XXX\. Solenoids for Decay, Phase Rotation, and Cooling Channels.

I.Bogdanov, S.Kozub, V.Pleskach, P.Shcherbakov, V.Sytnik, L.Tkachenko,
V.Zubko

Institute for High Energy Physics (IHEP), Protvino, Moscow region,
142284, Russia

**Introduction**

The Neutrino Factory (NF) concept includes several channels that treat
muon beam to allow its captured into the accelerating part of the
complex \[1, 2\]. First, there must be a \"drift\" channel where pions
decay generating muons. Also in this channel correlation develops
between muon energy and its position (mass separation). According to the
preliminary agreement, the length of this channel is 50 m. Due to a very
high beam emittance and energy spread after target, high magnetic field
and large channel bore are required to have a satisfactory beam
transportation efficiency. Second, there must be a \"phase rotation\"
channel where the correlation developed in the \"drift\" channel is used
to reduce muon beam energy spread. Low frequency RF section and
induction section (action principle of this section is similar to the
Linear Induction Accelerator (LIA) principle, so we will call this
channel a LIA channel) are considered now to make this transformation.
Estimated length of the RF channel is about 40 m. RF cavities installed
inside this channel accelerate or decelerate different parts of the beam
changing its energy distribution. The length of the LIA channel is about
100 m. Longer channel results in lower muon beam intensity because of
their decay; shorter channel requires higher accelerating gradients that
can be a technical problem. Both RF and LIA channels require
longitudinal magnetic field similar to that in the drift channel that
provides particle transportation. After «phase rotation» channels reduce
the energy spread, an additional \"cooling\" channel is needed to reduce
beam emittance. The ionization-cooling scheme is not finalized yet, but
it is developed to the extent that allows preliminary analysis of the
channel magnetic system. In this channel, beam transportation technique
makes use of an alternating magnetic field of high strength. Estimated
length of this channel is about 100 m. Emittance of the muon beam at the
output cross-section of the channel allows injection of the beam into
the RF accelerating structure.

Totally about 300 m of solenoids with different magnetic field strengths
and bore sizes must be built just to prepare the beam for injection into
the accelerating part of the NF. Combination of beam size and
longitudinal magnetic field strength satisfies the simple condition:

Br^2^ = 0.1125 Tm^2^. (1)

It requires magnetic field of 1.25 T if bore diameter is 0.6 m. With
this kind of magnetic field and bore combination, the choice of
superconducting solenoids for all the channels looks quite natural.

This chapter is to provide a preliminary layout of a magnetic system for
each of the four channels. It helps to identify possible technical
problems to work at during R&D stage of the project. Also preliminary
requirements to power supplies, cryogenic system, and cooling system can
also be found in this chapter. All this information can be used to make
a preliminary cost estimate.

**1 Drift Channel**

Preliminary study has shown that even if magnet bore is getting smaller
in accordance with (1) when magnetic field increases, magnet cost grows
up. It encourages us to choose lower magnetic field in channels that can
allow bore and field variations. A reasonable compromise between
magnetic field strength and bore size was achieved choosing B = 1.25 T
and R = 0.3 m for the first channel. The length of solenoids in the
drift channel was chosen to be 4.7 m. Totally 10 magnets are used in the
channel with 0.2-m gap between them. This leaves enough space for
service ports that can also be used for installation of beam diagnostic
equipment. The solenoid coil is placed in a cryostat that provides
needed mechanical support to the coil structure and insures thermal
insulation allowing using NbTi wire at 4.2 K. Required mechanical
supports are different for magnets in the middle and at the ends of the
magnet string. For example, axial force on the magnet in the middle of
the string is 170 kN. For the first and the last magnets in the string
this force is 230 kN. Radial pressure developed at coil location is
about 0.6 MPa that makes magnet design quite straightforward. Solenoid
has two-layer coil wound using NbTi cable. Stainless steel barrel is
used to support the coil structure inside stainless steel cryostat with
warm bore. Cable size is 12.0 x 2.1 mm^2^, and amount of copper used in
the cable is defined by a Cu/SC ratio of 7:1. Dimensions of
superconducting cable, quantity of copper for stabilization, and
nominal-to-critical current ratio were determined taking into the
account safe evacuation of energy stored in the magnet during quench.
Calculated temperature during quench is less than 300 K and maximal
voltage does not exceed 1000 V. Cable in the coil is insulated using
0.1-mm kapton insulation. The coil is cooled by liquid helium flowing
through copper piping soldered to copper shells and connected by
collectors on the ends of the coil. Copper thermal shield cooled by
liquid nitrogen is used to reduce heat leaks to the inner and outer
surfaces of the superconducting coil. Super-insulation is installed
between the coil and thermal shield and between the thermal shield and
cryostat wall. Space inside the cryostat is pumped out to further
improve thermal insulation. Main parameters of the solenoid magnet for
the drift channel are listed in the table 1.

