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Challenges in the Design of the Detector Solenoid for
the Mu2e Experiment
R. Ostojic, R. Coleman, I. Fang, M. Lamm, J. Miller, T. Page, Z. Tang, M. Tartaglia, R. Wands
Abstract— The Mu2e experiment at Fermilab is being
designed to measure the rare process of direct muon to electron
conversion in the field of a nucleus. The experiment comprises a
system of three superconducting solenoids which focus secondary
muons from the production target and transport them to the
stopping target, while minimizing the associated background.
The Detector Solenoid is the last magnet in the transport line and
it consists of an axially graded-field section at the upstream end,
where the stopping target is located, and a spectrometer section
with uniform field at the downstream end for accurate
momentum measurement of the conversion elections. The
Detector Solenoid has a warm bore of 1.9 m and is 10.75 m long.
The stored energy of the magnet is 30 MJ. The conceptual design
of the magnet is presented, in particular the challenge of
achieving tight magnetic field specification in a cost-effective
design.
Index Terms—Detector magnets
I. INTRODUCTION
HE Mu2e experiment at Fermilab is being designed to
measure the rare process of direct muon to electron
conversion in the field of a nucleus [1]. The experiment
comprises a system of three superconducting solenoids: the
Production Solenoid (PS), which houses the production target,
the Transport Solenoid (TS) which focuses the secondary
muons and transports them to the stopping target, and the
Detector Solenoid (DS) where the stopping target, the tracker,
calorimeter and other experiment equipment are installed. The
magnet system of the Mu2e experiment is described in more
detail in ref. [2].
The main functions of the DS are to provide a graded field
in the region of the stopping target and to provide a precision
magnetic field in a volume large enough to house the tracker
downstream of the stopping target. The inner diameter of the
magnet cryostat is 1.9 m and its length is 10.75 m. The inner
cryostat wall supports the stopping target, tracker, calorimeter
and other equipment installed in the DS. This volume is under
vacuum during operation. It is open on the upstream side,
where the DS cryostat interfaces with the TS, and sealed on
the downstream side by the muon beam stop.
The DS is designed to satisfy the field and operational
requirements defined in the DS specification document [3].
Manuscript received October 9, 2012. This work was supported in part by
the Fermi Research Alliance under DOE Contract DE-AC02-07CH11359.
R. Ostojic is with CERN, Geneva, Switzerland. Phone: +41-22-767-5146,
fax : +41-22-766-7973, e-mail: ranko.ostojic@cern.ch.
R. Coleman, I. Fang, M. Lamm, T. Page, R. Tartaglia and R. Wands are
with Fermilab, Batavia, IL 60510, USA.
J. Miller is with Boston University, Boston, MA 02215, USA.
The overall layout of the solenoid is shown in Fig. 1. It
consists of two sections: a “gradient section”, which is about
4 m long, and a “spectrometer section” of about 6 m. The
magnetic field at the entrance of the gradient section is 2 T
and decreases linearly to 1 T at the entry of the spectrometer
section, where it is uniform over 5 m.
The DS coil design is based on a high purity aluminum
sheath surrounding a Nb-Ti Rutherford cable. This type of
conductor has been used successfully in many similar
superconducting detector solenoids [4]. Aluminum has very
small resistivity and a large thermal conductivity at low
temperatures providing excellent stability. Furthermore,
aluminum stabilized conductors can be extruded in lengths of
several kilometers. Precise rectangular conductor shapes can
be obtained, allowing for high accuracy in the coil winding.
Two types of conductor are required, both 20 mm high. The
“narrow” (5.25 mm wide) conductor is used in the gradient
section, while the “wide” (7 mm wide) conductor is used in
the spectrometer section. The dimensions are optimized to
give the required field when identical current is transported in
both conductors. The conductors contain Nb-Ti Rutherford
cables with 12 and 8 strands, respectively. The strands have a
diameter of 1.3 mm, SC/Cu ratio of 1.0 and critical current of
2750 A/mm2 (4.2 K, 5 T). As a result, the conductors have
significant stability and safety margins.
In the baseline design, the gradient section is wound in two
layers using the “narrow” conductor (20 mm x 5.25 mm),
which is necessary to obtain a field of 2 T. The field gradient
is obtained by introducing several sets of spacers between coil
modules. The field uniformity in the spectrometer section is
achieved with a “wide” conductor (20 mm x 7 mm), wound as
a single layer coil.
