Fermi National Accelerator Laboratory

P.O. Box 500 -- Batavia, Illinois - 60510

TD-00-06

02/01/00

# *LHC INTERACTION REGION QUADRUPOLE BUS-BARS* 

# *TEST-SERIES 2*

P. Bauer, L. Chiesa, S. Feher, M. Lamm, A. Zlobin

Fermilab, Technical Division, T&D Department

Keywords: bus-bar, LHC, quadrupoles, quench, superconducting magnets

Superconducting quadrupole magnets with nominal field gradient of 215
T/m in a 70 mm bore, operating in superfluid helium at 1.9K, are being
developed at Fermilab and KEK in the framework of the CERN-US-KEK LHC
Accelerator Project for the interaction regions (IR) of the Large Hadron
Collider (LHC).

This note reports the results of a test of bus-bar prototypes for the
interaction region (IR) quadrupoles. The bus-bar design consists of a
superconducting cable used as well for the inner layer of the Fermilab
IR quadrupoles, soldered to similar Rutherford-type cables as
stabilizers. The stabilizers in this test-series were NbTi/Cu composite
cables with the same characteristics as the main superconducting
bus-cable. In one case the superconducting cable was stabilized with
one, in another with two stabilizers. The different designs are
motivated by the attempt to find a compromise between

-   maximum stability against quenching during normal operation

-   minimum temperature rise in the bus-bar after a quench

-   maximum quench propagation velocity to accelerate detection of
    quench

> The samples were submitted to operational conditions and characterized
> with respect to quench propagation velocity and voltage profile during
> normal zone growth. Additionally, unlike test-series 1, the bus-bars
> in test-series 2 were tested together with the magnet.
>
> The following note presents the measurement results and a quantitative
> analysis of the data.

## 1) Scope of IR QUADRUPOLE Bus-Bar Measurement-Series 2

![](media/image3.wmf)The bus-bar test-series 1 was mainly conceived to
test 2 different bus-bar prototypes, which had emerged as possible
candidates from a design study. The design study and the results of
these tests are reported in the note TD-99-059. The bus-bar protoypes in
test-series 1 consisted of one superconducting cable stabilized with two
similar superconducting cables -- in one case the three cables were
soldered together, in the other the superconductor was insulated from
the stabilizer (except in the ends) with a polyimide sheet. The hope,
that at equal level of heating after a quench, the quench would
propagate faster in the "segregated" case was deceived (the quench
propagation velocity was equal for both types). Since the fully soldered
sample is more stable against thermomechanical disturbances, and
sufficiently flexible to allow strong bending (extension loops), it was
decided to retain a fully soldered design for test-series 2. A lack of
space as well as lower operation current (8 kA vs 11 kA) in the KEK IR
quadrupoles are more appropriately addressed with a thinner bus-bar,
consisting of one superconductor and one stabilizer. Therefore
test-series 2 was conducted with a combined bus-bar using a so called
2-bus (1 stabilizer) for one branch (+) and a 3-bus (2 stabilizer) for
the other (-). Furthermore, unlike test 1 in which the bus-bars were
tested alone, the main purpose of test 2 was the test of the bus
together together with the magnet. Figure 1 shows how the bus was
assembled into model magnet HGQ08.

Figure 1: LHC IR model quadrupole with bus-bar assembly for test 2.
Before connecting to the magnet (left end) the bus runs a full loop
through the bus slots in the magnet yoke.

This allowed not only to practice the installation of the bus-bar into
the magnet but also to check eventual magnetic coupling between the bus
and the magnet. To obtain sufficient length to measure the quench
propagation and to test length related mechanical behavior, the bus-bar
was extended by one full turn around the magnet. It was first inserted
into one of the instrumentation slots in the magnet yoke, bent at the
magnet return end and reinserted into the bus channel, such that it
formed a 2.5 m long loop. The bus-bar was mechanically supported only in
the magnet ends. Within the magnet the bus-bar assembly was free to
move.

## 3) EXPERIMENTAL SET-UP 

Figure 2 shows the cross-section of the bus-bar assembly. The 2-bus
(go-) and 3-bus (return-) were separately insulated with a single 50%
overlap wrap of 75 μm adhesive Kapton^^, followed by a shrink-sleeve
wrap and firmly attached together with a tight wrap of Kevlar^^ string
(\~ 1 knot per inch). The repulsive force (see equation (1)) between 2
bus-bars (distance d=1 mm) carrying I=11 kA in opposite direction is
estimated to be 2⋅12 kN/m, which is \~140 lbs/inch.