In the drift channel, all the magnets are connected in series using
superconducting cable cooled by a pipe carrying liquid helium. One 180
kW power supply it used, and it takes 200 seconds to reach the nominal
current of 6 kA.

The protection method is shown schematically in Figure 1 below. When
quench detector sees an appearance of a normal zone in the coil, the
dump resistor R~d~ is turned on by switch S~2~ and power supply is
switched off by S~1~. At that moment the stored energy of the string
starts to dissipate on the dump resistor R~d~. During extraction of
energy out of magnet, maximal allowable voltage was accepted at the
level of 1000 V when R~d~ = 0.167 Ohm. Simulation of quench spread
through the coil was made for the case when quench was provoked on the
outer boundary of the inner layer of the coil. With quench detector
threshold of 1 V and time delay of 100 ms, almost 97% of stored energy
was dissipated outside the cryostat. Amount of energy dissipated in the
coil was sufficient for adiabatic heating of the coil up to 180 K in the
hottest area.

![](media/image1.wmf){width="4.450694444444444in"
height="1.7472222222222222in"}

Figure 1. Quench protection scheme for the decay channel

2.  **LIA-based phase rotation channel**

Main difference between the drift channel and LIA channel from the point
of view of beam transportation issue is that magnets in the LIA channel
are placed inside accelerating structure of LIA. This puts strict
limitation to the magnet length that cannot exceed the length of LIA
section. More over, LIA accelerating gap is formed by surfaces of the
two neighboring magnet cryostats. For this study, 1-m LIA section length
was accepted with bore diameter of 0.6 m and longitudinal magnetic field
of 1.25 T. The total number of magnets in the channel is 100. The length
of each magnet is 0.85 m, and gap between cryostats is 0.15 m. Table 2
shows main parameter of a magnet in LIA channel. Another critical issue
for this channel is that the fringe magnetic field outside the channel
must be rather low because LIA inductor performance gets worth at the
field level higher than a certain limit. Some optimization of coil shape
is required to have this fringe field as low as it is possible. This
optimization includes but is not limited to coil thickness variation
along the coil length. Nevertheless, because of the voltage gaps, some
level of fringe field will form a part of LIA inductor\'s working
environment. Coil design is very similar to that in the first channel.
NbTi cable cross-section is 8.3 x 3.0 mm^2^. Radial pressure at coil
location is about 0.6 MPa. Axial forces depend on the magnet location in
the string. For a magnet in the middle of the channel, axial compressive
force is about 150 kN; for the magnets at the ends, it is about 200 kN.
So precautions must be made to keep magnet displacements within an
acceptable limit, especially during quench when axial force can appear
in the middle of the string if quench protection scheme does not work
properly.

Total energy stored in the channel is 20 MJ. This energy is about twice
as large than that for the drift channel. To make an efficient quench
protection system, all magnets in the channel are subdivided into two
groups. In each group, magnets are connected in series and powered by
180 kW power supply. Quench protection concept is shown on the picture
in Figure 2.

![](media/image2.wmf){width="4.545138888888889in"
height="2.490972222222222in"}

Figure 2. Quench protection scheme for the LIA channel

In each group of magnets there is the only magnet with protective
heaters. After quench is detected in each string, the power supply is
switched off by S~1~, the dump resistor R~d~ is turned on by switch
S~2~, and heater is switched to heater power supply by S~h~. Stored
energy of both strings is dissipated on the dump resistors R~d~ = 0.167
Ohm. Maximum voltage does not exceed 1000 V. As simulation of quench
process shows, hot spot temperature does not exceed 200 K in the magnet
where quench originates and 170 K in magnets with heater-initiated
quench.

