [2](#requirements)

3.1 Wire receiving and handling [2](#wire-receiving-and-handling)

3.1.1 Wire supplier responsibility [2](#wire-supplier-responsibility)

3.1.2 Cable vendor responsibility [3](#cable-vendor-responsibility)

3.2 Technical requirements for cable
[3](#technical-requirements-for-cable)

3.2.1 Mechanical properties [3](#mechanical-properties)

3.2.2 Electrical properties [3](#electrical-properties)

3.3 Processing [4](#processing)

3.3.1 Identification [4](#identification)

3.3.2 Cable Map [4](#cable-map)

3.3.3 Cable production lengths [4](#cable-production-lengths)

3.3.4 Strand Welds [5](#strand-welds)

3.3.5 Cable surface condition [5](#cable-surface-condition)

3.3.6 Crossover or broken strands [5](#crossover-or-broken-strands)

4 PREPARATION FOR DELIVERY [5](#preparation-for-delivery)

4.1 Reels/Spools [5](#reelsspools)

4.2 Spooling requirements [5](#spooling-requirements)

5 QUALITY ASSURANCE AND MANUFACTURING PLAN
[5](#quality-assurance-and-manufacturing-plan)

5.1 Quality Plan [5](#quality-plan)

5.2 Certificate of compliance [5](#certificate-of-compliance)

5.2.1 Nonconforming material [6](#nonconforming-material)

5.3 Shipping [6](#shipping)

5.4 Marking/Identification Requirement
[6](#markingidentification-requirement)

Appendix I Cable Critical Current Determination
[8](#appendix-i-cable-critical-current-determination)

I.1 Introduction [8](#i.1-introduction)

I.2 Definition of Critical Current
[8](#i.2-definition-of-critical-current)

I.3 Sample Mounting [8](#i.3-sample-mounting)

I.4 Electrical Instrumentation [9](#i.4-electrical-instrumentation)

I.5 Measurement Procedure [10](#i.5-measurement-procedure)

I.6 Temperature Calculation [10](#i.6-temperature-calculation)

I.7 Magnetic Field Correction [11](#i.7-magnetic-field-correction)

I.8 Critical Current of the Thin Edge:
[11](#i.8-critical-current-of-the-thin-edge)

Appendix II Cable R(293) and RRR Determination
[12](#appendix-ii-cable-r293-and-rrr-determination)

Appendix III Copper/Superconductor Ratio
[13](#appendix-iii-coppersuperconductor-ratio)

Appendix IV Sharp Bend Test [14](#appendix-iv-sharp-bend-test)

#   {#section .unnumbered}

# 1 SCOPE {#scope .unnumbered}

This specification establishes the requirements for the fabrication,
inspection, test, identification and delivery of superconducting NbTi
cables for Fermilab LHC IR quadrupole magnets.

## 1.1 Cable definition {#cable-definition .unnumbered}

The cable is composed of superconducting wires which are twisted around
a hollow core and pressed into a keystoned shape. Two types of cable are
required, one for the inner coils and one for the outer coils.

# 2 REFERENCE DOCUMENTS {#reference-documents .unnumbered}

The following documents form a part of this specification to the extent
specified herein:

5520-MA-369677 LHC IR QUAD magnet inner cable drawing

5525-MA-344389A LHC IR QUAD magnet outer cable drawing

SSC-M35-000014 NbTi Superconducting Wire for SSC Dipole Magnets (1.3
grade inner)

SSC-MAG-M-4146 NbTi Superconducting Wire for SSC Dipole Magnets (Outer)

SSC-M35-000110 Packaging and shipping of superconducting cable

SSC-MAG-402 Appendix A, B

# 3 REQUIREMENTS {#requirements .unnumbered}

## 3.1 Wire receiving and handling {#wire-receiving-and-handling .unnumbered}

The wire shall be inspected and tested upon receipt to check that it
complies with the following requirements:

### 3.1.1 Wire supplier responsibility {#wire-supplier-responsibility .unnumbered}

Table 1 summarizes the strand parameters.