$\frac{\text{dF}}{\text{dl}} = \frac{2\mu_{0}I^{2}}{4\pi d}\ Nm$ (1)

An additional Nomex^^ wrap protected the bus-assembly during insertion
into the magnet.

Figure 2: Test series 2 LHC IR bus-bar assembly: The so called 2-bus and
3-bus form the positive and negative branch of the magnet power leads.

On the side closer to the magnet connection (left side in Figure 1) both
bus-bars were equipped with a set of 2 spot-heaters (one active, one as
a reserve) to trigger quenches, and voltage taps along four 4-inch long
segments to monitor quench propagation. The spot heaters were pressed
against the superconductor with a simple clamp consisting of 2 plates
and bolts ( Figure 3). Voltage taps were attached to the ends of the
bus-bars to measure the voltage over the total length in both branches.

Figure 3: Exploded view of quench measurement instrumentation on bus-bar
assembly. Each bus-bar is equipped with a spot heater and voltage taps
that delimit 4 segments (--1 to +2). The heaters (in segment 0) are
pressed against the bus-bars with two plates which are bolted together
with the bus-bars and heaters in between.

## 3) QUENCH PROPAGATION VELOCITY MEASUREMENTS 

The quench propagation velocity is measured using the time of flight
method. The magnet is ramped to the chosen current and a quench is
initiated in a voltage segment (segment 0) with the spot heater. The
quench propagates to neighboring segments. The quench propagation
velocity is calculated from the known length of the voltage segment and
the time it takes the voltage onset in the conductor to travel through
the voltage taps delimiting this particular segment. Figure 4 and Figure
5 show the voltage traces following a quench for 2 particular cases (7
kA in 2-bus and 11 kA in 3-bus). The error inherent to this method can
be estimated from the difference in the segment +/-1 signals, which are
mainly caused by asymmetric quench propagation (v~q~^left^≠v~q~^right^)
and differences in voltage segment length. The error range is typically
± 10 %.

![](media/image4.wmf){width="5.378472222222222in"
height="3.6840277777777777in"}

Figure 4: Quench Propagation in 2-bus, current \~7 kA. The heater
initiates a quench in segment 0, segments +/-1 are adjacent to 0,
segment 2 is next to 1. The segments are 4 inches long.

![](media/image5.wmf){width="5.236111111111111in"
height="3.5805555555555557in"}

Figure 5: Quench Propagation in 3-bus, current \~11 kA. The heater
initiates a quench in segment 0, segments +/-1 are adjacent to 0,
segment 2 is next to 1. The segments are 4 inches long.

The measured quench propagation velocity data for both bus prototypes at
different currents are shown in Figure 6.

![](media/image6.wmf){width="5.995138888888889in"
height="4.0993055555555555in"}

Figure 6: Quench propagation velocity measurements on 2-bus and 3-bus
(test-series 1 and 2). Calculated results were obtained with Dresner's
formula.

The fits of the experimental curves in Figure 6 (dashed) were obtained
with Dresner's quench propagation velocity formula \[[^1]\].

$v_{q}^{\text{cooled}} = \frac{1}{{\overline{c}}_{p}}\sqrt{\frac{\text{apk}}{A}}\frac{{\alpha i}^{2} - 2 + i}{\sqrt{\left( 1 - \frac{i}{2} \right)\left\lbrack {\alpha i}^{2} - \left( 1 - \frac{i}{2} \right) \right\rbrack}}\left( 1 + \alpha^{- 1\text{.}\text{45}} \right)$
(2)

where "i" refers to the ratio of transport current I~t~ and critical
current I~c~ and α is:

$\alpha = \frac{I_{c}^{2}\rho_{\text{Cu}}}{A_{\text{Cu}}\text{pa}\left( T_{c} - T_{b} \right)}$
(3)

The purpose of fitting the experiment with (2) is to obtain a reliable
quench propagation formula that can be used in the exploration of other
possible bus-bar designs in the future.