3.  **RF-based Phase Rotation Channel**

There are no full understanding yet whether this channel is needed at
all and what it can add to improve muon beam quality. One of main ideas
of using it is to have a preliminary phase rotation stage that can
simplify requirements for LIA-based system. There must be RF cavities
installed in this channel. Transverse dimensions of these cavities will
determine inner diameter of magnets that generate longitudinal magnetic
field for beam transportation. It is obvious that one must choose the
magnets with lowest field to reduce the channel cost. Because RF
frequency to be use in this channel is 175 MHz, inner radius of the
channel bore was chosen to be 0.7 m to accommodate the cavities.
Magnetic field in the channel is 1.25 T, and the direction of field is
the same for all solenoids in the channel. Length of a magnet in the
channel must agree with the length of RF cavities. The cavities must be
installed inside the magnet in a way that allows feeding of all the
cavities by RF power. As the first approach, the length of the magnets
was chosen to be about 1.8 m with 0.2 m gap between the magnets, so
totally 20 magnets are used in the channel. RF power dissipation in the
channel is about 50 kW per 1 m, so an additional water-cooling system is
required to reduce power load on the inner wall of the magnet cryostat.
Because it is logical to cool RF cavity wall, we will not describe this
additional cooling in detail, except to mention that total water
consumption must be about 2000 liter per minute to remove this power
from the channel. Cross-section of a magnet in the RF channel is
significantly higher than magnet cross-section in the drift or LIA
channels; so axial magnetic forces are also higher, although radial
pressure in the coil is at the same level of 0.6 MPa. For magnet in the
middle of the magnet string, axial force acting on the magnet end is
about 550 kN; for the first and the last magnets in the channel, this
force is about 900 kN. This force level requires strong support
structure and reliable protection system that can simultaneously and
quickly remove all the energy stored in the magnets during quench.
Magnet design is similar to that of the drift and LIA channels. The
difference is that stronger bandage is required to manage higher
longitudinal forces. Cable with 10.5 x 3.0 mm^2^ cross-section made of
NbTi wire is used for coil fabrication. The coil is cooled by liquid
helium flowing through cooling pipes. A shell cooled by liquid nitrogen
is used to lower heat leaks from the coil to cryostat walls, and
superinsulation is used to further increase cryostat efficiency.
Cryostat and coil support barrel are made of stainless steel. The inner
space of the cryostat is pumped out.

Main parameters of a magnet in this channel are listed in the table 3
below:

Quench protection scheme is very similar to that of the LIA channels.
Twenty magnets of the channel store 40 MJ of energy. All the magnets in
the channel are subdivided into two groups. The magnets of each group
are connected in series with their own power supplies. The scheme of one
string is presented in Figure 2. 180 kW power supply is used in each
string to rise current up to 6 kA during 10 minutes. One magnet in each
is equipped with protective heaters like it was in the LIA channel.
These heaters are necessary for synchronizing of energy extraction from
the strings. Resistance growth rate stimulated by the heater is higher
than that of the original normal zone; this reduces a difference in
resistances of the two strings. The two strings will have then close
time constants of current decay that will reduce unbalance of forces in
the string. After quench detection, power supply is switched off by
S~1~, dump resistor R~d~ is turned on by S~2~, and heater is connected
to heater power supply by S~h~. Stored energy of all strings is
dissipated on the dump resistors R~d~ = 0.167 Ohm. Maximum voltage does
not exceed 1000 V.

**4 Cooling channel**

The channel is to reduce beam emittance to an acceptable level using
\"ionization cooling\" mechanism. RF cavities installed inside the
channel compensate for energy loss during \"cooling\" process.
Transverse dimensions of the cavities of about 1.4 m will determine
diameter of solenoids in the channel. Length of the cooling channel is
about 100 m. High strength, alternating along the channel length
magnetic field must provide an optimal field configuration for better
cooling efficiency. Several schemes of the channel were built that
differ by magnetic field amplitudes and longitudinal field periods. One
of the latest schemes makes use of a magnetic field that changes along
the channel length following the sine law with period of magnetic field
change T = 2.2 m and field amplitude B~m~ = 3.6 T. There were proposals
of the channel configuration with field alteration period T = 1.5 m and
amplitude B~m~ = 3.4 T. Increasing field amplitude up to 5.5 T was also
considered. In this chapter, we will discuss the magnetic system with
longitudinal period T = 2.2 m and amplitude B~m~ = 3.6 T. Longitudinal
period determines the length of a magnet, which in this case has to be
less than 1 m. Realization of magnets for the cooling channel is quite
challenging. First of all, magnetic field is rather high in comparison
with the drift and phase rotation channels. Also, alternation of field
direction along the channel length results in high longitudinal forces.
Combination of both factors makes significant impact on the magnet
design.

Figure 3 shows engineering current density (that is the critical current
divided by coil cross-section) for different superconducting materials.

