#  The Muon Storage Ring

## Introduction

The 50-GeV storage ring for neutrino production has been designed using
a racetrack configuration. A racetrack is the optimal geometry for
maximizing the proportional length of a single straight section to
circumference, hence maximizing the number of muons converted into a
neutrino beam. Although this particular ring was designed to meet
limitations and target physics detectors specific to the Fermilab site,
its design concepts, parameters, components, and dynamics are generally
applicable. The racetrack design is simple, containing a downward
straight, called the production straight, a return straight pointed
towards the surface and two arcs with their associated matching and
dispersion suppression
sections.![](media/image1.jpeg){width="4.631944444444445in"
height="5.9944444444444445in"}

One of the parameter constraints of the design arises from the
underlying geology of the site as shown in Figure 1. The vertical
distance between the surface of the site and the bottom of the Galena
Platteville rock layer is approximately 680 feet. Below this dolomite
layer is a sandstone layer, which must be avoided because it is a poor
substrate for tunnel construction and it contains the water supply for
the municipalities surrounding Fermilab. Of the 680 feet, 600 have been
allocated to the ring for its vertical drop (Table 1). The "vertical
drop" is the vertical distance between two parallel planes: one plane
through the topmost part of the ring and a second plane through the
bottommost part of the ring.

This vertical constraint is a limitation because at least part of the
ring must be tilted at a vertical angle to direct the neutrino beam
through the earth to a long-baseline detector. Tilting the entire ring
obviates the need for additional, "out-of-plane" bending. For a
significant angle of declination and vertical height restriction,
tilting increases the relative arc length and matching and dispersion
suppression sections, thereby decreasing the relative length of the
production straight and the fraction of decays occurring in this
straight.

An assumption used in designing this ring is the choice of the angle at
which the ring must direct the neutrinos to illuminate the long-baseline
physics detector. For directing the neutrino beam to the West Coast
(including SLAC, LBNL, etc.), the downward angle corresponds to about
13. This 13-degree angle combined with the vertical drop limit of 600
feet (183 meters) gives a cross-sectional profile of the ring (shown in
the top part of Figure 1) of 813 meters. The "cross sectional profile"
is the distance between the uppermost point of the ring and the
bottommost point of the ring.

The cross-sectional profile constraint, when combined with a dipole
field of 6T and muon beam energy of 50 GeV, provides a straight section
for neutrino production which is about 39% of the entire ring
circumference. This is to be compared to a mathematical maximum possible
value of 50%. The choice of 6T is based on Figure 2 which shows the
production straight length divided by the circumference as a function of
dipole bend field. The ratio is calculated based the 813 meter
cross-sectional profile constraint and, thus, is specific to the geology
under the Fermilab site. Releasing this constraint would allow one to
increase the circumference. If, for example, one chooses to keep the
arcs the same and increase the straight sections by a large factor, the
ratio approaches the mathematical limit. On the other hand, one could
use lower field magnets in larger arcs along with larger straight
sections and still maintain a large decay fraction.

![](media/image2.jpeg){width="6.0in" height="4.427777777777778in"}

In terms of the optics design, achieving a large admittance competes
with the need to form a collinear neutrino beam---collinear, at least,
to within limits set by the decay kinematics. To prevent the dynamics of
the parent muon beam from contributing significantly to the angular
spread of the secondary neutrino beam, the divergence of the muon beam
in the production straight must be much less than the mean decay angle,
which is 2 mr at 50 GeV. A straight with high-beta functions (implying
large transverse beam sizes) is required. The challenge, then, in the
design of the storage ring is to preserve the exceptionally large
emittance transmission of the arc design through a transition to a
high-beta region. The betatron function values are primarily determined
by the transverse emittance combined with a user-defined limit that the
divergence in the high-beta straight be equal to or less than one tenth
the rms decay angle, or 0.2 mr. In terms of the unnormalized emittance
and the betatron functions, the angular divergence is given by:

$\theta = \sqrt{\varepsilon\frac{\left( 1 + \alpha^{2} \right)}{\beta}}\text{.}$

The design conditions are summarized in Table 2. In the following
paragraphs, details of the design are described.

