# SPY: A Magnet System for a High-pressure Gaseous TPC Neutrino Detector

Andrea Bersani  Alan D. Bross  Michael Crisler  Stefania Farinon  Christopher
Hayes  Donald Mitchell  Riccardo Musenich  Colin Narug  Jay Theilacker  Terry
Tope  Erik Voirin  Vivek Jain

###### Abstract

We present a novel conceptual design for a magnet system that provides the
magnetic field necessary for the analysis of tracks in a high-pressure gaseous
argon TPC while simultaneously serving as a pressure vessel to contain the TPC
gas volume. The magnet was developed within a Near Detector proposal for the
Deep Underground Neutrino Experiment (DUNE). The high-pressure gaseous argon
TPC is a component proposed to be one of the elements of an ensemble of near
detectors that are needed for DUNE.

##  1 Introduction

A key aim of the DUNE experiment is to measure neutrino interaction rates from
which the oscillation probabilities for muon (anti)neutrinos to either remain
the same flavor or oscillate to electron (anti)neutrinos can be extracted. The
DUNE Far Detector, located at the Sanford Underground Research Facility,
$1300\,\mathrm{km}$ away from the neutrino source at Fermilab, will measure
the neutrino interaction rate after oscillations. The Near Detector complex,
located on the Fermilab site $\simeq 570\,\mathrm{m}$ from the neutrino
target, will measure the un-oscillated neutrino flux, providing the
experiment’s control sample. A robust understanding of the neutrino flux at
the source will require measurements both on and off the beam axis at the near
site, in addition to continuous monitoring of the on-axis flux which will be
done by a beam monitor called SAND (System for on-Axis Neutrino Detection).

Detailed studies of the neutrino flux both on and off axis will be be done
using a modular liquid argon detector with pixel readout called ND-LAr,
supplemented by an iron range stack to measure the momentum of muons exiting
ND-LAr. This will be the initial configuration. In order to meet all of DUNE’s
physics goals, a detector that can measure neutrino interactions on argon with
a precision even better than in ND-LAr is needed, however. This detector must
also measure the momentum of muons that exit ND-LAr as mentioned above. A
proposal for this enhanced Near Detector, called ND-GAr, includes a high-
pressure (10 bar) gaseous argon time projection chamber (HPgTPC) system [1]
surrounded by an electromagnetic calorimeter where both are in a magnetic
field. ND-GAr must also be designed to be movable and to operate in multiple
positions. The DUNE Near Detector system including ND-GAr is shown in Figure
1.

Figure 1: The Near Detector Suite of Detectors: the neutrino beam travels from
the right to the left, crossing in sequence ND-LAr, ND-GAr and SAND

The focus of this paper is the conceptual design of an integrated magnet and
pressure vessel system for ND-GAr. The magnet system consists of a
superconducting solenoid surrounded by an iron return yoke. To control the
physical size and cost of the magnet system, we have developed an integrated
design for the superconducting solenoid cryostat so that it will also serve as
the cylindrical component of the pressure vessel for the HPgTPC, while at the
same time providing support for the HPgTPC and calorimeter elements located in
its bore. The mechanical design and stress analysis of the solenoid cryostat
will be presented in subsequent sections. Additionally, the design of the iron
magnet yoke uses the mechanical strength of the yoke’s pole faces to eliminate
the large domed heads that would normally be required for a large-diameter
pressure vessel. The stayed-head design that closes the pressure vessel will
be described in detail in Section 6. The stayed-head design shortens the
overall dimension of the system transverse to the beam by approximately 4m.
The incremental cost of strengthening the solenoid cryostat is small compared
to the cost of a separate pressure vessel which is estimated to be greater
that half the cost of the superconducting solenoid. An important design
requirement for ND-GAr is the ability to accurately measure the momentum of
muons that originated in ND-LAr. This requirement limits the amount of
material allowed on the upstream side of ND-GAr and forces us to adopt an
unsymmetrical iron yoke. To address this issue, we have developed an iron yoke
that eliminates a portion of the iron along the entering particle paths. The
system is called SPY – Solenoid with Partial return Yoke. A schematic of ND-
GAr is shown in Figure 2 where the missing section of the yoke is shown. A
cut-away view is shown in Figure 3 which shows the coils, ECAL components, and
the HPgTPC. A possible location for the cryogenic feed can is also shown.
Development of the design concepts for the HPgTPC and the ECAL continue, but
the overall dimensions and requirements have been defined in an earlier phase
of the proposal’s development [2], allowing for a reliable design of the
magnet system.

Figure 2: The SPY magnet system.

.

Figure 3: Cut-away view showing the various components of ND-GAr.

In this document we will layout the requirements for the SPY magnet system and
present details of the conceptual design. The superconducting solenoid design
is conservative, following the design of existing magnets and using known best
practices in the field of superconducting magnet technology. We have analyzed
the impact of the partial yoke design on magnetic field uniformity and on
fringe fields and show that both can meet the requirements of the experiment.

##  2 Magnet design evolution

Two alternate magnet designs were considered prior to selecting the design
presented here. The first option considered was a conventional (non-
superconducting) magnet, similar to the magnet that was used in UA1 and is now
in use in the T2K near detector. For the field strength and volume required by
ND-GAr, a conventional magnet was quickly ruled out due to its power budget,
$\simeq 6\,\mathrm{MW}$, and because it was too large to fit within the
required space. When considering superconducting solutions, a superconducting
solenoid was felt to be the best technical option, but was not initially
considered based on the anticipated cost. The first superconducting design
considered used 5 coils in a Helmholtz coil configuration and became the
baseline design [3, 2].

