[^1]

*Abstract*---We report on the fabrication, assembly, and test of the
Nb3Sn dipole magnet HD2. The magnet, aimed at demonstrating the
feasibility of Nb3Sn superconductor in high field accelerator-type
dipole magnets, 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
4.5 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 magnetic field
quality 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 \[1\]-\[3\], has
fabricated and tested the Nb~3~Sn dipole magnet HD2. After a preliminary
description of goals and conceptual design reported in \[4\], we
presented the results of a detailed mechanical analysis of coil and
structure in \[5\], and documented the final design, the fabrication and
assembly procedure, as well as the field quality expectations, in \[6\].
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,
ramp-rate studies and quench locations.

# 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 (Nitronic 40) bore tube with a clear aperture of 36 mm.
The coil has a straight section of about 480 mm, and it tilts up
(flares) at a 10^o^ angle in both ends through hard-way bends. The
tilted ends are vertically supported by aluminum-bronze wedges
surrounding the bore tube. Field quality. The support structure is based
on an external 41 mm think aluminum shell pre-tensioned with
water-pressurized bladders. The force provided by shell is transferred
to the coil pack through two yoke halves, made of 50 mm thick iron
laminations, separated by vertical gaps which remain open during all the
magnet operations. Horizontal and vertical pads and pushers surround the
coils and include slots to provide rooms for bladders and loading keys
In the end regions, 50 mm thick stainless steel endplates (Nitronic 40),
connected by four 18.5 mm diameter aluminum rods, constitute the coil
axial support system. Three complete magnet assemblies and loadings were
carried out (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 feature a lower RRR and non-Cu ratio than the one
implemented in coil 2 and coil 3. Both virgin (round) strands and
strands extracted from cables were reacted with the coils to predict
magnet performance.

![](media/image4.wmf){width="3.176388888888889in"
height="2.5694444444444446in"}

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

![](media/image5.wmf){width="3.2708333333333335in"
height="2.588888888888889in"}

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

In Fig. 3 and Fig 4 the critical current measurements are plotted as a
function of the applied 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 parameterization curves
described in \[7\]. 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. 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).

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 loading, cool-down,
and test. Fig. 4 and Fig. 5 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 characterized 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. After warm-up, the magnet was
cooled-down to 4.3 K without disassembly 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
bore field of 14 T.

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 peak field of 14.0 T. In the
second test (HD2b), the magnet, still ramped at 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~), 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 analysis of the change in voltage signals recorded
after training quench #12 is presented in \[8\].

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

![](media/image8.wmf){width="3.2423611111111112in"
height="2.588888888888889in"}

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 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).

## Quench Locations

The time-of-flight method was used to locate the quench origins as
discussed. 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 measurements
obtained from the test of the SQ02 magnet \[9\]. 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, the origins are projected to a plane parallel to the
coil mid-plane (all viewed from the top of the coil pack).

![](media/image10.wmf){width="3.4444444444444446in" height="1.2in"}

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

![](media/image11.wmf){width="3.44375in" height="1.2in"}

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

![](media/image12.wmf){width="3.44375in" height="1.0951388888888889in"}

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

The voltage signals recorded during the HD2a test allowed determining
precisely 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), despite the difference in expected short sample
current (see Table II). They all occurred in the pole turn of layer 1,
which features 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 conductor are hard-way
bent.

All the training quenches of HD2b were located but one. Before quench
#12, 4(6) quenches occurred in coil 1(2), confirming that the lower
current limit of coil 1 was not the limiting factor of the magnet
performance. 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. Eighteen out of 31
training quenches were located in coil 3. Fourteen out of the 18 coil 3
quenches were concentrated around 9 cm away from the voltage tap A4
towards the center of the coil. Quenches in coil 2 spread in the
straight sections of both the lead and return side. Eleven training
quenches occurred in both coils were observed during the HD2c test.
Quench started in each coil with a typical time difference of \<\~ 1 ms.
In most cases, both coils quenched independently as the quench origins
were not close to each other. However, this could be related to the
possible movement of both coils with respect to the mid-plane shim.

## 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 initiated both before and after
training: no degradation was observed.

![](media/image13.wmf){width="3.2402777777777776in"
height="2.589583333333333in"}

Fig. 9. Ratio of quench current with respect to the short sample current
as a function of ramp-rate

# Conclusions

The Nb3Sn 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.

Most of the quenches were located at the end of the straight section of
the pole turn of layer 1, which features a 4% margin in field with
respect to the pole turn in layer 2. No difference in quench performance
was observed between coil with different critical current. An lack of
support in a critical coil region appear at the moment as a possible
cause of the training quenches. As a next step: field quality, removal
of the bore tube, increase of pre-stress, test at 1.9 K

# References {#references .Reference-Head}

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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>).).