## The Lattice

### The Arcs

Strong focussing FODO cells were chosen for the arcs to achieve a large
momentum acceptance as compared with more complicated focussing
structures. To shorten the arc lengths, high-field superconducting
dipoles with 6T fields are assumed. Since strong gradients and large
apertures are needed to accommodate and contain the large transverse
emittance and the large displacement of off-momentum orbits,
superconducting quadrupoles are also used.

The parameters of the magnets in the arc cells are listed in Table 3
along with calculated beam sizes based on the emittances in Table 2. The
dimensions of the magnet apertures also include a 1-cm beam-stay-clear
and a 1-cm thick tungsten liner for shielding. A 90 phase advance per
cell was chosen so as to support strong sextupole correction of linear
chromaticity while simultaneously maintaining an acceptable level of
transverse acceptance. This phase advance is also the best choice to
minimize transverse beam sizes both vertically and horizontally. The
sextupole field has been superimposed on the quadrupole field (at the
peak of the dispersion and betatron function) to minimize both the
strength needed as well as the tune shift with amplitude aberration.
Superconducting quadrupoles have been designed with a sextupole field
component added. Each arc contains 31 half-cells, giving a total of 62
arc dipoles and 62 arc quadrupoles for the entire ring. For control
purposes the defocusing and focusing quadrupoles are on separate buses.
The arc lattice functions are plotted in Figure
3.![](media/image3.jpeg){width="5.023611111111111in"
height="3.1645833333333333in"}

### Production Straight

The neutrino production straight, in contrast to the arcs, is a
high-beta function, weak focussing structure. This production straight
is matched to the arcs using a quadrupole doublet, and it has been
designed to transmit a large momentum range in addition to forming a
near parallel beam of muons. To form the insert, the short FODO cells of
the arcs are matched into much longer, high-beta FODO cells that are the
building blocks of the production straight. Use of a periodic unit
allowed flexibility in the length of this region. The production
straight represents about 39% of the 1.75-km ring circumference.

Table 5 gives the parameters of these production straight cells. The
very low field gradient required by the quadrupoles in this region
offers the possibility of using permanent magnets. The lattice functions
for the production straight are shown in Figure 4.

### Return Straight

The return straight is approximately equal in length and opposite to the
production straight. It has been simply designed using 90 cells, 50-m
long. The parameters of the return straight cells are shown in Table 4,
and the lattice functions are shown in Figure 5. It cannot be identical
to the production straight because of the anticipated need for higher
order corrections for the ring. Tuneshift with amplitude corrections are
planned using octupoles and /or sextupoles inserted in this straight.
The cell parameters in the return straight will then be adjusted to
enhance the dynamic aperture of the ring. It is planned that not only
tuneshift-with-amplitude terms from the arc sextupoles will be
corrected, but also those arising from the strong fringe fields
associated with the unusually large bore of the quadrupoles.

### Matching and Utility Sections![](media/image5.jpeg){width="4.923611111111111in" height="3.020138888888889in"}

A combined matching section and dispersion suppressor was placed at each
end of the arcs for efficient transition into the high-beta straight. A
conventional two-cell dispersion suppressor was utilized for the return
straight. Four more dipoles and sixteen quadrupoles are contained in the
four matching/dispersion suppression sections. If conventional
dispersion suppression is used for the high-beta straight, the length of
the straight is reduced by about 4% of the total circumference, from 39%
to about 35%.

### Injection

The Muon Storage Ring has need of an injection kicker system that will
deflect the incoming beam on orbit. The injection kickers are placed in
the downward (or production) straight in order to inject into the ring
at the top near the surface. Injection kickers with large apertures
\[2\] will be needed for this purpose. The main parameters for the
kicker system are given in Table 6.

The required total field integral is given by 24 magnets of length 1
meter and with a field of about 300 Gauss. This choice is based on two
engineer-defined limits that were design constraints. Experience has
suggested that the maximum system voltage should be limited to 50 kV and
the maximum switch tube current should be limited to 5 k Amps. These two
requirements imply a system impedance of 5 ohms.