1.  Critical current. The conductor for the inner layer shall have a
    minimum critical current of 378 A, measured at 7 T and 4.22 K. The
    conductor for the outer layer shall have a minimum critical current
    of 185 A, measured at 7T and 4.22 K. The critical current will be
    determined according to a criterion of ρ=10^-14^ Ωm, based on the
    wire cross section area and with the applied magnetic field
    perpendicular to the wire axis.

2.  Copper to non-copper ratio. The copper to non-copper ratio shall be
    (1.3±0.1):1 for the inner layer conductor and (1.8±0.1):1 for the
    outer layer conductor.

3.  Wire diameter. The conductor for the inner layer shall have a
    diameter of 0.808±0.0025 mm. The conductor for the outer layer shall
    have a diameter of 0.6505±0.0025 mm.

4.  Surface condition. The wire surface shall be free of all surface
    defects, slivers, folds, laminations, dirt, copper fines, or
    inclusions. No NbTi filaments shall be visible at 10x under a
    lighting level of at least 1076 lux.

5.  Wire twist pitch. The conductor for the HGQ cable shall be twisted
    so that the filaments follow the opposite rotation as the cable lay
    direction. The inner layer wire twist pitch at final size shall be
    (13 ±1.5) mm. The outer layer wire twist pitch at final size shall
    be (13 ±1.5) mm.

6.  Residual Resistance Ratio(RRR). The conductors for inner and outer
    cable shall have a minimum RRR value of 70 after annealing. The test
    procedure of RRR is described in Appendix II.

    Table 1. Strand mechanical and electrical specifications

  ----------------------- ------ ------ ------- ---------- ----------- --------- ------- ---------- ----------- ---------
  Parameter               Unit          Inner                                    Outer                          
                                        cable                                    cable                          

                                        Value              Tolerance             Value              Tolerance   

  Diameter                       mm             0.808                  ± 0.0025          0.6505                 ± 0.0025

  Cu/SC ratio                                   1.3 : 1                ± 0.1             1.8 : 1                ± 0.1

  Surface coating                               None                   \-                None                   \-

  Anneal                                        None                   \-                None                   \-

  Minimum critical               A              378                    \-                185                    \-
  current                                                                                                       

  Minimum RRR                                   70                                       70                     

  Twist direction                               Left                                     Right                  

  Twist pitch                    mm             13                     ± 1.5             13                     ± 1.5
  ----------------------- ------ ------ ------- ---------- ----------- --------- ------- ---------- ----------- ---------

### 3.1.2 Cable vendor responsibility {#cable-vendor-responsibility .unnumbered}

1.  Mechanical properties. The wire shall survive a sharp bend test
    (Appendix IV).

2.  The wire awaiting cable fabrication shall be identified, protected,
    and handled in a manner to prevent degradation or damage.

## 3.2 Technical requirements for cable {#technical-requirements-for-cable .unnumbered}

Figure 1 shows the cable size parameters and Table 2 summarizes the
cable mechanical and electrical parameters.

### 3.2.1 Mechanical properties {#mechanical-properties .unnumbered}

1.  Cable size, strand number, cable transposition pitch, lay direction,
    surface coating, and strand anneal are specified in drawing numbers
    MA-369677 and MA-344389A for the inner and outer cable,
    respectively. The method for determining that the cable dimensions
    comply with the requirements are described in Appendix A of document
    SSC-MAG-M-402 (Test Method 402-1 - Cable Thickness. Width and
    Keystone Angle). The cable mid-thickness is measured under a
    pressure of 5 ksi (34.47 MPa).

> If the cable has a \"right lay\" pitch the strands should be spiraled
> in the same direction as right handed screw thread. The converse is
> true for a left lay direction. Figure 1 shows the cable size
> parameters and Table 2 lists the specifications.