We eventually became aware of a magnet produced by ASG Superconductors in
Italy for the Multi Purpose Detector (MPD) at the NICA Collider at JINR [4].
The MPD-JINR magnet has a smaller bore than is required for ND-GAr, but
otherwise would meet all the requirements for the ND-GAr magnet. In addition
ASG felt that they could deliver a solenoid magnet suitable for ND-GAr at a
cost significantly below our estimated cost for the Helmholtz coil system. The
magnet group within ND-GAr then focused on a solenoid solution which has now
become the baseline design. The ND-GAr solenoid design closely follows the
concepts developed for the MPD-JINR magnet. Table 1 compares the operational
specifications of the JINR magnet to the current design parameters for the
solenoid and yoke for ND-GAr.

Table 1: JINR MPD magnet specifications (as tested) vs. the ND-GAr magnet system design parameters. | JINR-MPD | ND-GAr
---|---|---
Field (T) | 0.5 | 0.5
Field uniformity (%) |  $\pm$ 0.1 |  $\pm$ 1
Stored energy (MJ) | 25 | 32.5
Warm bore (m) | 4.7 | 6.725
Length (m) | 7.9 |  $\simeq$ 7.8
Yoke thickness (mm) | 350 | 150-400
Yoke mass (t) | 725 | 757
Detector mass (t) | 166 |  $\leq$ 185

##  3 Magnetic system specifications

As discussed in Section 1, ND-GAr is one component of a potential three-
component suite of detectors at the DUNE near site. As such, the magnetic
system has to meet ND-GAr specifications and has to operate within a number of
constraints imposed by the 3-detector configuration. They are:

  * •

Magnetic: The momentum analyzing power of ND-GAr must provide at least 3%
momentum resolution for the ND-LAr muons. For particles produced as a result
of neutrino interactions in the argon gas, the analyzing power must produce a
resolution in neutrino energy reconstruction at least as good as that of the
DUNE far detector

  * •

Geometrical: ND-GAr must provide good acceptance for muons exiting ND-LAr and
must fit within the space constraints imposed by the Near Detector hall
design.

  * •

Mechanical: ND-GAr’s magnet system must present as little material as possible
in the path of the muons exiting from ND-LAr and must have a minimum quantity
of material in the downstream face of the yoke to assist in the discrimination
of muons from pions.

In this section we will describe in detail the SPY magnet system design
specifications.

###  3.1 Magnetic: Field and field quality

The main requirement for the SPY magnet system is on the magnetic field that
will be needed by the tracker that will be used in this detector. The HPgTPC
design is based on the ALICE TPC [5] at the LHC. The TPC will be cylindrical,
$\simeq 5.2\,\mathrm{m}$ long and $\simeq 5.2\,\mathrm{m}$ in diameter. The
TPC axis will be horizontal and perpendicular to the neutrino beam direction.
The HPgTPC will provide excellent tracking resolution and we have determined
that a relatively low magnetic field of $0.5\,\mathrm{T}$ will be sufficient
to attain the desired momentum resolution.

Thanks to the recent and expected future improvements in software
reconstruction and computing power, the requirement on field uniformity is
significantly looser than in previous TPC-based detectors. From this
perspective, the requirement is $\pm 10\%$ with the stipulation that an
accurate field map of the “as-built" system is performed. The field quality
achieved in the simulation of our current magnet system design already
significantly exceeds this specification. See Table 3.

###  3.2 Geometrical constraints

The outer size of the magnet system is constrained by the available space in
the experimental hall. The maximum height is defined by the $12\,\mathrm{m}$
clearance under the overhead crane. This is not a real constraint for the
magnetic design, but it may impact the design of the cryogenic feed can (see
Figure 3). The width of the iron return yoke, in the beam direction, is the
most constrained dimension as shown in Figure 1. The available space is
$8.82\,\mathrm{m}$, in which a stay-clear between ND-GAr and ND-LAr on one
side and between ND-GAr and the wall on the other side is required. To achieve
the best utilization of the available space, a novel integration approach has
been developed, which uses the solenoid cryostat as the HPgTPC pressure vessel
body and uses the mechanical strength of the magnet yoke to close the pressure
vessel ends with very thin covers using a stayed head design.

###  3.3 Mechanical: Material budget

An important systematic uncertainty on the measurement of muons that exit the
LAr detector arises from muon energy loss in non-active material between ND-
LAr and ND-GAr. In order to determine the muon momentum with the required
precision, we have imposed a requirement, based on simulations, that the total
amount of dead material in the muon path as it travels from the active region
of ND-LAr to the active region of ND-GAr be less than 100 g/cm2. The dead
material in ND-GAr is limited to 50% of this amount, or 50 g/cm2. The opening
in the return yoke solves this problem for the iron, so this requirement
defines the total mass allowed for the solenoid and its cryostat/pressure
vessel. The material budget for the current solenoid design is shown in Table
2. The reported values already consider some contingency, namely on the coil
former thickness, and therefore we can conclude that the design fulfills the
50 g/cm2 limit.

