[^1]

*Abstract*---We report on the fabrication, assembly, and test of the
Nb~3~Sn dipole magnet HD2. The magnet, aimed at demonstrating the
application of Nb~3~Sn superconductor in high field accelerator-type
dipoles, features a 36 mm clear bore surrounded by block-type coils with
tilted ends. The coil design is optimized to minimize geometric
harmonics in the aperture and the magnetic peak field on the conductor
in the coil ends. The target bore field of 15 T at 4.3 K is consistent
with critical current measurements of extracted strands. The coils are
horizontally pre-stressed during assembly using an external aluminum
shell pre-tensioned with water-pressurized bladders. Axial pre-loading
of the coil ends is accomplished through two end plates and four
aluminum tension rods. The strain in coil, shell, and rods is monitored
with strain gauges during assembly, cool-down and magnet excitation, and
compared with 3D finite element computations. Magnet's training
performance, quench locations, and ramp-rate dependence are then
analyzed and discussed.

*Index Terms*---Dipole magnet, Nb~3~Sn

# INTRODUCTION

[THE]{.smallcaps} LBNL Superconducting Magnet Program, as part of the
development of Nb~3~Sn high field magnets for the next generation of HEP
colliders \[1\], has fabricated and tested the Nb~3~Sn dipole magnet HD2
(see Fig. 1). After a preliminary description of the conceptual design
reported in \[2\], we presented the results of a detailed mechanical
analysis of coil and structure in \[3\], and documented the final
design, the fabrication and assembly procedure, as well as the field
quality expectations, in \[4\]. In this paper, the results of three
tests carried out at the LBNL test facility are presented, including
strain gauges measurements, training performance, quench locations, and
ramp-rate studies.

# Magnet Design

The HD2 magnet design (Fig. 2) features two block-type coils wound
around a Ti alloy pole with a cut-out for a 36 mm aperture bore tube.
The coil has a straight section of 475 mm and in the ends tilts up at a
10^o^ angle through hard-way bends.

![](media/image1.jpeg){width="3.321527777777778in"
height="2.464583333333333in"}

Fig. 1. HD2 assembled and pre-loaded.

The peak field is located in the straight section of layer 2 pole turn:
layer 1 pole turn and the coil ends have a field margin of respectively
4% and 6%. The yoke cross-section has been design to have, in the
current range of 2-17 kA, a ∆b~3~ of ± 1.3 units and a ∆b~5~ of ± 0.1
units at a R~ref~ = 10 mm. The geometric harmonics, optimized for a
current of 16 kA, are within 0.1 units. The support structure is based
on a 41 mm think Al shell pre-tensioned with water-pressurized bladders.
With a pre-load level for a 15 T bore field, the coil reaches a peak
compressive stress of -180 MPa in the layer 1 pole turn.

![](media/image2.png){width="3.495833333333333in"
height="2.94375in"}Fig. 2. HD2 cross-section.

![](media/image3.png){width="3.4965277777777777in"
height="2.6847222222222222in"}

Fig. 3. HD2 coil end support.

Two 50 mm thick endplates, connected by four 18.5 mm diameter Al rods,
support the coil ends (see Fig. 3).

# Conductor and Magnet Parameters

Three coils, composed of two layers wound from a continuous length of
cable made of 51 RRP strands with a 0.8 mm diameter, were fabricated and
tested. The strand and cable parameters are listed in Table I. Both
virgin (round) strands and strands extracted from cables were reacted
with the coils to analyze magnet performance. In Fig 4 the critical
current measurements are plotted as a function of the total magnetic
fields, both for virgin and extracted strands used for coil 2 and 3. A
self-field correction of 0.4858 T/kA is included. Data are fitted and
extrapolated at different temperatures using the ITER standard
parameterization \[5\]. At 12 T and 4.2 K, the strands exhibit a
critical current cabling degradation of 4% in coil 1 and 2% in coil 2
and 3.

![](media/image4.wmf){width="3.2777777777777777in"
height="2.5902777777777777in"}

Fig. 4. Critical current (A) vs. total magnetic field (T) measurements
and parameterization curves of round (RW) and extracted wires (XS) for
coil 2-3.