2.  Residual twist. The residual twist shall be in the following range:
    between 0° and 90° in the direction of the cable lay. The twist is
    measured by suspending a 11.34 Kg (25 lb.) weight from a 1m length
    of cable.

### 3.2.2 Electrical properties {#electrical-properties .unnumbered}

Critical current at 7T, 4.22K must be higher than 14.0 kA and 8.5 kA for
inner and outer cables, respectively. The cable electrical properties
are also described in Table 2. The methods used to measure the
electrical properties are described in Appendix I.

![](media/image1.wmf)

Figure 1 The cable size parameters.

Table 2. Cable mechanical and electrical specifications

  ----------------------- -------- ------- ------- ---------- ------- ----------- ------- ---------- ------- -----------
  Parameter                        Unit            Inner                                  Outer              
                                                   cable                                  cable              

                                                   Value              Tolerance           Value              Tolerance

  Number of strands                        37                 \-                  46                 \-      

  Cable width             mm               15.40              ± 0.025             15.40              ± 0.025 

  Minor edge              mm               1.320                                  1.051                      

  Cable Mid-thickness     mm               1.465              ± 0.006             1.146              ± 0.006 

  Major edge              mm               1.610                                  1.241                      

  Keystone angle          degree           1.079              ± 0.05              0.707              ± 0.05  

  Transposition length    mm               114                ± 5                 102                ± 5     

  Lay direction                            Right              \-                  Left               \-      

  Minimum critical        kA               14.0               \-                  8.5                \-      
  current                                                                                                    

  Minimum unit length     m                180                \-                  200                \-      

  Residual twist          degree           0 - 90                                 0 - 90                     

  Minimum bending radius  mm               7                                      15                         
  ----------------------- -------- ------- ------- ---------- ------- ----------- ------- ---------- ------- -----------

##  {#section-1 .unnumbered}

## 3.3 Processing {#processing .unnumbered}

### 3.3.1 Identification {#identification .unnumbered}

Each piece of wire (strand) and cable in the cable fabrication process
shall be identified by a unique number code. Wire identification shall
be traceable to the final cable serial number. All cable fabrication
material, processing, inspection, tests, and delivery records shall be
retrievable to either wire or cable code numbers.

### 3.3.2 Cable Map {#cable-map .unnumbered}

The cable manufacturer shall supply a cable map giving the serial
numbers of the strand used in the cable.

### 3.3.3 Cable production lengths  {#cable-production-lengths .unnumbered}

The unit length of cable is 180 m for the inner layer cable and 200 m
for the outer layer cable. A cable production length is a continuous
length of cable which is an integer multiple of the unit length.

### 3.3.4 Strand Welds  {#strand-welds .unnumbered}

No cold welds are allowed in any production length of cable. Cold welds
used in setup must be clearly marked, and position of the cold welds
must be listed in the production report. These cold welds must be
removed before the cable is shipped to FNAL.

### 3.3.5 Cable surface condition {#cable-surface-condition .unnumbered}

The cable surface must be thoroughly clean and free from oil, metallic
particles or residue. The cable shall be cleaned with Abzol VG cleaner.
The cable must be free of roughness, sharp edges or burrs.

### 3.3.6 Crossover or broken strands {#crossover-or-broken-strands .unnumbered}

There can be no crossovers of strands or broken strands in the cable

# 4 PREPARATION FOR DELIVERY {#preparation-for-delivery .unnumbered}

## 4.1 Reels/Spools {#reelsspools .unnumbered}

The cable must be spooled with a radius larger than or equal to 0.3 m.
The spools must be constructed to prevent damage to the cable during
spooling and unspooling. The spools shall be boxed to prevent damage in
shipment. They should be stacked and shipped with the spool flanges
maintained in a vertical orientation (axis horizontal) in order to
prevent the cable from settling on the spool.