Table 2: Material budget for solenoid. Component | Material | Thickness (mm) |  $\rho$ (g/cm3) |  g/cm2
---|---|---|---|---
Outer vacuum vessel wall | Stainless steel | 25 | 7.87 | 19.68
LN2 shield | Al | 4 | 2.70 | 1.08
Coil former | Al | 40 | 2.70 | 10.8
Coil | mainly Al | 20 | 2.70 | 5.4
LN2 shield | Al | 4 | 2.70 | 1.08
Inner vacuum vessel wall | Stainless steel | 16 | 7.87 | 12.59
TOTAL |  |  |  | 50.63

##  4 Magnetic design

###  4.1 Design principles

The solenoid design is based on the decades-long evolution of internally
wound, aluminium-stabilised cable for superconducting magnets, starting with
CELLO [6], and including CDF [7], Delphi [8], BaBar [9], and many others. The
$0.5\,\mathrm{T}$ central field permits a single-layer coil to provide the
needed current density even with our very large magnetic volume. The design
parameters are conservative when compared to previously built magnets. The
main parameters of the proposed magnetic design are summarized in Table 3.

The magnetic calculations have been performed with ANSYS Maxwell finite
element software which is a state-of-art optimized tool for the simulation of
low-frequency electromagnetic fields in industrial components. It includes
3D/2D magnetic transient, AC electromagnetic, magnetostatic, electrostatic, DC
conduction and electric transient solvers to accurately solve for field
parameters including force, torque, capacitance, inductance, resistance and
impedance [10].

Table 3: SPY magnetic parameters. Parameter | Value | Unit
---|---|---
Central field | 0.5 | T
Field uniformity | $\pm 1$ | $\%$
Operating current | 4585 | A
Inductance | 2.75 | H
Force on coil (in neutrino beam direction) | 150 | kN
SAND magnet stray field in ND-GAr tracker | $<10^{-3}$ | T
SPY stray field in SAND tracker | $<5\cdot 10^{-4}$ | T
SPY stray field in ND-LAr fiducial volume | $<10^{-2}$ | T

###  4.2 Coil and coil former design

The coil design is based on a rectangular cable with dimensions $\simeq
20\times 7.5$ mm2 and will be wound on its long axis, the so-called “hard-way
bend" wind. With this cross section, the overall current density is $\sim
30.5\,\mathrm{A/mm^{2}}$. An analysis of the benefits of a reduction of the
inductance (fewer turns/higher current), to allow for faster charge and
discharge of the magnet, versus more turns with lower current, to keep the
voltage as low as possible during quenches drove this choice. The maximum
field on the cable, according to our calculations, is below $1\,\mathrm{T}$.
The cable supplier will be requested to supply a cable with a sufficient
amount of superconductor such that the cable can carry twice the design
current at twice the maximum field at the operating temperature, i.e.
$10,000\,\mathrm{A}$ at $2\,\mathrm{T}$ and at $4.5\,\mathrm{K}$. The
superconductor will be co-extruded in high purity aluminium to provide quench
protection in the worst case. A possible solution for the cable, based on
Niobium Titanium, could be a Rutherford cable made of 10 strands,
$0.8\,\mathrm{mm}$ diameter, 1:1 Cu/SC ratio, co-extruded in high purity
aluminum.

Figure 4: Conceptual cut-away view showing the coil in the coil former with
the main components of the cold mass. The complete solenoid will be built out
of six coil assemblies (coil + former), connected with spacers.

The coil will be built in segments (see Figure 3), to be joined before
insertion in the cryostat. Six identical subcoils are foreseen, each with a
$7000\,\mathrm{mm}$ internal diameter, $900\,\mathrm{mm}$ length and
$20\,\mathrm{mm}$ thickness. Each subcoil will be internally wound in a coil
former made of aluminium alloy. The subcoils will then be mechanically joined
with spacers and the electrical connections between the superconducting cables
will be made. Each subcoil will provide $550\,\mathrm{kA\cdot turn}$, for a
total of $3.3\,\mathrm{MA\cdot turn}$. As a design guideline, we decided to
keep the current below $5000\,\mathrm{A}$ to avoid high voltages during
quenches. This can be achieved with 120 turns for each subcoil operating at
$\sim 4585\,\mathrm{A}$. The calculated stored energy with this configuration
is $\sim 32.5\,\mathrm{MJ}$. The inductance of the magnet is $\sim
2.75\,\mathrm{H}$. The coil dimensions are given in Table 4.

Table 4: Coil Dimensions. Measurement | Former (mm) | Coil (mm)
---|---|---
ID | 7000 | 7000
OD | 7120 | 7040
Length | 1000 | 900

###  4.3 Thermal design philosophy and cryogenic delivery system

In order to reach an operating temperature of between 4.5K and 4.7K, the six
superconducting coils will be conduction cooled by a thermosiphon-driven flow
of liquid helium in pipes welded onto the outer surface of the coil former as
shown in Figure 4. An aluminum thermal shield is also required for stable
operation and to minimize heat load to the liquid helium. It will be either
cooled by cold helium gas or by liquid nitrogen, depending upon the final
refrigerator design. This implies that the shield would operate either near
50K or near 80K. The feed can design is only conceptual at this point, but we
have chosen high-temperature superconductor for the current leads to minimize
the liquefaction load on the cryogenic refrigerator and the thermal load in
general.

The cryogenic fluids will be provided through a cryogenic distribution system
in the experimental hall and will deliver liquid helium and liquid nitrogen in
vacuum insulated flex-hoses supported by an articulating pipe carrier. The
system provides cryogens to the feed-can that will be mounted on a work
platform that is secured to the top of SPY.

These cryogenic services will be installed in parallel during the construction
of ND-GAr. The feed-can installation followed by cryogenic connections and
coil lead splices will be the last activities necessary to complete the cryo
system. We note that the superconducting magnet assembly will have already
been tested at the vendor fabrication site for vacuum leaks, cryosgenic issues
at 4.5K, electrical shorts, splice resistances, etc. in the course of a
superconducting low-field test.

