[^1]

*Abstract*---We report on the fabrication, assembly, and test of the
Nb~3~Sn dipole magnet HD2. The magnet, aimed at demonstrating the
feasibility 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 maximum expected bore field of 15 T at 4.3 K is
determined through 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} Superconducting Magnet Program at Lawrence Berkeley
National Laboratory (LBNL), 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. After a preliminary
description of goals and a 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, after an overview of the magnet design parameters, 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. 1, left) features two block-type coils wound
around a titanium alloy pole.

![](media/image1.png){width="1.5541666666666667in"
height="1.5541666666666667in"}![](media/image2.png){width="1.7291666666666667in"
height="1.5472222222222223in"}

Fig. 1. HD2 cross-section (left) and coil end support system (right).

The pole includes a round cutout to provide room for a 3.65 mm thick
stainless steel bore tube with a clear aperture of 36 mm. The coil has a
straight section of 475 mm, and it tilts up (flares) at a 10^o^ angle in
both ends through hard-way bends. 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 coil
cross-section has been optimized to have, in the current range of 2-17
kA, b~3~ ranging from +2.4 to -0.1 units, and a b~5~ variation from -0.4
to -0.2 units at a R~ref~ = 10 mm. The support structure is based on an
external 41 mm think aluminum shell with an outer diameter of 705 mm
(see Fig.1, left). The shell is pre-tensioned with water-pressurized
bladders. With a pre-load level for a 15 T bore field, the coil reaches
a peak stress of 180 MPa in the pole turn of layer 1. Two 50 mm thick
endplates, connected by four 18.5 mm diameter aluminum rods, provide
support the coil ends (see Fig.1, right). The complete magnet assembly
is shown in see Fig. 2.

![](media/image3.jpeg){width="3.2180555555555554in" height="2.66875in"}

Fig. 2. HD2 assembled and pre-loaded.

# 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: the
strand used for coil 1 features a lower RRR and non-Cu ratio. Both
virgin (round) strands and strands extracted from cables were reacted
with the coils to analyze magnet performance. In Fig. 3 and Fig 4 the
critical current measurements are plotted as a function of the total
magnetic fields, both for virgin and extracted strands. A self field
correction of 0.4858 T/kA is included. Data are fitted and extrapolated
at different temperatures using the ITER standard parameterization as
described in \[5\]. At 12 T and 4.2 K, the strands exhibit a critical
current degradation after cabling of 4% in coil 1 and 2% in coil 2 and
3.

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

Fig. 3. Critical current (A) vs. total magnetic field (T) measurements
and parameterization curves of round (RW) and extracted wires (XS) for
coil 1.

![](media/image5.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 magnet current limits (short sample current I~ss~) at the magnet
test temperature of 4.3 K and at 1.9 K are estimated by intersecting the
parameterization curves with the magnet load-line. The load-line
represents the peak field in the straight section of the layer 2 pole
turn computed as a function of current. The predicted short sample
current at 4.3 K is 17.3 kA or 18.1 kA, 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 the short sample 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        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.

# Test Overview

HD2 was assembled and pre-loaded at LBNL and it underwent three tests at
4.3 K: HD2a and HD2b with coil 1 (limiting coil) 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 date we considered
consistent with model expectations, after warm-up, the magnet was
cooled-down to 4.3 K, without disassembly or chanage 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 room temperature, from 36 MPa to 49
MPa.

![](media/image6.wmf){width="3.185416666666667in"
height="2.588888888888889in"}

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

![](media/image7.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 quenches occurred with a ramp-rate ≤
20 A/s. 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, ramped at 20 A/s, had a first quench at 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, still at a ramp-rate of 20 A/s, 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 the magnet managed to achieve the previous level of bore
field only after a reduction of the ramp-rate from 20 to 10 A/s
(quenched #15 and #16). A detailed comparison of the voltage signals
recorded before and after training quench #12 is presented in \[6\].

![](media/image8.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/image9.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 the 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 to Fig. 11, the quench origins in HD2a, b and c 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/image10.wmf){width="3.5069444444444446in"
height="1.2715277777777778in"}

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

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

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

![](media/image12.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 a total of 16. The quenches
were almost evenly distributed between the coils: 6 in coil 1 and 8 in
coil 2 (which features 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.
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.
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), still close to the
beginning of the hard-way bend.

In the HD2c test, coil 1 was replaced by coil 3. Out of 30 training
quenches, 28 positions were determined. All but one were again located
in the pole turn of layer 1. Most of the 16 quenches occurred in coil 3
were concentrated towards to center of the coil, around 90 mm away from
the beginning of the ramp. 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), raising the
possibility of a shift of the stainless steel mid-plane shim placed
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 quench current with respect to the short sample current as a
function of ramp-rate. For each ramp rate, only the highest quench is
shown. High ramp-rate quenches were originated both before and after
magnet training: no degradation was observed.

![](media/image13.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 at 4.3 K
at LBNL. The magnet has a clear aperture of 36 mm, with coil optimized
to minimize geometric harmonics. Three tests were performed: the magnet
reached a maximum bore field of 13.8 T (87% of I~ss~), corresponding to
an estimated peak field of 14.5 T. The quenches were almost evenly
distributes among the three coils, being coil 1 short sample limit lower
than coil 2 and 3. In addition, they were almost all 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 out a 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 Nb3Sn
    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*., "", 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>).).