It is envisaged that the DS coil will be wound in
standardized modules on accurately machined collapsible
mandrels. After curing, the winding mandrels are extracted
T
Fig. 1. Layout of the Detector Solenoid coils and cryostat.
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and the outer aluminum support cylinders are placed over each
module and the assembly epoxy bonded. The preassembled
modules are then electrically connected and bolted together
with spacers in a single cold mass before installation in the
cryostat.
The DS (cold mass and cryostat) weighs about 39 metric
tons. With the stored energy of 30 MJ, the ratio of stored
energy to mass of the DS magnet is 3.4 kJ/kg, which places
the magnet within the range of conservative designs [5]. The
main parameters of the magnet are summarized in Table I.
II. M
AGNET DESIGN
A. Coil
The DS coil, shown in Fig. 2, consists of 11 modules, seven
in the gradient section and four in the spectrometer section.
Two module types are used in the gradient section. They are
wound in two-layers and differ only in the number of turns
(that is active length). The modules are separated by pre-
machined spacers to give the required field profile. The
spectrometer section contains three identical modules, wound
as single layer coils. Finally, to provide a sharp field fall-off, a
short two-layer module, identical to that used in the gradient
section, is mounted on the downstream end of the magnet.
The two-layer modules are bonded with epoxy to the inner
surface of a 2 cm thick 5083-0 aluminum support cylinder,
while the thickness of the cylinder is 1 cm for single layer
modules. These thicknesses are chosen so that the support
cylinder can resist the stress generated by the full magnetic
pressure. The cylinder also provides a load path to the cold
mass support system. This aluminum grade is non-heat-
treatable and can be reliably welded without loss of strength.
The thickness of the support cylinder is locally increased in
the downstream end to provide additional stiffness in the
region of the axial supports.
The equivalent stress in the coil at various loading stages is
shown in Fig. 3. The maximum equivalent stress in the
conductor is 39 MPa. In the support cylinder, the maximum
equivalent stress is 50 MPa. Both maxima occur in the first
module of the gradient section. The stresses in the major part
of the magnet are much lower. The maximum allowable
working stress of 5083-0 aluminum at 77 K is 107 MPa, so
that the support cylinder provides structural integrity of the
coil even in the case when it takes the full load. The maximum
equivalent stress in the coil is such that some plastic
deformation can be expected during the first powering of the
magnet. This is allowable as long as the strain is small [6].
B. Cryostat
The DS cold mass is held within the cryostat by radial and
axial support systems, shown in Fig. 4. The radial support
system consists of 8 pairs of tangentially opposed Inconel 718
rods, 4 pairs at each end. The rods are 66 cm long, and
12.7 mm in diameter. The axial support system consists of
eight 1.25" Schedule 10 Inconel 718 rods, located on the
downstream end only. At the ends of each rod there is a
spherical bearing to accommodate motion due to thermal
contraction. The warm ends of the axial supports connect
directly to the cryostat outer shell.
The support system was dimensioned on the basis of
maximum loads (weight and magnetic force). The asymmetry
of the DS inherently forces the magnet towards the TS, and
the axial support system is always in tension. This axial force
depends on how accurately the solenoid is positioned relative
to the TS. Axial and radial forces were calculated with a 3-D
finite element model that included both the TS and the DS
magnets. The assumption was made that the misalignments
would not exceed 2 cm. The axial force is at a maximum when
the TS is operating and equals 100 tons. The radial centering
force with the TS off can reach 1 ton for an installation 2 cm
from the nominally centered position.
The cryostat vessel consists of concentric 2 cm thick
stainless steel cylindrical shells connected by annular end
Fig. 2. Layout of the DS coil modules. TS coils are shown on the left.
Fig. 3
. Equivalent stress inside the first coil layer for the three load cases:
cooldown, powering, and combined cooldown and powering.
TABLE
I
SUMMARY OF DETECTOR SOLENOID PARAMETERS
Parameter
Coil inner diameter
2100 mm
Coil Outer diameter
2186 mm
Coil length
10150 mm
Coil mass (m)
8800 kg
Cryostat inner diameter
1900 mm
Cryostat outer diameter
2656 mm
Cryostat length
10750 mm
Cryostat mass 30,000 kg
Nominal temperature
4.5 K
Nominal current
6115 A
Peak field
2.2 T
Stored energy (E)
30 MJ
E/m
3.4 kJ/kg
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rings. The shells are sized according to ASME Section VIII,
Div. 1 rules for cylindrical shells under external pressure.