To obtain a reasonable agreement with the measured data the following
set of values was used in the calculation:

+-----------------------------------+-------+--------+--------+-------+
| Material Properties:              | s     | unit   | 2-bus  | 3-bus |
|                                   | ymbol |        |        |       |
+-----------------------------------+-------+--------+--------+-------+
| Average specific heat between     | c~p~  | J/     | 10000  | 11000 |
| T~b~ and T~c~                     |       | K/m^3^ |        |       |
+-----------------------------------+-------+--------+--------+-------+
| Linear heat transfer coefficient  | a     | W/     | 350    | 350   |
|                                   |       | m^2^/K |        |       |
+-----------------------------------+-------+--------+--------+-------+
| Average heat conductivity         | k     | W/m/K  | 40     | 40    |
+-----------------------------------+-------+--------+--------+-------+
| Critical current @ 0 T            | I~c~  | kA     | 300    | 450   |
+-----------------------------------+-------+--------+--------+-------+
| Critical temperature              | T~c~  | K      | 9.2    | 9.2   |
+-----------------------------------+-------+--------+--------+-------+
| Residual Copper resistivity       | ρ~Cu~ | nΩm    | 0.17   | 0.17  |
+-----------------------------------+-------+--------+--------+-------+
| ###### Operating Conditions       |       |        |        |       |
+-----------------------------------+-------+--------+--------+-------+
| Magnetic field                    | B     | T      | 0.25   | 0.25  |
+-----------------------------------+-------+--------+--------+-------+
| Bath temperature                  | T~b~  | K      | 1.9    | 1.9   |
+-----------------------------------+-------+--------+--------+-------+
| ###### Geometrical Data           |       |        |        |       |
+-----------------------------------+-------+--------+--------+-------+
| Cu/Sc ratio                       | λ     | \-     | 1.3    | 1.3   |
+-----------------------------------+-------+--------+--------+-------+
| Total cross-sectional area        | A     | mm^2^  | 40.8   | 61.2  |
+-----------------------------------+-------+--------+--------+-------+
| Area of superconductor in         | A~sc~ | mm^2^  | 17.73  | 26.6  |
| cross-section                     |       |        |        |       |
+-----------------------------------+-------+--------+--------+-------+
| Area of copper (+solder) in       | A~cu~ | mm^2^  | 23.07  | 34.6  |
| cross-section                     |       |        |        |       |
+-----------------------------------+-------+--------+--------+-------+
| Cooled perimeter (\~50% of total  | p     | mm     | 18     | 20    |
| perimeter)                        |       |        |        |       |
+-----------------------------------+-------+--------+--------+-------+

Table 2: Input parameters for quench propagation velocity calculation.

The critical current was calculated with a j~c~-parametrization found in
literature \[[^2]\]. However, at very low fields, the parametrization is
not very accurate. The magnetic field was kept constant in the
calculation (0.25 T), thus the critical current was not varied with the
transport current (and hence the self-field). The average specific heat
(c~p~) numbers required to obtain good agreement are reasonable, except
that a 30% difference in c~p~ between 2 and 3 bus (=30% difference in
conductor volume) produced a greater gap between the 2 curves than the
gap found in the experiment. Therefore the c~p~ difference in the
calculation had to be reduced to 10%. The linear cooling coefficient
a=350 W/m^2^/K (Table 2), required for the fit, corresponds to modest
cooling conditions, as for example in the case of conduction through the
Kapton insulation or heat transfer to gaseous helium and is thus within
the expected range. The measured RRR (to obtain the residual copper
resistivity ρ~Cu~) of both samples is 100.

## 4) QUENCH INTEGRAL vs TEMPERATURE MEASUREMENTS

The calculated peak temperatures as a function of quench integral (QI)
were compared to experimental data obtained during a series of tests in
which the quench detection threshold was increased such, that the
bus-bar could operate at higher quench integrals and rise to higher peak
temperatures. The formalism used in the calculation of the quench
integral is presented in the following.

The quench integral is defined in equation 4. Equation 4 was obtained
from the space independent and adiabatic form of the heat balance
equation describing heat generation due to current flowing in the normal
matrix in an infinitely thin wire, thus relating the c~p~dT term to the
Joule heat generation by the current in the normal-conducting matrix.
The peak temperature obtained from the quench integral calculation is
therefore overestimating the real case, where cooling and conduction to
the sides will result in reduced peak temperatures compared to the
calculated, adiabatic case.

