[^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, has fabricated
and tested the Nb~3~Sn dipole magnet HD2. The magnet applies for the
first time block-type coils to accelerator quality dipole magnets. After
a preliminary description of goals and conceptual design reported in
\[1\], we presented the results of a detailed mechanical analysis of
coil and structure in \[2\], and documented the final design, the
fabrication and assembly procedure, as well as the field quality
expectations, in \[3\]. 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 (Ti 6Al-4V) 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 481 mm and 475 mm, respectively in
layer 1 and 2, and it tilts up (flares) at a 10^o^ angle in both ends
through hard-way bends, whose minimum radius is 349 mm at layer 2. After
the hard-way bends, the flared region features a short straight section
of 117 mm in layer 1 and 135 mm in layer 2. The tilted ends are
vertically supported by aluminum-bronze wedges surrounding the bore
tube. The coils are supported by horizontal and vertical pads. Vertical
pushers and horizontal rails transfer the load from the pads to the
coils. Two yoke halves, made of 50 mm thick iron laminations, and a 41
mm thick aluminum shell provide the external coil pre-load through
vertical and horizontal interference keys. The diameter of the cold mass
is 705 mm. The structure is pre-loaded with water pressurized bladders.
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.

![](media/image3.jpeg){width="3.0597222222222222in"
height="2.532638888888889in"}

Fig. 2. HD2 assembled and pre-loaded.

# Conductor and MAgnet Parameters

The two coil modules of HD2 are composed of two layers wound from a
continuous length of cable made of 51 RRP strands with a 0.8 mm
diameter. The cable is 22.008 mm wide and 1.401 mm thick. Three coils
were fabricated: assuming strand properties from coil 1 (Fig. 2), the
magnet has a maximum bore field of 15.1 T (4.2 K), with a conductor peak
field of 15.9 T at a current of 17.4 kA. Coil 2 and 3 feature a short
sample peak field about 0.6 T higher than coil 1.

![](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.

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

Three tests of the magnet were carried out at the LBNL test facility.
The shell and the aluminum rods (see Fig. 4 and Fig 5) were instrumented
with strain gauges, and their stress conditions were monitored and
recorded during all room-temperature loading, cool-down, and magnet
operations.

![](media/image6.wmf){width="3.2423611111111112in"
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="3.2423611111111112in"
height="2.588888888888889in"}

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

The room-temperature pre-loading operation started with minimum stress
in the outer shell, but sufficient to ensure tight contact among all
magnet components (HD2a pre-assembly). Then, the tension in the axial
rods was increased to 70 MPa (load step 2). Finally, the bladders were
pressurized to bring the shell azimuthal pre-tension to 30 MPa (load
step 3). After cool-down, the rods reached a stress of 125 MPa,
corresponding to a total axial load on the magnet ends of about 270 kN,
while the shell tension rose to 95 MPa. At these conditions, the
computed coil compression in the straight section was about 120 MPa.
SQ02 was then tested at 4.3 K, and training, ramp-rate dependence, and
spot-heater induced quenches were performed through two thermal cycles.
After warm-up, the magnet was re-loaded at room-temperature (SQ02b) with
a rod tension of 130 MPa, maintaining the shell load at the same level.
The stress reached by the rods after cool-down to 4.5 K was 190 MPa,
corresponding to a total axial load on the magnet ends of about 415 kN.
The test at FNAL included training quenches, both at 4.5 K and 1.8 K,
and ramp-rate quenches, as well as temperature dependence studies and
magnetic measurements (not part of this paper).

# Test Results

## Training Quenches

During the HD2a test, the magnet had a first quench at 12.0 T of
conductor peak field, corresponding to 73% of the expected magnet limits
and to a bore field of 11.4 T (Fig. 10). The highest current was reached
at quench #18, with a conductor peak field of 14.0 T, corresponding to
87% of the expected magnet limits and to a bore field of 13.3 T. During
the HD2b test the magnet had a first quench at 11.5 T of conductor peak
field, corresponding to 71% of the expected magnet limits and to a bore
field of 11.0 T (Fig. 10). The highest current, identical to the one
recorded during the previous test, was reached at quench #31. Because of
a failure of the extraction system, a higher number of MIITS where
released after quench #31. As a results, coil 1 exhibit an higher
ramp-rate sensitivity. After reducing the ramp rate, the magnet reached
the previous maximum current quench at #39.

![](media/image8.wmf){width="3.2708333333333335in"
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="3.3340277777777776in"
height="2.5833333333333335in"}

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

## Quench Locations

Out of 14 training quenches of the HD2a test, almost all evenly
distributed between the two coils, 12 were located in the layer 1 pole
turn, towards the end of the straight section (Fig. 11). During the HD2b
test (Fig. 12), before quench #31, 4 (6) quenches occurred in coil 1
(2). After quench #31 all quenches were located in coil 1.

![](media/image10.png){width="3.1694444444444443in"
height="1.1479166666666667in"}

Fig. 8. HD2a quench locations: coil 1 (gray markers) and coil 2 (pink
markers).

![](media/image11.png){width="3.171527777777778in"
height="1.1097222222222223in"}

Fig. 8. HD2b quench locations: coil 1 (gray markers) and coil 2 (pink
markers).

## Ramp-rate dependence study

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

Fig. 9..

# Conclusions

# References {#references .Reference-Head}

1.  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.

2.  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.

3.  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.

4.  

5.  S. Caspi, LBNL Internal Note, SC-MAG-691, October 1999.

6.  L. Chiesa, *et al.*, "Magnetic field measurements of the Nb~3~Sn
    common coil dipole RD3c", in *Proc. 2003 Particle Accelerator
    Conference*, Portland, OR, 2003, pp. 170--172.

7.  S. Hong, *et al*., "Latest improvements of current carrying
    capability of niobium tin and its magnet applications" *IEEE Trans.
    Appl. Supercond.,* vol. 16, no. 2, June 2006, pp. 1146--1151.

[^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>).).