Given that the bore of the solenoid may be evacuated while
the magnet is warm (at room temperature and pressure), both
the inner and outer shells have a design external pressure of
1 atmosphere. In addition, the inner shell must accommodate
approximately 10 metric tons of detectors, shielding and other
equipment. This load rests on rails attached to the inside of the
shell. The cryostat sits on two saddles, positioned very close to
the ends of the vessel, also shown in Fig. 4.
The cryostat provides the load path for cold mass reactions
through its support system. The axial supports bear directly
against the cryostat outer shell, and transmit the forces to the
saddle support. This arrangement essentially produces no
stresses on the cryostat. The warm ends of the radial supports
attach to the cryostat through towers, which transmit the load
through the outer shell to the saddles.
C. Quench Protection
The DS must be protected in case of a quench, whether
occurring in the body or in the leads of the magnet, and from
any malfunctions of the cooling and powering system. The
solenoid will be powered with a dedicated power convertor.
The circuit will contain protection elements for the solenoids
(circuit breakers and extraction resistors) as well as for
ancillary equipment (current leads, bus bars, grounding
circuit). The normal powering and discharge of the circuit will
be performed with ramp rates that pose negligible risk of
quench. In case of minor faults, a slow discharge of the circuit
will be launched without provoking a magnet quench. Only in
case of a major fault shall the fast discharge be engaged and
the magnet energy extracted quickly in a controlled way. This
mode of protection relies on extraction resistors, dimensioned
such that the peak voltage to ground is less than 500 V.
An analysis of the quench propagation using the QLASA
code [7], in the adiabatic regime, indicated that for a wide
range of parameters (starting quench positions and different
RRR of the Al-stabilizer) the peak temperature in the coil
remains below 85 K. As the DS design relies on Al-stabilized
conductor and an Al-support cylinder, it is expected that the
protection properties of the magnet will be strongly enhanced
by quench-back. A simulation model based on ANSYS was
developed to study behavior during quench in this case [8].
The model includes all material and dimensional features of
the conductors, and the field and eddy current distribution in
the coil and its support cylinder as function of time. This
model shows that without quench-back, the maximum
temperature in the coil is 80 K, very close to the adiabatic
result. In case of a full model including quench-back, initiated
by discharging the magnet through a dump resistor, all
sections of the magnet are resistive within a few seconds after
the quench begins. The maximum temperature in the coil is in
this case 30 K. These results indicate that the DS magnet can
be safely protected whatever the origin of the quench.
D. Thermal Analysis
The DS coil is indirectly cooled by liquid helium flowing in
tubes welded to the outer surface of the support cylinders. The
liquid helium will be supplied by either a forced-flow or
thermosiphon system. In the case of forced-flow cooling a
mass flow rate of 50 g/s and a pressure of 0.23 MPa are
provided by the Mu2e cryogenic system. Given the expected
heat load of 20 W at 4.5 K from mechanical supports and
radiation, the temperature of the liquid helium leaving the
magnet will be 0.1 degree above the entry temperature. The
maximum coil temperature rise is then 0.49 K and occurs in
the region of the axial supports.
III. M
AGNETIC FIELD ANALYSIS
For the purpose of field analysis, the DS can be divided into
four sections: DS1-DS4, shown in Fig. 5. The field on the axis
of the magnet is also shown in the figure. As can be seen,
there is a significant contribution of the TS in the gradient
section (DS1) which must be accounted for in the DS design.
Conversely, the DS coils C1-C3 have a large impact on the
field quality in the TS. Using an iterative procedure, the coils
of the DS and TS could be optimized to satisfy the field
requirements while minimizing the length of the magnets and
the volume of superconductor.
The peak field in the DS coils is 2.2 T and occurs in the first
module of the DS1 section. At the operating current of 6.1 kA,
the magnet is at 45% of conductor quench current, with a
temperature margin of 2.5 K with respect to the assumed
conductor temperature of 5.0 K. The field in other sections is
lower with a consequently larger temperature margin.
The precision of the magnetic field in the DS1 and DS3-
DS4 sections are the major design and fabrication challenges
for the DS magnet. The nominal on- and off-axis field profiles
in the DS1 and DS3-DS4 sections are shown respectively in
Fig. 6 and Fig. 7. The allowed field uniformity requirements
are also shown. The field uniformity requirements are most
stringent in the DS3 section (±1%), and are somewhat relaxed
in the DS1 and DS4 sections (±5%).