## 4.2 Spooling requirements  {#spooling-requirements .unnumbered}

The cable must be wound on the spool so that there are no crossovers of
the cable layers. Filler cord shall be used at the edges of the cable
layers as required so that the cable will be adequately supported over
the whole wide face and will lie flat. Only one production length of
cable is placed on each spool.

The cable will be wound onto a spool in the following manner: As an
observer is looking at the collecting spool, if the spool is rotating
clockwise, then the thick edge of the cable should be facing the
observer.

# 5 QUALITY ASSURANCE AND MANUFACTURING PLAN {#quality-assurance-and-manufacturing-plan .unnumbered}

## 5.1 Quality Plan {#quality-plan .unnumbered}

The cable manufacturer is responsible for performing the inspections and
the tests defined in Table 3 and the preparation and maintenance of
resultant data. BNL will perform the critical current and RRR
measurements on samples supplied by the cable vendor from the beginning
and end of each production length upon completion.

## 5.2 Certificate of compliance  {#certificate-of-compliance .unnumbered}

The cable manufacture shall provide a written statement certifying
compliance with the requirements of this specification with each product
shipment, together with a completed copy of test result data. The result
data is to be provided in an electronic form (ASCII file) also.

This documentation shall be provided to Fermilab after the completion of
all tests, measurements, and inspections, and Fermilab shall provide in
writing an acceptance certificate. No cable shall be delivered prior to
the receipt of this acceptance.

### 5.2.1 Nonconforming material  {#nonconforming-material .unnumbered}

Finished cable failing to meet the requirements of Table 2 shall be
identified by condition and segregated from conforming material.
Material shall remain on hold pending buyer notification and
disposition.

## Shipping

The cable spool shall be shipped as a palletized unit. (Ref
SSC-M35-000110)

1.  Place the spool on a pallet custom made to the size of the spool,
    with the spool flanges maintained in a vertical orientation (axis
    horizontal) in order to prevent the cable from settling on the
    spool. (Custom pallets are reusable.)

2.  Attach the spool to the pallet through the horizontal axis of the
    spool with banding material (palletized unit).

3.  Cover the entire package with a 5/8 inch plywood crate banded to the
    pallet holding the plywood cover in place.

## 5.4 Marking/Identification Requirement  {#markingidentification-requirement .unnumbered}

Spools and exterior packaging shall be identified with the following
information in the order shown:

> LHC IR QUAD superconducting cable
>
> Type (Inner or Outer) [I or O]{.underline}
>
> Wire manufacturer \_\_\_\_\_\_
>
> Buyer P.O. No. \_\_\_\_\_\_
>
> Reel ID. \_\_\_\_\_\_
>
> Drawing No. \_\_\_\_\_\_
>
> Length (m) \_\_\_\_\_\_
>
> Weight (kg) \_\_\_\_\_\_
>
> Cable Map No. \_\_\_\_\_\_
>
> Date of Manufacture \_\_\_\_\_\_
>
> Name of Manufacturer \_\_\_\_\_\_

The Reel ID in the list should be in format of 'L-3-A-Nxxxx.' 'L' means
LHC and '3' means inner cable. In the case of outer cable this number
will be '4.' The following 'A' indicates the wire manufacturer ('A'
means 'Alsthom,' 'I' means 'IGC' and 'O' means 'OST'.). The last field
shows the four digits of cable ID number after cable manufacturer('N'
means 'New England Electrical Wire').