###  4.4 Yoke design

The magnet system for a typical collider detector would have an iron yoke
which would include return sections of sufficient cross-sectional area to
fully contain the return magnetic field in iron and thus minimize any fringe
fields. Typically, the return sections would be azimuthally symmetric with
respect to the magnetic axis to minimize field distortions. Fully symmetric
return sections are not possible for the SPY magnet because of the two
requirements previously mentioned:

  1. 1.

We must eliminate any significant thickness of iron on the upstream face of
the yoke to minimize the energy loss of muons passing from ND-LAr to ND-GAr.

  2. 2.

A minimum quantity of material is required on the downstream face of the yoke
to assist in the discrimination of muons from pions.

The first requirement was satisfied by eliminating the iron from a segment of
the front face of the magnet, creating an “entrance window” for incoming
muons. A symmetrized magnet design was considered in which the corresponding
segment of iron on the down-stream face was removed and replaced by non-
magnetic material to meet the muon discrimination requirement while preserving
magnetic symmetry. The remaining iron was then thickened to meet the
requirement of field containment. The resulting design failed to meet the
space and weight requirements for ND-GAr, however. The SPY yoke design uses
only carbon steel and mirrors the open entrance window on the upstream face of
the magnet with a set of thinned return segments on the downstream side.
Because of the required design compromises, detailed simulations were required
to validate the final choice of design parameters. A field map within ND-GAr
is shown in Figure 5.

Figure 5: Magnetic field strength in ND-GAr: a complete 3D model has been
developed and a field map on the horizontal plane crossing the detector center
is shown. This section is the most asymmetric, due to the asymmetry of the
iron yoke. The TPC volume is defined by the black rectangle.

##  5 Stray field analysis

The SPY magnet will operate in close proximity to two other detectors and
therefore special attention to stray field is needed. Since the ND-GAr
detector will be movable, the cross talk between the three detectors has to be
evaluated in different configurations. A field map on the horizontal plane
crossing the center of ND-GAr is shown in Figure 6.

Figure 6: Magnetic field strength in the horizontal plane crossing the center
of ND-GAr: This model includes the complete set of detectors and several
calculations have been performed with different configurations. Here the
nominal one is shown, with ND-GAr and SAND magnetic fields at nominal value
(and in the same direction) and the three sub-detectors aligned on the beam:
SAND, ND-GAr and ND-LAr left to right. For a better visualization of the
fringe field, a logaritmic scale between $30\,\mathrm{G}$ and $3\,\mathrm{T}$
is used.

###  5.1 Field interactions with SAND

We evaluated the interaction between the SPY magnet system’s stray field and
SAND. Since SAND is a magnetic spectrometer as well, our analysis must also
consider the effect of the SAND field and iron yoke on ND-GAr. The operating
parameters for SAND have been obtained from KLOE publications[11, 12].

The magnetic field in SAND is provided by a superconducting solenoid and has a
central field design value of $0.6\,\mathrm{T}$. Its iron yoke is designed to
fully and efficiently contain the stray field. A small cross talk between the
two magnets exists and is due to SPY’s stray field interacting with the return
iron of SAND. The contribution from SPY in the active volume inside SAND is
negligible ($\leq 0.005\,\mathrm{T}$) and is well below SAND’s field
uniformity specification of 1%. The magnetic interaction with SAND introduces
on the order of a $0.001\,\mathrm{T}$ variation on the field in SPY with all
detectors on axis and the SAND magnet on. For the various other possible
configurations of the Near Detector, i.e. SAND magnet off and ND-GAr on-axis,
SAND magnet on and ND-GAr either on-axis or off-axis, we have calculated that
the maximum deviation from the field within SPY alone will be less than
$0.0025\,\mathrm{T}$ in all configurations. This is $0.5\%$ of the design
field, and this value is expected only in the peripheral volume of the HPgTPC.
It is well within the field uniformity specification (see Table 1).

###  5.2 Stray field on ND-LAr

The stray field on ND-LAr is more critical, due to the small thickness of
magnetic material between SPY and the liquid argon TPC. In the current design,
only a few millimeters of carbon steel are in the exit window of ND-LAr.

Due to the complexity of the design of ND-LAr’s cryostat support structure, a
simplification of the cryostat had to be introduced in the simulation. The
cryostat was modeled as a solid layer of iron of equivalent mass for each side
of ND-LAr’s cryostat.

The analysis shows that in the current design, SPY’s stray field will produce
some field throughout the entire volume of the LArTPC, ranging from
$0.001\,\mathrm{T}$ to $0.02\,\mathrm{T}$. The field quickly decreases from
the side facing ND-GAr to the side from which the neutrino beam is coming.
Even in the worst situation, in less than $5\%$ of the active volume does the
field exceed $0.01\,\mathrm{T}$. In the fiducial volume of the ND-LAr, the
stray field is in the range of $0.002\,\mathrm{T}$ to $0.005\,\mathrm{T}$. A
field map in this volume is shown in Figure 7.

Figure 7: The stray magnetic field strength in the fiducial volume of ND-LAr:
the volume is seen from above and the neutrino beam travels from the top to
the bottom of the figure. The support structure for this detector provides a
significant complication in the FE model and has therefore been simplified to
be just a layer of iron of equivalent mass for each side. The colored region
with field indication (colored) represents the 6m wide by 3.5m deep fiducial
volume, the shaded region just outside the fiducial volume shows the total
active volume (7m wide by 5m deep) of LAr and the outer box in red indicates
the the solid iron representation of the cryostat support structure.