Fig. 4. Radial and axial supports of the cold mass at
the downstream end of
the DS magnet. The downstream support saddle for the cryostat is a
lso
shown.
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Detailed sensitivity analysis has established that the length
of the coil modules is the most critical for field uniformity. A
somewhat lesser sensitivity is due to the relative axial position
of the coils, while the transverse geometry of the coils after
assembly of the support cylinder and final curing (coil radius
and ovality) are the least important. A full tolerance study was
performed, assuming random choice of geometric parameters
of each of the eleven coil modules. The tolerance intervals
assumed corresponded to the standards encountered in
precision machining. The so-obtained field distributions were
analyzed for a large number of cases. The most probable field
distributions in the gradient and spectrometer sections, as well
as the peak field deviations, were shown to be in all cases
within the field uniformity requirements.
The Mu2e experiment is very much dependent on
minimizing the background, and any deviation of the field
must be closely analyzed by sophisticated and time consuming
tracking using the full 3D field. To retain the possibility of
correcting the field once the conductors and coil modules are
in production, we are considering several possibilities for local
and global adjustment of the field profile in the DS3-DS4
sections. A promising technique is to modify the spacers
between modules C6-C8 and C10-C11 (Fig. 2), adjusting their
relative axial position. Other possibilities include custom-
made modules C8 and C11. The favored trimming technique
will be decided upon once the consequences of local field
deviations on the experimental background are fully
understood.
IV. C
ONCLUSION
The Detector Solenoid for the Mu2e experiment at Fermilab
is a 2 T magnet with a conservative E/m ratio. However, the
magnet is large and the main challenge in its design and
construction is achieving tight magnetic field uniformity
specification in a cost-effective way. The conceptual design of
the magnet is complete and procurement of test samples of the
superconducting cable and its pure-Al sheath are on order.
R
EFERENCES
[1] R. Tschirhart, “The Mu2e experiment at Fermilab”,
Nucl.Phys.Proc.Suppl. 210-211 (2011) 245-248.
[2] M.J. Lamm et al., “Solenoid Magnet System for the Fermilab Mu2e
Experiment”, IEEE Trans. Appl. Supercond. Vol. 22, submitted for
publication.
[3] Mu2e Conceptual Design Report (CDR) R. Ray et al. see:
http://mu2e.fnal.gov/public/hep/general/proposals.shtml
[4] H. Minemura et al., “Construction and testing of a 3 m diameter x 5 m
superconducting solenoid for the Fermilab collider detector facility
(CDF) ”, Nucl. Instrum. Methods A, vol. 238, pp. 18-34, July 1985.
[5] A. Yamamoto, T. Taylor, Y. Makida, K. Tanaka, “Next Step in the
Evolution of Superconducting Detector Magnets”, IEEE Trans. Appl.
Supercond., vol. 18, No. 2, pp. 362-366, June 2008.
[6] B. Blau et al., “The CMS Conductor”, IEEE Trans. Appl. Supercond.,
vol. 12, No. 1, pp. 345-348, March 2002.
[7] L. Rossi, M. Sorbi, “QLASA: a computer code for quench simulation in
adiabatic multicoil superconducting windings,” INFN/TC-04/13, July
2004.
[8] M. Wake et al., “Complete Quench Simulation of Large Soleniod
Magnet”, IEEE Trans. Appl. Supercond. Vol. 22, submitted for
publication.
Fig. 7.
Comparison of the magnetic field with field tolerance in the
spectrometer section (DS3-DS4). Field tolerance is shown in green. ∆
B is
relative to a uniform field of 1.0 T. The relative field errors ∆B/B
on axis
(blue), and at a radial distance of 0.7 m (red), are shown.
Fig. 6. Comparison of the magnetic field with field tolerance in the gradient
section (DS1). Field tolerance is shown in green. ∆B is relative to a
uniform
gradient of -0.25 T/m and a field of 1.5 T at the stoppin
g target. The relative
field errors ∆B/B on axis (blue), and on a radial cone from 0.3 m to 0.7
m
starting at the upstream end of DS1 section (red), are shown.
Fig. 5. Axial field on the axis of the DS magnet. There is an
important
contribution of the TS magnet in the gradient section (DS1).