$\text{QI} = \text{10}^{- 6}\int_{0}^{\infty}{I_{t}^{2}(t)\text{dt}} = \text{10}^{- 6}\frac{\lambda}{\lambda + 1}A^{2}\int_{T_{0}}^{T_{\text{peak}}}{\frac{c_{\text{pcomp}}(T')}{\rho_{\text{Cu}}(T')}\text{dT}'}\ \text{MIIts}$
(4)

The quench integral can be calculated either from the temporal current
profile (middle term in equation 4) or from basic material parameters
(right term in equation 4). In the case of the bus-bar test the current
remained constant during the measurement process. With the quench
starting at time t~0~ the quench integral in the experimental case
becomes

$\text{QI} = \text{10}^{- 6}\left\lbrack I_{t}^{2}\left( t - t_{0} \right) \right\rbrack\ \text{MIIts}$
(5)

where, for convenience, the quench integral is given in units of 10^6^,
the so called MIIts. The following formulas and data are used in the
calculation of the quench integral from the material properties. The
specific heat per unit of volume c~p~ \[J/K/m^3^\] of a NbTi/Cu
composite (subscript low refers to the low temperature range) is given
with:

$c_{\text{plow}} = {\beta T}^{3} + \gamma T\text{}$ (6)

In the normal (subscript n) state the low temperature c~p~ of the
composite is calculated from the specific heat functions of the matrix
material (here Cu) and the superconductor weighed with α (volume ratio
of superconductor versus total volume (α=1/(1+λ)):

$c_{\text{pnlow}}(T) = \left\lbrack \gamma_{\text{Sc}}\rho_{\text{Sc}}\alpha + \gamma_{\text{Cu}}\rho_{\text{Cu}}(1 - \alpha) \right\rbrack T + \left\lbrack \beta_{\text{Sc}}\rho_{\text{Sc}}\alpha + \beta_{\text{Cu}}\rho_{\text{Cu}}(1 - \alpha) \right\rbrack T^{3}\text{}$
(7)

ρ is the density in kg/m^3^. The specific heat over the whole
temperature range is obtained through fitting the function to the
(known) low temperature and high temperature data (c~p300~ is a known
data-point at 300 K using the rule of mixture to compute the
room-temperature value for the composite) with:

$c_{\text{pn}}(T) = \frac{1}{\frac{1}{c_{p\text{300}}} + \frac{1}{c_{\text{pnlow}}(T)}}$
(8)

The specific heat of NbTi in the superconducting state c~ps~(T,B)
affects the specific heat of the composite only in a negligible
temperature range (T~b~ to T~c~), and is therefore neglected. The
specific heat parameters for the above formulas are given in Table 3.

  -------------- --------------- --------------- ----------------------------
  Parameter      Unit            NbTi~(46.5%)~   OFHC Copper

  γ              \[J/K^2^/kg\]   0.1450          0.011

  β              \[J/K^4^/kg\]   0.0023          0.000744

  ρ              \[kg/m^3^\]     6000            8960

  c~p300~        \[J/K/m^3^\]    2.304⋅10^6\*^   3.454⋅10^6^

  B~0~           \[T\]           14.5            \-

  T~sc0~         \[K\]           9.09            \-
  -------------- --------------- --------------- ----------------------------

Table 3: Cp parameters from Dresner \[[^3]\] (\*calculated from c~p~ of
elemental Nb~0.54~ and Ti~0.46~).

T~sc0~ is the critical temperature of the superconductor at B = 0 T,
B~c0~ is the critical magnetic field at T = 0 K.

The normal matrix (Cu-) resistivity function ^(^[^4]^)^ is given in
equations 9-13:

$\rho_{1} = \frac{1\text{.}\text{171} \cdot \text{10}^{- \text{17}} \cdot T^{4\text{.}\text{49}}}{1 + \left\{ 4\text{.}5 \cdot \text{10}^{- 7} \cdot T^{3\text{.}\text{35}} \cdot \left\lbrack e^{- \left( \frac{\text{50}}{T} \right)^{6\text{.}\text{428}}} \right\rbrack \right\}}\text{}$
(9)