###  5.3 Stray field on services

Several locations for services, including front-end electronics and power
transformers, have been evaluated. The most critical volumes are above SAND
and above ND-LAr, where much of the electrical equipment (pumps, sensor
electronics, etc.) is expected to be installed. According to our calculations,
the stray field in a volume extending $2\,\mathrm{m}$ in height above ND-LAr
is limited to $0.01\,\mathrm{T}$. Two maps of the magnetic field in the whole
detector area, on two horizontal planes, are shown in Figure 8 and Figure 9 at
$10\,\mathrm{m}$ and $12.5\,\mathrm{m}$ height above the detectors’ center
plane, respectively.

Figure 8: Magnetic field strength in horizontal plane $10\,\mathrm{m}$ above
ND-LAr’s and ND-GAr’s center. Figure 9: Magnetic field in horizontal plane
$12.5\,\mathrm{m}$ above ND-LAr’s and ND-GAr’scenter.

##  6 Mechanical design

###  6.1 Design requirements

The design requirements for the mechanical system are as follows:

  1. 1.

Provide a vacuum cryostat capable of providing mechanical support and
cryogenic environment for the superconducting coils.

  2. 2.

The inner wall of the vacuum cryostat must be sufficiently strong to serve as
the outer wall of the pressure vessel for the HPgTPC.

  3. 3.

The vacuum cryostat walls must be sufficiently strong to provide mechanical
support for the ECAL and HPgTPC.

  4. 4.

Provide a carbon steel return yoke for the magnet that can sufficiently
maintain a uniform 0.5T central field over the length of the solenoid and
contain the fringe fields to the level required by the experiment.

  5. 5.

Provide flat carbon steel pole tips for the magnet return yoke that match the
magnetic field boundary conditions at the ends of the solenoid and provide the
mechanical support for the pressure vessel end flanges.

An additional physics requirement is to measure neutrino interactions in an
off-axis position. To meet this requirement, ND-GAr must be able to move
perpendicular to the beam.

###  6.2 Pressure Vessel design analysis approach

The analysis of ND-GAr’s pressurized system was performed to meet the
requirements of Fermilab’s Environment, Safety, and Health Manual (FESHM),
Chapter 5031[13] and the ASME Boiler and Pressure Vessel Code (BPVC). Due to
the unique design of the vessel, the design and analysis of ND-GAr’s
pressurized system has been performed to meet the vessel requirements using
the 2019 version of the ASME BPVC, Section VIII, Division 2 [14] which will be
referred to as The Code in the rest of this document. The safety factors used
for determining the thicknesses of components were calculated following the
requirements listed in The Code for a Class 2 vessel.

###  6.3 Vacuum cryostat

The cryostat design is shown in Figure 10. It is 7.512 m in diameter and 7.89
m length with a total weight slightly less than 151 tons. Figure 10 also shows
the positions of the axial and radial support connections. See Section 6.4 for
details on the support rods. The cryostat’s overall dimensions are shown in
Figure 11. Due to the span of the vessel, stiffening ribs are used to
strengthen the outer shell. The stiffening ribs have a thickness of 12.7 mm
and and have an outer diameter of 7.85 m. The stayed heads and cryogenic feed-
can are not included during the initial installation of the cryostat.

The cryostat is designed to serve as an insulated vacuum vessel that houses
the six internal superconducting coils (see Figure 12) and the radiation
shield. It also must support the neutrino detector in its bore which operates
in a 10-bar atmosphere. Note: See section 6.4, Figure 16 for more details on
the coldmass. The inner shell of the cryostat must accommodate this 10-bar
pressure. The 38.1 mm thick (1.5 inch) flat heads at each end of the cryostat
cannot withstand the 10-bar pressure on their own. The design requires that
the heads be supported by the yoke end plates using 798 stays per head. See
Section 6.7.

Figure 10: Cryostat external features Figure 11: Cryostat general dimensions.

We expect that the solenoid and its vacuum cryostat in SPY will be fabricated,
assembled, and tested at the vendor site and delivered to Fermilab as a
working unit. Although consideration was given to a design based on delivering
smaller sub-assemblies to Fermilab and completing the final assembly
underground, after considering cost, reliability, and logistical
complications, the vendor-integrated assembly emerged as the preferred option.

Figure 12: Sectioned cryostat blowup showing three of the six magnet coils and
the heat shield (in turquoise).

####  6.3.1 Vacuum failure analysis

Since the magnet’s cryostat also provides pressure containment, we did a
preliminary analysis regarding an insulating vacuum failure [15]. A loss of
insulating vacuum will allow a large amount of heat to be transferred among
the cold coil assembly, the liquid nitrogen shield, and the room temperature
vacuum cryostat. This heat transfer would cause thermal shrinkage of the
cryostat, and possible leakage at the large flanges which connect the stayed
heads to the magnet cryostat providing pressure containment. This could result
in an oxygen deficiency hazard and, depending on the rate of loss, cause
damage to the HPgTPC. This analysis is used to quantify the resulting
temperature changes of the cryostat versus time in the event of a loss of
insulating vacuum. Simple energy-balance calculations show an equilibrium
temperature of 220K.