The intersection of the magnet load-line and the 4.3 K (magnet test
temperature) parameterization curve provide an expected magnet current
limit (short sample current I~ss~) at 4.3 K of 17.3 kA or 18.1 K,
assuming respectively coil 1 or coil 2 and 3 properties (see Table II
for all magnet parameters). At 1.9 K, an increase of 1.5 T is expected
in maximum bore field.

TABLE I Cable Parameters

  ------------------------------------- ---------- ------------ ------------
  **Parameter**                         **Unit**   **Coil 1**   **Coil 2-3**

  Strand diameter (before reaction)     mm         0.802        0.801

  Process                                          RRP          

  Stack                                            54/61        

  Non Cu %                                         51           54

  RRR                                              16           287

  Twist                                 mm         13           14

  No. strands                                      51           

  Cable width (bare)                    mm         22.008       21.999

  Cable thickness (bare)                mm         1.401        1.406

  Insulation thickness                  mm         0.095        
  ------------------------------------- ---------- ------------ ------------

TABLE II Magnet Parameters

  ------------------------------------- ---------- ------------ ------------
  **Parameter**                         **Unit**   **HD2a-b**   **HD2c**

  Clear aperture                        mm         36           

  Magnet outer diameter                 mm         705          

  No. turns in layer 1 (quadrant)                  24           

  No. turns in layer 2 (quadrant)                  30           

  Short sample current I~ss~ at 4.3/1.9 kA         17.3/19.2    18.1/20.0
  K                                                             

  Bore field at 4.3/1.9 K I~ss~         T          15.0/16.5    15.6/17.1

  Coil peak field at 4.3/1.9 K I~ss~    T          15.9/17.4    16.5/18.1

  Fx/Fy layer 1 (quadrant) at 17.3 kA   MN/m       +2.3/-0.4    

  Fz layer 1 (quadrant)at 17.3 kA       kN         90           

  Fx /Fy layer 2 (quadrant) at 17.3 kA  MN/m       \+ 3.3/-2.2  

  Fz layer 2 (quadrant) at 17.3 kA      kN         126          

  Stored energy at 17.3 kA              MJ/m       0.84         

  Inductance                            mH/m       5.6          
  ------------------------------------- ---------- ------------ ------------

HD2a and HD2b were assembled with coil 1 and coil 2. HD2c was assembled
with coil 2 and coil 3.

# Assembly and Test Overview

HD2 underwent three tests at 4.3 K: HD2a and HD2b with coil 1 and coil
2, and HD2c with coil 2 and coil 3. The shell and the aluminum rods were
instrumented with strain gauges, and their stress conditions were
monitored and recorded during all room-temperature loadings, cool-downs,
and tests. Fig. 5 and Fig. 6 show the evolution of the shell and rod
stress, with a comparison with the expectations from a 3D finite element
model of the entire magnet assembly \[2\].

In order to mechanically characterize the structure and validate the
numerical model, a first cool-down to LN temperature was performed. Coil
1 and coil 2 were assembled and pre-loaded inside the structure. During
cool-down, the tension increased from 49 MPa to 135 MPa in the shell and
from 34 MPa to 83 MPa in the rods.

Since the data were considered consistent with model expectations, after
warm-up the magnet was cooled-down to 4.3 K, without disassembly or
change in pre-load, and tested (HD2a). At 4.3 K the measured shell
stress was 144 MPa, while a total axial force of 560 kN was provided to
the coil ends by the rods tensioned to 90 MPa. According to the model,
this stress conditions in the structure results in a coil peak stress in
the straight section of -149 MPa and ensures no separation coil-pole,
both in the straight section and in the end region, up to a 14 T bore
field.

HD2b test was carried out after a minor adjustment of the coil end
support, without unloading the shell.

The last tests (HD2c) followed a complete disassembly where coil 1 was
replaced by coil 3 and the shell tension was increased by 13 MPa at 293
K, from 36 MPa to 49 MPa.

![](media/image5.wmf){width="3.185416666666667in"
height="2.588888888888889in"}

Fig. 5. Azimuthal stress (MPa) of the 41 mm thick aluminum shell during
pre-load and tests: measured values (markers) and model expectations
(dashed lines).

![](media/image6.wmf){width="3.185416666666667in"
height="2.595138888888889in"}

Fig. 6. Axial stress (MPa) of the four 18.5 mm diameter rods during
pre-load and tests: measured values (markers) and model expectations
(dashed lines).