$\rho_{2} = \left\lbrack \frac{1\text{.}\text{69} \cdot \text{10}^{- 8}}{\text{RRR}} + \rho_{1} + 0\text{.}\text{4531} \cdot \left( \frac{1\text{.}\text{69} \cdot \text{10}^{- 8} \cdot \rho_{1}}{\text{RRR} \cdot \rho_{1} + 1\text{.}\text{69} \cdot \text{10}^{- 8}} \right) \right\rbrack\text{}$
(10)

$A = \text{log}\left( \frac{1\text{.}\text{553} \cdot \text{10}^{- 8} \cdot B}{\rho_{2}} \right)$
(11)

$a\text{=-}2\text{.}\text{662} + 0\text{.}\text{3168} \cdot A + 0\text{.}\text{6229} \cdot A^{2} - 0\text{.}\text{1839} \cdot A^{3} + 0\text{.}\text{01827} \cdot A^{4}$
(12)

$\rho_{\text{Cu}} = \rho_{2} \cdot \left( 1 + \text{10}^{a} \right)\text{}$
(13)

The normal state resistivity of NbTi at 4.2K is approximately 6⋅10^-7^Ωm
^(^[^5]^)^ - three orders of magnitude above that of copper. It is
therefore a reasonable approach to neglect current transport in the
NbTi-branch after super- to normal-conducting transition.

To convert the experimental voltage vs. time data to temperature vs.
quench integral data the following procedure was followed: The voltage
data of the segment quenched originally by the spot heater were
converted into a resistivity (knowing current , Cu cross-sectional area
and the length of the segment), assuming that the segment was

![](media/image7.wmf){width="5.445138888888889in"
height="3.729861111111111in"}

Figure 7: Comparison of experimental and calculated T~max~ vs. MIIts
relations for 2-bus at 7 kA.

isothermal over its full length. The resistivity was normalized to the
residual resistivity (here \~ 1.7⋅10^-10^Ωm) and converted to
temperature by comparison with the known temperature dependence of the
equally normalized resistivity function in equation 9. The experimental
MIIts data are calculated from current and time with equation 5.

Figure 7 and Figure 9 show the comparisons for both bus-bar samples in
their operational conditions: 7 kA in the KEK- and 11 kA in the FNAL IR
quadrupole cases. The comparison indicates a good agreement between
measured data and data calculated from the material parameters. In
general it was found, that the higher the current the better the
agreement between the adiabatic model and the experimental data. In the
7 kA 2-bus case the adiabatic model overestimates the peak temperatures.
Figure 8 shows T~max~ vs. QI plots for the 2-bus, derived from two
measurements at different currents. A plot of the variation of the
T~max~ vs. QI for quenches at different currents is given as well for
the 3-bus in Figure 10.

It seems that with decreasing currents the peak temperatures for a given
number of MIIts decrease (and thus the T~max~ vs. QI curve diverges from
the adiabatic limit the lower the current). The current dependence of
the above mentioned effect hints toward a cooling effect. This result is
consistent with the fact that cooling (even if only a modest amount) is
required to approximate the experimental quench propagation velocity
data with Dresner's formula. The effect of cooling was also noted in the
analysis of test-series 1.

![](media/image8.wmf){width="5.435416666666667in"
height="3.7104166666666667in"}

Figure 8: Peak temperatures versus MIIts plots for the 2-bus, measured
after quenches at magnet currents 7 and 11 kA.

![](media/image9.wmf){width="5.5875in" height="3.813888888888889in"}

Figure 9: Comparison of experimental and calculated T~max~ vs. MIIts
relations for 3-bus at 11 kA.

![](media/image10.wmf){width="5.549305555555556in"
height="3.7944444444444443in"}

Figure 10: Peak temperatures versus MIIts plots for the 3-bus, measured
after quenches at magnet currents 7 and 11 kA.

## 4) QUENCH DETECTION VOLTAGE VS QUENCH INTEGRAL

Based on the quench propagation model presented in the test-series 1
report (TD-99-059), the voltage generated along the bus as a function of
quench integral is given by:

$V_{q} = I_{t}\rho_{\text{Cu}}\left( \text{MIIts}_{\text{max}} \right) \ast L_{\text{MPZ}}\left( I_{t} \right)\frac{1}{A_{\text{Cu}}} + 2 \cdot \text{10}^{6}\frac{v_{q}}{I_{t}A_{\text{Cu}}}\int_{0}^{\text{MIIts}_{\text{max}}}{\rho_{\text{Cu}}\left( \text{MIIts} \right)d(\text{MIIts})}$
(14)

The voltage in equation 14 is a superposition of:

-   the voltage generated in the initially quenched zone of length
    L~MPZ~ (Minimum Propagating Zone) and

-   the voltage rise generated in the rest of the bus through quench
    propagation.