Preliminary structural FEA modeling using uniform thermal shrinkage shows that
the proposed flexible bolted connection on the stayed-head flange is capable
of remaining sealed. We used commercial Computational Fluid Dynamics code to
simulate the partially laminar, partially turbulent, transient buoyancy driven
convection of the incoming air, and the heat transfer among the components and
from the cryostat to the room temperature yoke. The analysis shows that the
cryostat falls in temperature very slowly, taking approximately 2000 minutes
to reach its minimum value. The average temperature of the cryostat at 2000
minutes is 271.5K, a drop of $\simeq$ 21.5K from its original 293K
Temperature. The minimum temperature of the cryostat was 260 K, which was
located at the bottom of the inner gaseous argon surface, near the center of
the cryostat. We note that although a design of HPgTPC gas system is not
currently available, we believe that in an emergency scenario, controlled
venting to 1 bar from 10 bar can be accomplished in a time short compared to
2000 minutes.

Figure 13 shows the transient average and minimum temperatures of the
cryostat, the LN2 shield, and the coils in degree K. The temperature profile
of the cryostat at the end of the 2000 minute simulation is shown in Figure
14.

Figure 13: Transient average and minimum temperatures of the cryostat, magnet,
and LN2 shield Figure 14: Temperature profile of the cryostat at the end of
the 2000 minute simulation when minimum temperature had been reached.

Figure 15 shows the heat transfer to/from the cryostat from three sources.
These are: radiation heating from the yoke, convective heating from the
outside air, and convective cooling. The convective cooling is via the
internal air between the cryostat, the LN2 shield and crossover part of the
magnet. The net energy transfer to the cryostat is the sum of the three.

Figure 15: Heat transfer to the cryostat from the 3 sources described in the
text. In addition, the total net energy transfer to the cryostat (sum of the
three) is also shown.

###  6.4 Coldmass

The coldmass consists of six superconducting coils surrounded by a 4 mm thick
aluminum thermal shield as outlined in Section 4.2. The coil and bobbin
assembly weighs 30 tons and is supported inside the cryostat both radially and
axially. The assembly’s outer diameter is 7040mm with an inner diameter of
7000mm. The coil layout is shown in Figure 16.

The coils are connected in series, and due to the nature of the symmetry, a
force balance in the magnet is achieved. Having the coils powered in series
also means that potential coil failures will force the power to ramp down
uniformly. Any potential imbalance of force produced by the proximity of the
SAND magnet is constrained by six axial restraints mounted at only one end of
the magnet. We do not have a detailed design for these supports in SPY, but
the configuration used in the JINR MPD solenoid ([4]) as shown in Figure 17 is
appropriate for SPY also.

Figure 16: Coil Dimensions Figure 17: Axial Support Rods

The radial supports, as shown in Figure 18, are designed to support the

Figure 18: Radial support configuration

coil assembly’s dead load, the magnetic load created from the proximity of the
SAND magnet, and the loading due to the non-symmetric yoke design. In
addition, forces develop on the radial supports when the magnet shrinks due to
cooling from room temperature to operating temperature. To minimize and
potentially completely cancel out the loading due to shrinkage, the radial
supports are designed at an angle and with ball-joint end connections which
allows the supports to rotate as the coil bobbin shrinks radially inward. With
this design, the support rods will simply rotate to the new alignment position
and not develop any additional axial loading.

We have developed two viable options for the radial supports. Both options
utilize an intermediate heat sink operating at between 50K and 80K. Both
designs also support the dead load of the coils with the downward hanging
vertical supports. The other radial supports in the assembly maintain the
circularity and center the coil bobbin assembly. They will withstand the
magnetic forces on the assembly. In design option 1 (Figure 19), solid invar
rods are used with a thermal sink as indicated above. This design option is
simple to design, analyze, and manufacture but produces a large heat leak.
Design option 2 for the radial supports is an assembly as shown in Figure 20.
The support has two components which make the transition at the 50K to 70K
thermal sink. This allows for very efficient heat shunting. One part of the
support is constructed from an invar (or a similar material) rod, while the
other part is constructed from G10 or carbon fiber thermal straps. The lengths
of the stages can be fine tuned by adjusting the mounting angle as shown in
Figure 18 to optimize the strength of the support and to minimize the
stresses. Commercial sources for this type of strap exist. This option greatly
reduces the thermal leak and allows for some assembly adjustment during
construction and maintenance.

Figure 19: Radial support - Option 1 Figure 20: Radial support - Option 2

Regardless of the axial and radial supports used in the final design,
attention must be given to shipping and installation requirements. Either of
these support options must withstand shipping loads or additional shipping
restraints will need to be incorporated into the design that can be removed
after installation.

###  6.5 Finite element analyses (FEA)

To determine the safety of the system, a combination of design by rule and
design by analysis methods were used. Analysis was performed using the load
factors of a Class 2 vessel, $\beta$ = 2.4, and were derated by 0.85 to
account for the joint efficiencies of the welds. To meet the FESHM 5031
requirements, an additional deraiting 0.8 deraiting was applied to the loads.
When it was possible, initial calculations were performed using part 4 of the
ASME VIII Div. 2 specifications and the calculations were verified using the
Design by Analysis Methods as described in part 5 of the ASME VIII Div. 2
specifications. Due to the complex loading conditions and asymmetrical design
of the cryostat, the elastic-plastic stress analysis process was performed for
all components as recommended in 5.2.1.2 of The Code. By using an elastic-
plastic material model, limits are set based on the allowable plastic strain
the assembly can withstand instead of an allowable stress limit.

There are generally four steps that are needed to be performed to show an
acceptable design:

  1. 1.

Protection against plastic collapse

  2. 2.

Protection against local failure

  3. 3.

Protection against collapse from buckling

  4. 4.

Protection against failure from cyclic loading

Two general areas of analysis were performed: an analysis of the cryostat head
and an analysis of the shell thicknesses of the cryostat. Protection against
plastic collapse, local failure, and collapse from buckling have been
considered in this initial design.