Table 3. Finished cable acceptance inspection/test

  ---------------- ------------- ------------- ----------------- -----------
  Characteristic   Requirement   Test Specimen Frequency         Test method
                   value         sample ^1^                      ^1^

  Cable            Table 2       TM-402-1      Each 30 m         TM-402-1
  mid-thickness                                                  

  Cable width      Table 2       TM-402-1      Each 30 m         TM-402-1

  Cable keystone   Table 2       TM-402-1      Each 30 m         TM-402-1
  angle                                                          

  Cable lay        Table 2       TM-402-3      Beginning and end TM-402-3
  direction                                    of each           
                                               production length 

  Cable lay pitch  Table 2       TM-402-2      Beginning and end TM-402-2
                                               of each           
                                               production length 

  Bend strength    No cable      TM-402-5      Beginning and end TM-402-5
                   damage                      of each           
                                               production length 

  Residual twist   See 3.2.1.2   1 m           Beginning and end 3.2.1.2
                                               of each           
                                               production length 

  Surface          See 3.3.5     100%          100%              
  condition                                                      

  Strand integrity No broken     100%          100%              Visual test
                   strands                                       

  Cable critical   Table 2                     Beginning and end Appendix I
  current                                      of each           
                                               production length 

  RRR              Table 1                     Beginning and end Appendix II
                                               of each           
                                               production length 
  ---------------- ------------- ------------- ----------------- -----------

1\. Test method descriptions are included in Appendix A of
SSC-MAG-M-402.

2\. The cable measuring machine shall be used as described in TM-402-1
for the noted tests.

# Appendix I Cable Critical Current Determination {#appendix-i-cable-critical-current-determination .unnumbered}

## I.1 Introduction {#i.1-introduction .unnumbered}

The sections below describe the test method used at BNL to determine
transport critical currents of meter long cable samples. These
procedures have proven suitable for production testing.

The critical current of a cable, I~c~, is less than the sum of the
individual wire values as there is invariably some degradation during
the fabrication of the cable. This is expressed as follows:

$\text{D = }1 - \left( \frac{I_{c}}{\sum_{}^{}I_{\text{cw}}} \right)$

where Σ I~cw~ = sum of the Ic's of the wires in the cable. An allowance
for degradation, is D \< 0.05 (=5%).

The critical current is a function of temperature, T, and magnetic
field, B. It is necessary to convert (or \"correct\") short sample test
results obtained at particular values of T and B, to values
corresponding to a standard temperature and field. The steps in this
conversion are as follows:

a)  Obtain raw data for several applied fields: I~ct~, critical current
    at bath temperature, T, and applied field, B~a~. For LHC quadrupole
    cable, the applied fields are 6.7, 7.0, 7.3 T for inner cables, and
    5.6, 6.3, 7.0 T for outer cable.

b)  Calculate the peak field, B: the sum of the applied field and the
    self-field, due to the measurement current.

c)  Convert I~ct~ at field B to I~c~, the value corresponding to
    reference temperature T~ref~.

d)  Plot I~c~ vs. B and calculate I~c~ at the reference field from a
    linear fit to the data.

The calculations used in the above steps are described in detail below..

## I.2 Definition of Critical Current {#i.2-definition-of-critical-current .unnumbered}

The critical current is a property of the reversible portion of the V-I
curve. It is defined as that current for which

$VI\text{ = }\frac{\text{10}^{- \text{14}}}{\left( \frac{{N\pi d}^{2}}{4} \right)}$

where V = voltage drop per m, I = current in amps N = no. of wires in
cable d = wire diameter in m. The shape of the V-I curve is of the form
V = constant × *I^n^*^+1^. (Note that n is defined from the equation ρ =
constant × *I^n^* ). The quantity *n* is routinely measured as required
by the specifications.

## I.3 Sample Mounting {#i.3-sample-mounting .unnumbered}

The samples are mounted in a compression fixture, which is illustrated
in Figure I.1. The test arrangement involves four bare cable samples. As
these are keystoned, (i.e., they are trapezoidal in cross-section), care
is taken to alternate thick and thin edges so that pairs of conductors
present parallel surfaces to the clamping faces. As indicated in Figure
I.1 there are a series of separators: 0.76 mm. thick G-10 strips which
carry electrical instrumentation described below, and 0.25 mm. thick
Mylar strips which insulate adjacent samples of the upper and lower
cable pairs.