![](media/image3.wmf){width="5.039583333333334in"
height="2.8097222222222222in"}

Figure 3. Engineering current densities for different superconducting
materials.

It is possible to see that NbTi can not be used in magnetic field higher
than 9 T at 5.2 K. Using NbTi at 2.2 K allows to extend field range up
to 12 T. Nb~3~Sn can work in field up to 15 T at 5.2 K and has superior
magnetic properties in comparison with NbTi at 2.2 K. High temperature
superconductors (HTS) like Bi-2212 can work at much higher field (up to
30 T) practically without any reduction in critical current density, but
it will take some time until long enough pieces of HTS superconducting
cable will be available commercially.

For magnetic field with alternating direction, magnetic fluxes from
neighboring solenoids add in the gap between them, so in the coil,
maximal field can be higher than on the magnet axis. Figure 4 shows
longitudinal distribution of magnetic field in the cooling channel for
the case when coil thickness **w** = 50 mm, and solenoid length L = 1 m.
Sine-like line shows magnetic field along the axis of solenoid; the
other lines show field components **B~r~, B~z~** and absolute value
**B~t~** on the inner surface of the coil. One can see that the
component **B~r~** gives the main contribution to the edge field. Here
magnetic field reaches almost 10 T. According to Figure 3, NbTi wire
cannot be used in such a field, and it is necessary to use Nb~3~Sn
alloy. From the same chart, it is clear that Nb~3~Sn coil thickness must
be more than 65 mm.

![](media/image4.wmf){width="4.3069444444444445in"
height="2.9923611111111112in"}

Figure 4. Magnetic field distribution in the cooling channel for
solenoid length L = 1 m.

Magnetic field inside the magnet coil can be reduced if to choose
optimal coil length. Figure 5 shows how maximal field in the coil
depends on solenoid length. Magnetic field near the edge of the coil
(upper curve in Figure 5) is 9.2 T when the coil length is about 0.8 m.
Magnetic field in the coil in the central area of the magnet (lower
curve) is about 8.2 T with this coil length.

![](media/image5.wmf){width="4.732638888888889in"
height="2.988888888888889in"}

Figure 5. Maximal field in the coil versus solenoid length.

Increasing coil thickness, it is possible to further reduce field in the
coil, as it is shown in Figure 6. Again, the upper curve here shows
magnetic field near the magnet edge and the lower curve shows magnetic
field in the coil in the center of the solenoid. It should be mentioned
that quantity of superconducting material does not necessary increase
with coil thickness because more copper can be added into
superconducting wire to reduce engineering current density. This
addition can also be useful as a protective measure at quench. The
choice of coil thickness and wire and cable design must be finalized
after quench protection system is developed.

![](media/image6.wmf){width="4.622222222222222in" height="2.99375in"}

Figure 6. Maximal field in the center (B~c~) and near the edge (B~e~) of
the solenoid versus coil thickness

Figure 7 shows longitudinal distribution of magnetic field in the coil
when solenoid length L = 0.8 m and coil thickness w = 175 mm. One can
see that magnetic field in the coil reaches now only about 8.3 T, field
does not change significantly along the length of the solenoid. It is
also possible to see that magnetic field near the edge of solenoid is by
about 0.5 T higher than field in the central part of the coil. An
additional improvement of field distribution in coil is possible if to
use more elaborate optimization procedure.

![](media/image7.wmf){width="4.456944444444445in"
height="3.115972222222222in"}

Figure 7. Magnetic field distribution for solenoid with L = 0.8 m and d
= 175 mm

Radial distribution of magnetic field for this case is shown in Figure 8

![](media/image8.wmf){width="4.409722222222222in"
height="3.092361111111111in"}

Figure 8. Radial distribution of magnetic field. Dotted line is the
field in the center plane of solenoid; the other lines show end field
components.

For the case with L = 0.8 m and w = 175 mm, calculated radial stress on
the outer surface of the coil is about 15 MPa. This stress can be
managed using strong bandage. Simple mechanical analysis shows that to
withstand radial pressure, 6-mm stainless steel bandage is required that
does not seem to be a problem. Longitudinal stress in the middle of the
coil can be found if we know magnetic field distribution and details of
magnet design. Simple integration of forces along the length of the
magnet gives axial stress in the middle of the magnet of about 90
MPa**.** Although with the use of an external bandage, friction between
turns and layers will reduce this stress to some extent depending on
initial coil pre-loading, thorough mechanical design involving stress
management features and elaborate mechanical analysis must be performed
to insure proper coil performance. Probably, it will be useful to
subdivide the solenoid coil by several sections using strong stainless
steel walls so that stress in the coil does not exceed the yield stress
of copper in superconducting wire. Epoxy impregnation will also help to
improve coil mechanical stability.