To show protection against plastic collapse, the loads that are applied on the
model are scaled by the loading factor $\beta$. If the model is able to
converge on a solution it is shown to meet the plastic collapse requirements.
As scaled loads are used to determine the acceptable limit of the vessel, the
resulting deformation shown will be higher than what will occur in the actual
components. To show protection against local failure the model is solved at
$\beta$ = 1.7. Additional load deraiting is performed using the FESHM and weld
joint efficiencies. Solving the analysis model with loads scaled to the local
failure load factor, the limiting triaxial strain can be found and compared to
the equivalent plastic strain in the model. Modifying the equations in chapter
5.3.3 of The Code, protection against local failure is shown when the
following expression is satisfied at every point in the model:

$\frac{\epsilon_{peq}}{\epsilon_{Lu}*exp[-(\frac{\alpha_{sl}}{1+m_{2}})(\frac{\sigma_{1}+\sigma_{2}+\sigma_{3}}{3\sigma_{e}}-\frac{1}{3})]}\leq
1$ (6.1)

Where:

  * •

$\epsilon_{peq}$ and $\epsilon_{Lu}$ are the equivalent plastic strain and
limiting triaxial strain.

  * •

$\sigma_{1}$, $\sigma_{2}$, and $\sigma_{3}$ are principal stresses.

  * •

$\sigma_{e}$ is the equivalent stress.

  * •

$\alpha_{sl}$ and $m_{2}$ are material dependent properties.

Protection against buckling was determined using Type 3 methods as per 5.4.1.2
of The Code which reexamines the model for protection against plastic collapse
loads while accounting for imperfections that would generate buckling shapes.

####  6.5.1 Pressure vessel head analysis

The stayed head design for the integral pressure vessel of SPY is based on the
observation that the 0.28 m thickness required for a flat pressure vessel head
is comparable to the thickness of carbon steel needed for the pole tips of the
return yoke. To reduce the required minimum thickness of the pressure vessel
heads, a grid of 798 3/4" stay bolts through each pole tip will be used to
brace the pressure vessel heads against the magnet yoke, allowing the heads to
be relatively thin. The stay bolts are simple threaded rod leveling pads. See
Figure 21.

Figure 21: Stayed head conceptual design.

Following the rules for stayed heads, a range of parameters was defined. Using
a fixed constraint at each of the stay bolt locations, the resulting minimum
spacing pitch distance with respect to the minimum plate thickness was
determined. Following the results of the calculations, a simplified model of
the stayed flathead was created following the calculated parameters. Stay bolt
spacing and sizing was examined in the model to conceptually verify the
design. Further refinement and optimization is needed to finalize the design.

Using the simplified stayed head model, the cover was examined using a 10 bar
internal pressure. The results of the local failure and plastic collapse
analysis for the analysis model can be seen in Figure 22 and Figure 23.

Figure 22: The simplified initial stayed head analysis: Deformation Figure 23:
The simplified initial stayed head analysis: Local failure check

The results of this analysis of the stayed head showed that convergence was
achieved and the local failure criteria requirements were met meeting the
requirements of The Code for this model.

####  6.5.2 Pressure vessel/Cryostat shell analysis

The cryostat shell wall thickness was optimized within the 10 bar pressure
constraint. Using elastic-plastic methods as described in The Code, a
simplified symmetrical model shown in Figure 24 was evaluated.

Figure 24: Model used in cryostat shell analysis.

The simulation was able to converge on a solution, meeting the protection
against plastic collapse requirements. The simulation also shows that the
assembly meets the protection against local failure requirement of having a
local strain limit lower than the value 1.0. These results can be seen in
Figure 25 and Figure 26. Additional load cases that occur during the
manufacturing and transport of the vessel will require a future analysis.

Figure 25: Results of cryostat shell analysis: Plastic collapse requirement.
Figure 26: Results of cryostat shell analysis: Local failure requirement.

The loaded shell from this analysis was then used to determine if the shell
would be able to resist buckling. A collapse analysis was performed using
imperfections generated through an elastic-plastic buckling review. The
buckling mode shapes used to generate a set of imperfections in the model of
the Cryostat shell. These imperfections can be seen in Figure 27. Using the
generated imperfect model, a plastic collapse analysis was performed again to
determine if buckling occurred. The model was able to converge on a solution,
meeting the protection against buckling requirements.

Figure 27: Results of Cryostat buckling mode shapes.

Before the design of the cryostat can be finished, additional detailing is
needed to account for the interaction between the finalized magnet design and
detector equipment. Additionally for the final stayed head design aspects such
as the attachment methods of the stay bolts, pattern of the connection, and
additional failure modes will need to be examined. Despite additional work
being needed, the results of the analysis indicate that the design of the
cryostat for the superconducting solenoid in SPY is feasible for withstanding
operational loading.

###  6.6 Pressure vessel head failure mode analyses

The SPY pressure containment system utilizes a very large flat circular flange
(6.6m in diameter) which is designed to hold 10 bar of gaseous argon. The
flange and flange bolts themselves are not strong enough to support the
pressure (4kt of force) over such a large area. This force will be contained
by the yoke as described in Section 6.5.1. Figure 28 shows a cross section of
the cryostat, flange, and yoke, where the central axis of the cylinder is the
z-axis, and the bolted flange connection of interest is called out.

Figure 28: Cross section of the cryostat, flange, and yoke, where the central
axis of the cylinder is the z-axis.