Compression is applied by tightening 9.53 mm (3/8 in.) bolts. A torque
of 53 N-m (240 inch-pounds) is used to tighten the bolts. This produces
a clamping pressure of 54± 7 MPa for the 15 mm wide HGQ cables at room
temperature. The standard configuration for quality control testing is
the perpendicular one, i.e., the applied dipole field is perpendicular
to the sample faces. Rotation of the sample fixture relative to the
magnet is prevented by means of a locating key on the fixture and a
slotted plate at the bottom of the magnet.

Figure I.2 shows schematically how the cables are connected to each
other and to the gas cooled leads. The connections are made using
ordinary soft solder over a 15 cm. length. A typical joint resistance is
about 10^-9^ ohm. The samples are excited in pairs, either A-B, or C-D.

![](media/image2.wmf){width="3.8222222222222224in"
height="1.9590277777777778in"}

Figure I.1 Mechanical assembly of 2 pairs of cable.

![](media/image3.wmf){width="3.897222222222222in"
height="1.8569444444444445in"}

Figure I.2 Electrical Wiring Schematic.

## I.4 Electrical Instrumentation {#i.4-electrical-instrumentation .unnumbered}

Primary instrumentation consists of the following:

-   Five voltage taps and thin foil heater element for each sample.
    These are contained on the G-10 strips shown in Figure I.2. The
    voltage taps work by the pressure contact of a copper wire across
    the width of the sample. The heater element is a strip of stainless
    steel foil, 0.013 mm. thick x 3 mm. x 6 mm, which is located in a
    shallow well formed in the G-10 strip.

-   Hazemeyer DCCT secondary current standard.

-   Digital voltmeters, 6-1/2 digit, 0.1 μV sensitivity.

-   Nicolet 12 bit, 4 channel digital oscilloscope.

-   Two calibrated carbon resistor thermometers, located at each end of
    the magnet.

-   Isolation preamplifiers, 1 mV noise level.

Secondary instrumentation consists of the following:

-   Quench current protection circuits for the magnet, the gas-cooled
    leads, and the samples.

-   DC power supplies for persistent switch, and sample heater element.

-   Pulse power supply for sample heater element.

## I.5 Measurement Procedure {#i.5-measurement-procedure .unnumbered}

The cable samples are energized in pairs, either A-B or C-D in Figure
I.2 and the V-I curves are determined simultaneously for each member of
the bifilar pair. In quality control tests of production cables, the
match between samples is close enough that I~c~\'s can usually be
determined for all four samples. In the rest of this section we shall
describe the procedure for testing one cable only, it being understood
that a pair of samples, or all four, are under simultaneous test.

The measurements are made with the helium bath level above the upper
sample and well above the top of the dipole magnet. The magnet field is
set to a desired value and locked in with the persistent switch. The
standard arrangement is such that the field is oriented perpendicular to
the cable face.

The relative direction of the current flow and of the magnet field is
very important for reasons which will be discussed below. Therefore, the
polarity of the power supply connections is carefully checked. Before
the V-I curve is measured the sample is trained. This is done by ramping
the current until a quench occurs. For relatively high Cu/SC ratio
cables, as in the RHIC design, one quench is usually sufficient to reach
the plateau value of I~q~.

Voltage-current readings are taken with a current ramp of \~200A/s.
On-line the V-I data are converted to log ρ - log I data and fitted by a
straight line. This gives the 10^-14^ ohm · m current and the n-value
(the slope of the log-log plot). However off-line a separate analytical
technique is used for calculating I~ct~ and n-value. The results of this
analysis are reported: B~a~, T, I~ct~ I~q~, n, where B~a~ is the applied
field, and I~q~ is the quench current or a lower limit of it. This
procedure is repeated for each of the four cables at several fields in
the vicinity of the specification field.