# Test Results

## Training Quenches

The training histories of the three tests are shown in Fig. 7, where the
bore field is plotted for all the low ramp-rate quenches. The bore field
was measured with a Hall probe placed in the longitudinal center of the
magnet (see Fig. 8 for a measured and computed bore field vs. current).

HD2a had a first quench at a bore field of 11.4 T (73% of I~ss~). After
16 quenches it reached a maximum bore field of 13.3 T (87% of I~ss~),
corresponding to an estimated coil peak field of 14.0 T. In the second
test (HD2b), the magnet did not exhibit memory of the previous quench
performance, and, after a first quench at 11.0 T (71% of I~ss~), it
trained to the same maximum field after 12 quenches.

Because of a failure of the extraction system during quench #12, the
number of MIITS released to coil 1 (quenching coil) increased from 16 to
23. As a result, higher ramp-rate sensitivity was observed, and a
reduction of the ramp-rate from 20 to 10 A/s was required to achieve the
previous level of bore field (quenches #15 and #16). A detailed
comparison of the voltage signals recorded before and after training
quench #12 is presented in \[6\].

![](media/image7.wmf){width="3.2493055555555554in"
height="2.5902777777777777in"}

Fig. 7. Training quenches in HD2a, HD2b, and HD2c. The short limit of
15.0 (15.6) T bore field corresponds to a coil peak field of 15.9 (16.5)
T. All the plotted quenches occurred at a current ramp rate ≤ 20 A/s.

![](media/image8.wmf){width="3.2493055555555554in"
height="2.5902777777777777in"}

Fig. 8. Measured and computed bore field (T) vs. magnet current (A).

After a 13 MPa increase of shell tension and the replacement of coil 1
with coil 3, the magnet was retested as HD2c. Despite an increase of the
expected short sample limit (see Table II), the training was similar as
in the previous tests; the magnet, at a ramp rate of 5 A/s, reached a
maximum bore field of 13.8 T (87% of I~ss~) at quench #30, corresponding
to an estimated peak field of 14.5 T.

## Quench Locations

The time-of-flight method was used to locate the quench origins. The
voltage signals were monitored using derivative amplifier with a
resolution of 5 kHz. Normal zone propagation velocity was determined
based on the correlation between I~q~/I~ss~ and the velocity v given by
v = a ⋅ exp(b ⋅ I~q~/I~ss~), where a = 0.590, b = 4.554, I~q~ is the
quench current, and I~ss~ is the current limit of the quenching segment.
The correlation was obtained from test results of the SQ02 magnet \[7\].
Equal and constant velocities of both normal fronts were assumed. In
Fig. 9-11, the quench origins in HD2a, HD2b and HD2c are plotted. The
inner and outer loops represent respectively the pole turn of layer 2
and layer 1, while the vertical dashed lines indicate the end of the
straight section, approximately where the cable hard-way bend starts.
For each magnet test, the origins are projected to a plane parallel to
the coil mid-plane.

![](media/image9.wmf){width="3.5069444444444446in"
height="1.2715277777777778in"}

Fig. 9. HD2a quench locations: coil 1 (diamond markers) and coil 2
(round markers).

![](media/image10.wmf){width="3.490972222222222in"
height="1.2715277777777778in"}

Fig. 10. HD2b quench locations: coil 1 (diamond markers) and coil 2
(round markers).

![](media/image11.wmf){width="3.490972222222222in"
height="1.2715277777777778in"}

Fig. 11. HD2c quench locations: coil 3 (diamond markers) and coil 2
(round markers).

The voltage signals recorded during the HD2a test allowed determining
the position of 14 training quenches out of 16 (see Fig. 9). The
quenches were almost evenly distributed between the coils: 6 in coil 1
and 8 in coil 2 (which featured a higher expected short sample current).
They all occurred in the pole turn of layer 1, which has a 4% margin in
field with respect to the pole turn in layer 2. In addition, they were
all located towards the end of the straight section, close to the region
where the conductors are hard-way bent.

All the training quench locations of HD2b were identified but one (see
Fig. 10). Before quench #12, 4(6) quenches occurred in coil 1(2),
confirming that the lower current limit of coil 1 was not affecting the
magnet training. After quench #12, the remaining four quenches took
place all in coil 1 (indicating a possible conductor damage). Most of
the quenches (12) were again located towards the end of the straight
section of layer 1 pole turn, while three occurred in the pole turn of
layer 2 in coil 1 (peak field region).