The MPZ becomes shorter with rising current. Only the central zone
experiences the full MIIts number (MIIts~max~), whereas the MIIts
accumulation in the other parts of the bus starts only upon quench
arrival. In test--report 1 (TD-99-059) the main interest was focused on
the minimum quench propagation velocity v~q~ required to obtain a given
threshold detection voltage at a given MIIts budget (MIIts~max~ was set
to 270, which corresponds to a calculated temperature limit of 160 K for
the 3-bus). It was found that the range of experimental quench
propagation velocities (0.3-0.6 m/s) was compatible with the stipulated
MIIts limit (270) and typical magnet protection system threshold
voltages (100 -- 500 mV). The MIIts accumulation tests in test-series 2
allow a more precise determination of the quench detection voltage as a
function of MIIts and peak temperature. To obtain this result, the
experimental voltage vs. time traces of the intitially quenched segment
during a quench, at a given current, were transformed into resistivity
versus quench integral curves in a procedure similar to the one
described in chapter 3) and fitted with polynomes. These polynomial
ρ~Cu~(MIIts) relations were inserted together with the experimental
quench propagation velocities into equation 14 to calculate the quench
voltage. This procedure allows to extrapolate the voltage-temperature
relation beyond the experimental range. The results for both bus samples
in near operating conditions are presented in Figure 11 and Figure 12.
In the plots the calculations are compared to the actual voltage
measured on the total bus. In the calculations the MPZ was assumed to be
0.05 m at 11 kA and 0.1 m at 7 kA, which is of the same order as the MPZ
length calculated in test-report 1.

![](media/image11.wmf){width="5.445138888888889in"
height="3.729861111111111in"}

Figure 11: Comparison of calculated and measured voltage development
during a quench. 2-bus, 7 kA, 1.9 K.

Figures 11-13 can easily be interpreted in terms of peak temperatures
refering to the T~max~ vs. quench integral plots in chapter 4. For the
cases presented in the plots above the peak temperatures for a 0.5 V
quench detection voltage would be \<100 K for the 2-bus at 7 kA and
\<120 K for the 3-bus at 11 kA. Overall, these temperature indications
are only approximate because the actual magnet quench process, which
adds another \~20 MIIts to the process, is not considered. Nevertheless,
these temperature data show that the bus-bars are well protected in case
of a quench.

![](media/image12.wmf){width="5.445138888888889in"
height="3.729861111111111in"}

Figure 12: Comparison of calculated and measured voltage development
during a quench. 3-bus, 11 kA, 1.9 K.

![](media/image13.wmf){width="5.445138888888889in"
height="3.729861111111111in"}

Figure 13: Comparison of calculated and measured voltage development
during a quench. 3-bus, 7 kA, 1.9 K.

## 5) CONCLUSIONS 

The bus-bar samples tested in this test-series are suited for operation
in the LHC interaction region environment. The bus-bars did not quench
spontaneously during the entire test of the magnet, which involved
accelerator type current cycles as well as long dwell times at operation
current. The amount of copper-stabilizer in the bus cross-section is
adequate for the quench detection threshold voltages foreseen for the
LHC IR quadrupole quench protection system. The bus- bar stays within
less than 200 K after a quench.

## 6) Acknowledgments

Many thanks to Don Nurczyk, Paul Mayer, Jim Rife, Jesus Alvarez, Roger
Bossert for the sampleholder preparation, Kerry Ewald for drawings and
Daryl Orris as well as the cryogenic support team for their assistance
in the measurements.

[^1]: "Stability of Superconductors", L. Dresner, Plenum Press NY, 1995

[^2]: "NbTi alloy superconductor -- present status and potential for
    improvement", D. Larbalestier, Adv. in Cryog. Eng. Mat., Vol. 26,
    ICMC 1979

[^3]: L. Dresner, "Stability of Superconductors", Plenum Press, NY, 1995

[^4]: N. Simon, R. Reed, "Cryogenic properties of Copper and Copper
    Aloy", NIST, 1997

[^5]: M. Wilson,"Superconducting magnets", Oxford Press 1983