## I.6 Temperature Calculation {#i.6-temperature-calculation .unnumbered}

Calculations of the critical currents at temperatures other than that at
which I~c~ is measured are made using the same procedure as that for
wires. The specification temperature is usually 4.222 K, that of boiling
helium at standard atmospheric pressure. The bath temperature is
recorded with the aid of cryogenic thermometry with a precision of ±
0.002K (2 mK). A \"linear T\" type of correction is applied for
temperatures different from 4.222 K:

$\frac{I_{c}}{I_{\text{ct}}} = \frac{T - 4\text{.}\text{222}}{T_{c} - T_{\text{bath}}}$

$T_{c}(B)\text{ = 9}\text{.}2\left\lbrack \text{1 - }\frac{B}{\text{14}\text{.}5} \right\rbrack^{0\text{.}\text{59}}$

where T~c~(B) is the transition temperature at the specified magnetic
field. I~ct~ is the current measured at temperature T, and I~c~ is the
critical current at the specification temperature. The field B is not
just the applied field but that which takes into account the field
produced by the cables as explained below.

## I.7 Magnetic Field Correction[^1]  {#i.7-magnetic-field-correction .unnumbered}

The magnetic field is the sum of the applied field produced by the
dipole magnet and the self-field produced by the measuring current. The
following assumptions give results that are self-consistent for a wide
variety of geometry and which give reliable predictions of magnet
behavior.

a)  The critical current of the sample is determined by the peak
    magnetic field. This depends, of course, on the orientation of the
    applied field and the direction of the sample current.

b)  The sample current is distributed uniformly over, and normal to, the
    area of the trapezoid that encloses the cable cross-section.

c)  The geometry is accurately reproducible; this is a matter of care in
    assembly.

With the dipole field perpendicular to the wide face of the sample, the
peak field occurs at a point on the surface of the sample where the
self-field and the applied field are very nearly parallel; that is, they
are simply additive. For the standard test configuration, the self-field
correction can be written:

$\text{B } = \text{ B}_{\text{peak}} = B_{a} + c \times I_{\text{ct}}$

where B~a~ = dipole field and c = geometric constant. Below is given the
value of c for HGQ cable, for B~a~ perpendicular to the sample, and for
the standard BNL test geometry in which the bifilar samples are
separated by 0.25 mm

Self-field constant, c, T/KA, for HGQ Cable1: 0.02480

Self-field constant, c, T/KA, for HGQ Cable2: 0.02530

## I.8 Critical Current of the Thin Edge: {#i.8-critical-current-of-the-thin-edge .unnumbered}

The thin edge of a keystone-shaped cable is of interest. The bifilar
sample test arrangement with applied field perpendicular has the
characteristic feature that the peak fields occur at diagonally opposite
points, at the two thin edges (c.f. Figure I.3). the quality control
test determines the critical current for the thin edge; i.e. the field
and current direction are oriented as in Figure I.3.

![](media/image4.wmf){width="4.236111111111111in"
height="1.636111111111111in"}

Figure I.3 Contours of constant field magnitude for perpendicular
applied field of 6T and current of 10kA. The peak field of 6.4T occurs
at the thin edge of the cable.

# Appendix II Cable R(293) and RRR Determination {#appendix-ii-cable-r293-and-rrr-determination .unnumbered}

As in the case of wires, the cable resistance at 293 K and that at 10 K
is determined using the same set-up used for Ic determination. The
residual resistance ratio, RRR, is defined to be R(293)/R(10). R(293) is
measured with an accuracy of 0.5%; R(10) is measured with an accuracy of
2%.