In Figure 6 we show a proposal for the cross section of the magnet. The
mechanical design for the support structure and vacuum vessel is
non-existent and will need to be addressed for the next level design.
The actual magnet length and number of pulsers will need to be nailed
down at that time.

The PFN that will be used to drive each magnet will have an impedance of
5 ohms and a pulse length of 2.25 sec. A ***SPICE*** simulation of both
the PFN and magnet has been completed.

### Superconducting Magnets for the Arcs

The two arcs of the Muon Storage Ring will be composed of
superconducting magnets. The 31 identical arc-cells include 62 dipoles
and 62 quadrupoles, with sextupoles combined with the quadrupole coils.
All the magnets are designed to work at 4.5 K in one-phase liquid helium
flow, and are also designed to work under the quite high beam losses
heating of about 5 W/meter on average, with a peak value twice as high.
The highest operating field for these magnets is 6 T, which allows the
use of NbTi superconductor. Critical current data for the inner coil
strands of the SSC 50 mm dipole were used as a reference for estimating
the coil geometry and the superconductor volume. This critical current
was \~ 340 Amps at 7 T and 4.2 K for the strands with 0.84 mm diameter.
The average current density for the cable with insulation inside the
coil was assumed to be 500 Amps/mm^2^. The basic conceptual designs for
all magnets use the single layer cos coil geometry and RHIC type
mechanical structure for the cold mass design.

![](media/image6.jpeg){width="5.620138888888889in"
height="4.341666666666667in"}

The basic parameters of the magnets for the arcs of the storage ring are
presented in Table 7.

A cross-section of the dipole cold mass inside the cryostat is shown in
Figure 7. Here one sees the single layer superconductor coil surrounded
by plastic spacers and collared by iron yoke laminations. Stainless
steel shells that are welded around the yoke complete the cold mass
assembly. The cold mass has two connections to the "spider" type
suspension in the middle plane. This assembly is fixed to the vacuum
vessel by four bolts. The thermo-shields that are placed around the cold
mass will have a temperature of about 80 K and could be cooled by liquid
nitrogen. Multi-layer insulation blankets are used to reduce the heating
of the thermo-shields from the vacuum vessel. The vacuum vessel has
reinforcement in the areas of the magnet suspensions.

The quadrupole and sextupole coils will be assembled like spool-pieces:
that is, the sextupole coils will be placed around the quadrupole coils
and will be collared together by iron yoke laminations. Stainless steel
shells will be welded around the yoke. The complete cold mass assembly
of the spool-piece and the dipole magnet assembly will be welded
together in a common helium vessel. This vessel forms the basic
half-cell unit of the arc. The longitudinal view of this arc half-cell
cryostat is shown in Figure 8.

The cryostat has two suspensions along the length of the magnets. One is
placed in the middle of the quadrupole and is an anchor point to keep
the center point of the quadrupole in place during cool-down of the
magnets. As shown in the top view of Figure 8, the dipole magnet has
significant bending of the cold mass in the horizontal plane with a
sagitta of about 68 mm. This bending should be done for the beam tube as
well to preserve beam aperture. The superconductor coil must be
protected from the electrons coming from muon decay, and is provided by
a 10 mm cylindrical wall of tungsten as shown in Figure 7. As shown in
section 8.4.1 below, the heat load on the tungsten will be about 50
W/meter on the average, with a peak value about twice as large. Cooling
could be provided by two flattened tubes with liquid nitrogen flow or
cold helium gas. Some additional tubes come through the suspension and
are used for bus-bar returns and as a heat exchanger for the helium
flow.

A summary of the mechanical dimensions and cryogenic loads of the
arc-half cell are shown in Table 8.

![](media/image7.jpeg){width="4.3in" height="3.3222222222222224in"}

### Power Supplies for the Muon Storage Ring

Schematics for the power supplies for the arcs of the storage ring are
shown Figure 9. The power supply design assumes the dipole circuit
requires 15 kAmp DC and each quadrupole (focusing and defocusing)
circuit requires 10 kAmp DC. Since all circuits are superconducting, the
resistance of the warm bus connecting the power supplies to the load and
an acceptable ramp rate sets the voltage requirement. For the purposes
of this study, the supplies were designed in units of 150 kWatt modules
each capable of 30 volts and 5000 amps. Such supplies are common around
Fermilab and have well known costs and operating characteristics. The
dipole bus would require 3 of these supplies operating in parallel while
the quad buses would each need 2. Assuming an 0.4 henry dipole circuit
inductance yields a ramp rate of 75 Amps/sec (200 sec to ramp to 15
kAmp).