It is necessary to mention that the tensile yield strength of
oxygen-free high conductivity soft copper is about 65 MPa at room
temperature \[3\], so one can expect wire critical current degradation
at the expected stress level. On the other hand, oxygen-free high
conductivity hard copper has tensile yield strength of about 230 MPa at
room temperature, and the tensile yield strength of especially hardened
copper can reach 340 MPa \[3,4\]. Using copper with this high yield
strength can help to solve the solenoid design problems. Large inner
radius of solenoid allows using "react and wind" technology that will
help to keep wire copper in \"hard\" state. Fabrication and studying a
wire that consists of Nb~3~Sn superconductor and copper matrix are the
subjects for R&D. Another way of solving the problem of stress in the
magnet coil is increasing the coil thickness. For example, if the coil
thickness increases from 175 mm to 350 mm, axial pressure drops from 90
MPa to 55 MPa. However, stored energy, total current in magnet, and coil
volume (amount of superconducting material and copper) grow when coil
thickness increases. Coil geometry optimization as initial step will
help to reduce maximal magnetic field in coil and improve other magnetic
and physical parameters. This work can be done more efficiently if
cavity geometry and beam envelope are defined.

Significant repulsive forces between magnets in the channel can
significantly complicate the channel design if not to take special
precautions. For magnets in the middle of the channel, repulsive force
can reach approximately 20 MN from each neighboring magnet. These forces
are balanced for a magnet inside the channel, but the first and the last
magnets must have an adequate support to withstand the force. If one of
the magnets inside the channel quenches, the balance of forces for
neighboring magnets breaks that results in unacceptable longitudinal
forces. This requires using rigid support for each magnet in a channel
that significantly complicates mechanical design of the channel. To
avoid this, it is possible to consider removal of stored energy
simultaneously from all magnets in the channel. For this purpose,
reliable and fast quench detection scheme is required. One of possible
solutions can be a quench detector of bridge type. When voltage on the
resistive section of a coil exceeds threshold value, quench detector
generates a signal to start protective actions.

Total number of magnets in the cooling channel is 90. Each magnet is
placed in each own cryostat. Cryostat inner diameter is 1.4 m and outer
diameter is 2.2 m. Gap between the neighboring cryostats is 10 cm. The
magnet coil is wound using Nb~3~Sn cable with cross-section 8.0 x 10.6
mm^2^. Copper-to-superconductor ratio is 35:1 for this cable for quench
protection purpose. The coil has 1600 turns in 16 layers. Total length
of cable is 8.5 km, and its weight is about 3.6 ton, so several cable
splices is to be done during winding. Main parameters of a magnet in the
cooling channel are listed in table 4.

Total energy stored in the channel is 4.3 GJ that makes development of
quench protection system for the channel a first priority issue. As it
was mentioned earlier, some protective precautions must be used like
fast quench detection and fast removal of stored energy from the channel
into the external dump resistor and/or \"smearing\" of this energy
inside the magnets using heaters. Protection circuit for the cooling
channel that takes into account its special features is discussed below.
Quench protection scheme is presented in Figure 9. All magnets of the
channel are connected in series into one string. 3 MW power supply is
used that allows reaching the nominal current level within 1 hour. There
is no dump resistor in this scheme because it appears inefficient for
the cooling channel. All magnets are equipped with heaters that are
fired by switches S~h~ simultaneously. Stored energy of each magnet is
dissipated inside its cryostats, in the magnet coil. Maximum temperature
reaches about 230 K in the magnet where quench has originated; for other
magnets, maximum temperature is below 190 K. Quench process diagrams for
the magnets of the channel is shown in Figure 10.

![](media/image9.wmf){width="3.435416666666667in"
height="1.9597222222222221in"}

Figure 9. Quench protection sketch of magnets for the fourth channel.

![](media/image10.wmf){width="3.0652777777777778in"
height="2.5840277777777776in"}

Figure 10. Quench process in magnets of the cooling channel.

**5. Power supply and cryogenic system requirements**

Table 5 below summarizes requirements to power supply for each channel
described above.