We have developed a bolting method for the flange which is a simply-supported
type connection. This flexible bolted connection eliminates the bending moment
on the bolts, as it allows rotation about the new fulcrum point, which is
placed near the O-ring groove instead of at the outer edge of the flange.
Since it is more flexible, it also results in more of the total force being
transferred to the yoke, as opposed to the flange itself. This connection
method is achieved by using a machined recess in the flange as well as spring
washers of an appropriate spring constant and excess deformation range. Figure
29 shows the flange connection. Bolt pre-tension must be high enough to keep
the fulcrum point on the flange in contact with the vessel’s mating flange.
The analysis shows this flexible flange connection is able to keep the flange
sealed, and has adequate bolt strength. Choosing the correct spring washers
with additional working deformation, along with the appropriate pre-tension,
will be of vital importance in making this connection work as intended.

Figure 29: Flexible bolted flange connection allows rotation of the flange
end, eliminates the prying force and moment on the bolts, and keeps the vessel
sealed.

###  6.7 Yoke

The steel yoke and cradles of SPY (see Figure 30) weigh 881 tons. The yoke
must be fabricated from low carbon steel in order to contain the magnetic
flux. The four cradles do not contribute to the development of the magnetic
field and will be either 18-8 or 304 stainless steel. Each component of the
yoke system will be under the crane limit of 60 tons and will fit within the
constraints of the access shaft. The four end plug sections are the heaviest
pieces of the yoke assembly, each weighing 54.5 tons. There are two end rings
and each weighs 46.3 tons. The long, axial steel plates that make up the
barrel of the yoke come in two thicknesses, 150 mm and 400 mm. The 400 mm
thick plates each weigh 26 tons. The cradles each weigh 10.7 tons.

Figure 30: Full Yoke w/o solenoid.

The steel axial plates will be bolted to the four cradles and after the
solenoid is installed, the remaining yoke components will be assembled via a
bolted construction. Finite element analysis results show that the steel under
gravity loading has minimal deflection but under magnetic loading and creep
conditions, begin to deform. The yoke will need a constraint system of either
bolts, welds, or straps to preserve the design alignment of the separate
components. Once the end plugs are installed, the stay bolts must be tightened
to provide contact to the pressure containment end flanges. See Figure 31.

The infrastructure needs of the magnet system and the requirements of the
experiment will impact the yoke design. Cables and piping will need to pass
through the yoke without affecting the structural stability of the assembly.
Instrumentation may also be installed inside the yoke for monitoring
experimental parameters and the yoke itself. Material considerations will also
need to be accounted for to account for long term stability of the iron.
Further refinement and optimization of the yoke assembly will need to be
performed as the cryostat design matures.

Figure 31: Motorized industrial rollers and support cradles.

####  6.7.1 Yoke FEA analysis

To determine if the yoke will be able to support and absorb the loads of the
assembly, a simple FEA analysis using reaction forces from the FEA analyses of
the pressure-vessel head and the cryostat/pressure-vessel shell was performed.
Using only the gravitational loads of the yoke and solenoid, the initial
results, in Figure 32, show that an unrestrained assembly will not maintain
design tolerances. To maintain design tolerances, the individual yoke sections
will be bound together with hoop sections.

Figure 32: Deformation of the Yoke. The red zones indicate a deformation of
slightly over one-half of a mm.

The hoops help to evenly distribute the gravitational loads and make the yoke
assembly sufficiently strong. Additionally, the results indicate that the
assembly is sufficiently strong. The boundary conditions of the simulations
can be seen in Figure 33. The stress and deformation results of the simulation
can be seen in Figure 34, and Figure 35. The results show that the deformation
is negligible and the stresses in the model are manageable. Due to
simplifications of the assembly FEA model, non-realistic stresses develop at
localized regions. Further refinement of the design and FEA model is required
to finalize the yoke design.

Figure 33: Boundary conditions of yoke structural simulations. Figure 34:
Results of hoop yoke analysis: Total deformation. Figure 35: Results of hoop
yoke analysis: Equivalent stress.

##  7 Preliminary parameter set

In Table 5 we list the preliminary parameter set for the SPY magnet system.

Table 5: Preliminary parameter set for SPY magnet system. Parameter | Value | Notes
---|---|---
Central field | 0.5T |
Field uniformity |  $\pm$ 10% |  Current design achieves $\pm$ 2%
Ramp time to full field | 30 min |
Stray field |  $\leq$ 0.01 T |  Stray field in SAND negligible, in LAr FV $\simeq$ 10G
Bore | 6.725m | Reduction possible with HPgTPC and ECAL optimization
OD | 7.85m | Cryostat diameter at stiffening rings
Length |  $\simeq$ 7.8m | Cryostat length
Solenoid weight |  $\simeq$ 150t |
Yoke total weight |  $\simeq$ 757t |

##  8 Conclusion

A magnetic and mechanical conceptual design for the magnet system for a high
pressure, gaseous argon neutrino detector has been developed. This design
relies on the experience on numerous magnets built over the past decades, but
features several unique characteristics. Its bore would make it the largest
superconducting magnet ever used in particle physics and the requirement for a
low material budget for the solenoid is reflected in a thin solenoid design.
The iron yoke is asymmetric to allow for particles that enter from an upstream
detector to be tracked in the HPgTPC in the magnet’s bore. Finally, the
integration of the detector and the solenoid cryostat is complete, using the
inner shell of the magnet vacuum chamber as the outer shell for high pressure
containment for the HPgTPC. To limit the overall length of the assembly, the
pressure is also transferred to the iron yoke end caps with a dedicated system
of stay bolts, thus accommodating the use of thin, flat end flanges for gas
containment.

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