![](media/image8.jpeg){width="2.8645833333333335in"
height="2.9479166666666665in"}![](media/image9.jpeg){width="2.4375in"
height="2.9479166666666665in"}

Since it is quite costly to transport 15 kAmp, the power supplies should
be located near the feed cans in the beam enclosure. This should be no
problem at the near-surface end of the ring, but requires some
consideration for the deep end. The present plan is to locate the power
supplies at the tunnel level and provide the 480 VAC power from the
surface. The exceptionally high cost of a 15 kAmp, 800-foot long
vertical DC bus system drove this decision. The cryogenic problems with
operating a long vertical superconducting power transmission line ruled
out the possibility of a superconducting feed from the surface. Further
optimization studies may indicate additional cost or performance savings
by installing the 13.8KV/480VAC transformer at the tunnel level.
Presently, it is planned to use passive filters to smooth the output of
the power supplies. This is the common practice at Fermilab for storage
ring systems.

### Quench Protection Dumps

This study assumes the quench protection dump switches and resistors
will be integrated with the power supply filter. The switch itself will
be similar to the 15 kAmp dump presently operating at the Fermilab
magnet test facility. The resistors could be water-cooled stainless
steal elements or air-cooled elements mounted to the wall of the
vertical access shaft. The present plan does not include backup DC
breakers in the dump switch because of the high cost of such devices. In
the event that the dump switch fails, the Quench Protection Monitoring
system would protect the magnets by firing all the magnet heaters in the
string.

### Muon Storage Ring Quench Detection & Protection

The MµSR will consist of 6 separately excited superconducting magnet
strings. Each of the two arcs will have a dipole, and two quad circuits.
The dipole circuits will store much more energy (45 MJ each) than the
quad circuits, but quench protection will be implemented in the same
manner for each. One embedded Quench Protection Monitor (QPM) will be
needed in the "Power Supply Room" at each arc.

For quench detection, one voltage tap from each magnet will need to be
connected with a coax to the QPM. VFC or ∆∑ technology can be used for
data acquisition. For quench protection, each magnet will need an
embedded heater connected to a capacitive discharge Heater Firing Unit
located in the PS room. Also located in the PS room, will be the dump,
dump switch, and two Quench Bypass Switches (QBS), as shown in Figure
10. Only one safety lead is needed in the center of each arc.

## Lattice Performance and Tracking

Overall physical characteristics of the storage ring are summarized in
Table 9. The dynamic aperture and momentum performance of the ring
lattice has been studied by tracking for 1000 turns to high order
including not only full kinematical effects but also fringe field
characterization of the large-bore quadrupoles \[3\].

This is a very conservative number of turns to track since the intensity
of 50 GeV muons decays by 1/e in only 178 turns. Tracking plots are
shown in Figure 11 in steps of 0.5 as given by a normalized emittance
(rms) of 3200 mm-mr. The top plots show the dynamic aperture of the
storage ring with fringe fields of all quadrupoles included. Further
study showed that only the fringe fields from four strong quadrupoles in
the matching/dispersion suppression sections about the production
straight caused a deterioration in dynamic aperture. Turning the fringe
fields off in these four quadrupoles improved the dynamic aperture
considerably as can be seen in the lower plots. Since fringe fields
depend strongly on poletip field, the simplest solution is to lengthen
these quadrupoles and reduce their poletip field correspondingly. To
date, tracking has not included field and alignment errors. Given the
relatively short lifetime of the beam, \<1% field errors and all but the
lowest-order resonances are not expected to be important.