  -------------------------------------- ----------- -------- --------- -------------
  **Channel**                            **Drift**   **RF**   **LIA**   **Cooling**

  Operating current, kA                  6           6        6         6

  Voltage, V                             30          30       30        500

  Power, kW                              180         180      180       3000

  Current stability                      10^-3^      10^-3^   10^-3^    10^-3^

  Total inductance of magnets, H         0.61        4.0      1.1       230

  Ramp rate, A/s                         30          10       30        1.7

  Energizing time, s                     200         600      200       3600

  Number of power supply                 1           2        2         1
  -------------------------------------- ----------- -------- --------- -------------

Table 5. Power supply parameters for the NF front end magnet channels

Table 6 below presents calculated budget of heat leak in the cryogenic
system that can be considered as initial requirements for cryogenic
plant providing cooling agent to the channels.

  -------------------------- ----------- -------- --------- -------- --------- -------- ------------- --------
  **Channel**                **Drift**            **RF**             **LIA**            **Cooling**   

  **Temperature**            **4.5**     **80**   **4.5**   **80**   **4.5**   **80**   **4.5**       **80**

  1\. Cryostats:             52          650      86        1480     187       1370     300           3400

  Radiations, W              30          550      52        1300     45        1120     100           2500

  Supports, W                10          80       20        160      83        160      137           800

  Voltage taps, W            10          20       10        20       42        90       45            100

  Seals between coils, W     2                    4                  17                 18            

  2\. Transfer line, W       1           20       2         20       10        200      10            200

  3\. 30% margin, W          17          230      32        500      63        430      90            1000

  4\. Total, W               70          900      120       2000     260       2000     400           4600

  5.Current leads, l/h       21                   41                 41                 21            

  Required power, kW         115         26       219       57       331       57       383           133
  -------------------------- ----------- -------- --------- -------- --------- -------- ------------- --------

Table 6. Budget of heat leak in the cryogenic system.

The essential feature of the channel is the long time of cooling down
magnets. In the protection scheme that was described it may take several
days to reach 4.5 K after quench. More efficient protection scheme with
dissipation of energy out of cryostat is a subject for R&D.

**Conclusion**

As part of FNAL Neutrino Factory study, preliminary analysis has been
made to realize feasibility and complexity of magnetic systems for NF
drift channel, phase rotation channels, and cooling channel. For each
channel, simple optimization was made with the goal to reduce its cost.
It was impossible during this short study to identify and to address all
the problems that can arise during magnet development and design. Some
of these problems can be resolved in a normal way. Others need an
additional research stage. Although design and implementation of every
channel discussed above is a nonstandard technical task, one can expect
to meet the most challenging problems working at the cooling channel.
Both radial and axial ponderomotive forces in this channel are extremely
large as well as the interacting forces acting on the first and the last
magnets in the string. Because mechanical behavior of a magnet in this
channel is the main issue to study, thorough modeling of the system is a
must in this case. Another objects of study are optimization of quench
protection system and analysis of stress in coil during cooling down and
warming up. Undoubtedly, development of magnetic system for the NF front
end must be accompanied by modeling and prototyping of channel magnets.
The next R&D scenario could be suggested for the nearest future:

1.  Optimization of the magnet design for the cooling channel with the
    goal to reduce mechanical stress in coil;

2.  Mechanical stability analysis for the magnets of the cooling
    channel, development of the channel mechanical scheme, and design of
    a mechanical support for coils and magnets in the cooling channel;

3.  Development of Nb~3~Sn cable to use in the cooling channel;
    development of coil fabrication technology;

4.  Development and optimization of quench protection system and cooling
    scheme for each channel with the goal to increase system reliability
    and reduce time for cooling down and warming up;

5.  Building full-scale prototypes of magnets in each channel.

Preliminary cost of the magnetic system construction and operational
expenditures can be estimated based on the data obtained during this
study. This cost estimate can be updated after R&D program is completed
at the stage of technical proposal. For each channel, it was shown that
the major portion of the cost is the cost of superconducting magnets.
Cost of the drift channel makes up the bulk of the cost of the entire
magnetic system. Technical difficulties to build the cooling channel
result in the situation when future R&D program must be devoted mainly
to analyzing and modeling of this channel.

**References**

1.  The ^+^ ^-^ Collider Collaboration. "^+^ ^-^ Collider. A Feasibility
    Study." BNL-52503, July 1996.

2.  M.A.Green et al. Superconducting Solenoids for the Muon Collider.
    MT-16, 1999, Ponte Vedra Beach, Fl, USA.

3.  http:/www.matweb.com/SpecificMaterial.com/

4.  Handbook on physical and technical basis of cryogenic. Editor by
    M.P.Malkov. Moscow, Energoatomizdat, 1985, p.234.