The room temperature measurement is made using a DC current of 1 A, and
voltage contacts 61 cm apart (see Figure I.2). A thermocouple device of
0.1^0^C accuracy is used to determine the ambient temperature. Normally
occurring room temperature variations produce significant variations in
the measured resistance. Designating this resistance as R~m~ and the
ambient temperature as t(^0^C), the resistance at the reference
temperature of 293 K is calculated as follows:

$R(\text{293}) = \frac{R_{m}}{1 + 0\text{.}\text{0039}\left( t - \text{20} \right)}$

The effect of the Nb-Ti is negligible for the purpose of this correction

The low temperature measurement is a dynamic one, made by inducing a
superconducting-normal state quench while the cable is carrying current.
Referring to Figure I.2, a quench is triggered in Cable A, for example,
by means of heater HA. The resulting waveform observed at nearby voltage
taps, A2-A3 or A3-A4, consists of three parts: a superconducting state
baseline voltage, a linear ramp voltage corresponding to the passage of
the superconducting-normal interface between the voltage taps, and a
slowly increasing signal characteristic of the normal state resistance.
The latter increases in time due to normal state heating. However, at
first the voltage is almost constant due to the residual resistance
characteristic of the copper. Thus, there is a kink in the voltage
waveform at the beginning and at the end of the linear ramp portion. The
voltage difference between these two points equals the current times the
residual resistance of the section of cable between the voltage taps.
The resistance per centimeter is determined for two pairs of taps (A2-A3
and A3-A4 in the above illustration) and averaged. The taps are
relatively close to the heater in order to minimize the effect of
current fall-off which results from the increase of normal state
resistance as the quench propagates. Routinely the resistance in zero
field is measured.

# Appendix III Copper/Superconductor Ratio {#appendix-iii-coppersuperconductor-ratio .unnumbered}

The copper/superconductor ratio of the cable is determined in nearly the
same manner as for the wire where the copper: superconductor volume
ratio (x) is calculated from R(293) and RRR by means of the formula

$\text{x = }\frac{\text{1 - R}(2\text{93})\text{ A/}\rho_{s}}{R(\text{29}3)\text{ A/}\rho_{\text{Cu}}\text{ - 1}}$

1

where R(293) = resistance of the strand at 293K in ohms/m

ρ~Cu~ = resistivity of the copper at 293K, in ohm · m

= $r_{i}\frac{\text{RRR}}{\left( \text{RRR} - 1 \right)}$

r~i~ = resistivity of pure copper at 293K

= 1.682 x 10^-8^ ohm · m

ρ~s~ = resistivity of Nb-Ti at 293K

= 60 x 10^-8^ ohm · m

and A = wire cross section area in m^2^

= πd^2^/4 (d = wire diameter in m)

The same formulas are used for strand but with two exceptions:

a)  The area is that of all the wires, viz., Nπd^2^/4 .

b)  The spiral path of the wires necessitates applying a length
    correction to the measured value of R(293). For HGQ conductor R(293)
    is replaced by 1.049 × R(293) in the formula for the inner cable and
    1.056\*R(293) for the outer cable.

# Appendix IV Sharp Bend Test {#appendix-iv-sharp-bend-test .unnumbered}

The sharp bend procedure is to simulate the deformation of the strand
that may occur during cabling.

1.  Fabricate a test fixture consisting of a slot in a metal block plus
    an armature that freely slides in the slot, as indicated in inset A1
    below.

![](media/image5.wmf)

2.  Cut a length of strand sample approximately 20 cm long. Bend the
    strand sample in half over a rod approximately 2 mm in diameter as
    indicated below.

![](media/image6.wmf)

3.  Remove the rod and place the bent sample in the slot of the fixture
    as indicated in inset A1. Slide the armature into the slot of the
    fixture to squeeze the bent sample to the value of 2.6 mm (two
    strand diameters) to obtain a hairpin shape.

4.  Examine the bend region at a magnification of at least 10X under a
    lighting level of at least 1076 lux and verify that the surface of
    the copper is not cracked, split, or otherwise deformed to prevent
    successful cabling.

5.  Etch the bend region in dilute nitric acid and examine the filaments
    at a magnification of at least 10X and a lighting level of at least
    1076 lux and verify that no filaments have been broken.

[^1]: ^2^ " The effect of self field on the critical current
    determination of multifilamentary superconductors", M.Garber et.al.,
    IEEE Trans. on Magnetics, Vol25, p1940 (1989)