## Beam Induced Energy Deposition And Radiation Fields![](media/image10.jpeg){width="3.4097222222222223in" height="3.8097222222222222in"}![](media/image11.jpeg){width="3.5097222222222224in" height="3.30625in"}![](media/image12.jpeg){width="3.0097222222222224in" height="3.3333333333333335in"}![](media/image13.jpeg){width="2.709722222222222in" height="3.209722222222222in"}![](media/image11.jpeg){width="3.5097222222222224in" height="3.30625in"}![](media/image13.jpeg){width="2.709722222222222in" height="3.209722222222222in"}

Realistic Monte Carlo simulations have been performed with the
MARS14(2000) code \[1\] for the arcs and straight sections of a muon
storage ring using the above lattice for 30 and 50 GeV muon beams.
Detailed analysis of radiation levels inside the magnets, around the arc
tunnel and at large distances from the ring (neutrino hazard) is
done.![](media/image14.jpeg){width="3.4in"
height="3.1951388888888888in"}

### Arc Magnets

Forced muon decays and shower simulation with MARS are done in the arc
FODO cells. The cells are 9.8 m long each and made of 45 T/m 1-m quads
and 6 T 2.4-m dipoles. At 50 GeV, the muon decay rate is 1.6x10^10^
decays/m/s. For a 240 kW beam, there is 84 kW power dissipation in the
1750 m storage ring, or 47.8 Watts per meter on average. A thick bore
tube made - as calculations show - of tungsten must intercept most of
this power. The longitudinal distributions of both power density and
power dissipation oscillate in the arc cells (see Figure 12), with about
10% of power dissipated in the SC coils and 90% in the protective bore
tube. The power density peaks in the orbit plane with a strong azimuthal
variation (see Figure 13).![](media/image15.jpeg){width="3.7in"
height="3.3958333333333335in"}

As a result of thorough optimizations, it was found that the radiation
load to the superconducting coils of the arc magnets due to 50 GeV muon
beam decays is reduced to tolerable levels if the dipole is bent and
there is a tungsten eccentric bore tube. The latter can be made of a
1-mm thick SS pipe (100x80 mm elliptical aperture) and a 1-mm thick SS
pipe (122x102 mm elliptical aperture) shifted inward by 5 mm with the
space between filled with tungsten. With such a tube the peak power
density in the coil is 0.15 mW/g and the peak power dissipation in the
bore tube (at nitrogen temperature) and in the rest of the magnet (at
helium temperature) is about 90 and 9 W/m, respectively. Averaged over
the arc length values are about two times lower. Residual dose rates on
the magnets are quite acceptable.

### Radiation Around The Arc Tunnel And Downstream Of The Straight Sections

Full-scale MARS calculations have shown that the normal occupancy limit
of 0.25 mR/hr is provided by 2 meters of dolomite type shielding below,
above and radially inward from the arc tunnel enclosure walls. Six
meters of such shielding is needed to provide that limit radially
outward (see Figure 14). Power supply rooms and other underground
enclosures should be placed inward from the arc tunnel.

![](media/image16.wmf){width="3.7in" height="3.182638888888889in"}

The off-site limit of 10 mR/yr due to neutrino-induced radiation in the
arcs is reached at 50 meters radially outward from the beam orbit. The
height of such a controlled disk is only +-10 cm from the orbit plane.

Neutrino-induced radiation downstream of the straight sections is more
severe. The off-site limit of 10 mR/yr is met at 4.2 km for a 50 GeV
MuSR and at 1.8 km for a 30 GeV MuSR. The maximum half-width of a
tolerable isocontour is 4.3 m and 2.7 m at 50 and 30 GeV, respectively.

REFRENCES

1.  N.V. Mokhov, "The MARS Code System User Guide, Version 13(95)",
    Fermilab-FN-628 (1995); N.V. Mokhov et al., Fermilab-Conf-98/379
    (1998); LANL Report LA-UR-98-5716 (1998); nucl-th/9812038 v2 16 Dec
    1998; <http://www-ap.fnal.gov/MARS/>.

2.  E. Keil, Muon Storage Ring Design with Simple Mathematica Packages,
    CERN-SL-99-053-AP, August 31, 1999.

3.  F. Zimmerman et al, MUCOOL Note 95, March 3, 2000