In the HD2c test, coil 1 was replaced by coil 3. Out of 30 training
quenches, 28 positions were determined (see Fig. 11). All but one were
again located in the pole turn of layer 1. Most of the 16 quenches
occurred in coil 3 were concentrated at a single location 90 mm from the
ramp towards to center of the coil. The 12 quenches in coil 2 spread in
the straight sections of both the lead and return side. It was also
recorded that, for 11 times during training, quenches occurred
simultaneously (within 1 ms) in both coils and in adjacent locations
(pole turn, layer 1, similar longitudinal location, same coil side),
indicating that quenches started at the mid-plane in between the two
coils.

## Ramp-rate dependence study

Ramp-rate dependence studies were performed during the HD2c test.
Ramp-rate was varied from 300 A/s to 5 A/s. In Fig. 12, we plot the
ratio of the highest quench current with respect to I~ss~ as a function
of ramp-rate. High ramp-rate quenches were originated both before and
after magnet training: no degradation was observed.

![](media/image12.wmf){width="3.2402777777777776in"
height="2.589583333333333in"}

Fig. 12. Ratio of quench current with respect to I~ss~ as a function of
ramp-rate

# Conclusions

The Nb~3~Sn dipole magnet HD2 was assembled, loaded, and tested three
times at 4.3 K at LBNL. The coil design includes a clear aperture of 36
mm and has been optimized to minimize geometric harmonics. The magnet
reached a maximum bore field of 13.8 T (87% of I~ss~), corresponding to
an estimated peak field on the conductor of 14.5 T. The quenches were
almost evenly distributes among the coils, despite of differences in
conductor properties. In addition, they were mostly located at the end
of the straight section of the layer 1 pole turn, where the field is
about 4% lower than in layer 2. At the moment, the quench performance
seems to point at a possible lack of mechanical support in the mid-plane
area close to the coil hard-way bend. Further tests are considered in
the coming months to perform field quality measurements, to increase the
clear aperture, and to optimize coil pre-load.

# References {#references .Reference-Head}

1.  A. F. Lietzke, *et al.,* "Test results for HD1, a 16 Tesla Nb~3~Sn
    dipole magnet", *IEEE Trans. Appl. Supercond*., vol. 14, no. 2, June
    2004, pp. 345-348.

2.  G. Sabbi, *et al.,* "Design of HD2: a 15 T Nb~3~Sn dipole with a 35
    mm bore", *IEEE Trans. Appl. Supercond.,* vol. 15, no. 2, June 2005,
    pp. 1128-1131.

3.  P. Ferracin, *et al.,*"Mechanical design of HD2, a 15 T Nb~3~Sn
    dipole magnet with a 35 mm bore", *IEEE Trans. Appl. Supercond.,*
    vol. 16, no. 2, June 2006, pp. 378-381.

4.  P. Ferracin, *et al.,* "Development of the 15 T Nb~3~Sn Dipole HD2",
    *IEEE Trans. Appl. Supercond.*, vol. 18, no. 2, June 2008, pp.
    277-280.

5.  A. Godeke, B. ten Haken, H. H. J. ten Kate, and D. C. Larbalestier,
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    Nb~3~Sn", *Supercond. Sci. Technol.,* vol*.* 19, 2006, pp.
    R100--R116.

6.  J. Lizarazo, *et al*., "Use of High Resolution DAQ System for Fast
    Voltage Transients to Aid Superconducting Magnet Diagnosis",
    presented at *2008* *Applied Superconductivity Conference*, Chicago,
    IL, USA, August 17-22, 2008.

7.  P. Ferracin, *et al.,* "Assembly and Tests of SQ02, a Nb3Sn
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[^1]: ^^Manuscript received 19 August 2008. This work was supported by
    the Director, Office of Energy Research, Office of High Energy and
    Nuclear Physics, High Energy Physics Division, U. S. Department of
    Energy, under Contract No. DE-AC02-05CH11231.

    All authors are with Lawrence Berkeley National Lab, Berkeley, CA
    94720 USA (phone: 510-486-4630; fax: 510-486-5310; e-mail:
    <pferracin@lbl.gov>).).