# Cryogenic Systems

## Introduction

The proposed Neutrino Factory will require an extensive helium cryogenic
installation to provide sufficient cooling for subsystems that are based
on superconducting technology, e.g. the target solenoid, the solenoid
channels, the various accelerating stages and the storage ring. The
design of such a system is an iterative process of optimization of cost
and performance with respect to the many requirements, both quantitative
and qualitative. The starting point of the iteration is a system concept
with point designs for the major processes. In the following paragraphs
a first approximation to such a starting point is presented.

## Refrigeration Plant and System Layout

An important feature of the cryogenic system of the Neutrino Source is
the variety of components in the system, and the mixture of warm and
cold components along the beam lines. It is inevitable in the Neutrino
Factory that distribution of cryogens to a system of cryogenic modules
is a major issue. It is reasonable to investigate a system that has one
refrigeration plant first. A possible layout of this type is pictured in
Figure 1. The refrigeration plant is centrally located, and five cryogen
transfer lines distribute cooling to the cryogenic modules in five
subsystems: one line serving the injector components and the
pre-accelerator linac; one line for the linacs of RLA1; two lines (a
loop) for the two linacs and the superconducting magnet systems of RLA2;
and one line for the superconducting magnet systems of the storage ring.
Figure 1 is schematic. The lengths of the lines given here are estimated
from the site layout in chapter 13 on civil
construction.![](media/image1.wmf){width="3.4in"
height="4.5465277777777775in"}

## System Process

Refrigeration is provided by the plant in four forms. Table 1 lists the
refrigeration plant streams and gives appropriate thermodynamic details.

1)  4.5 K refrigeration is provided by a flow of helium at 3 bar
    pressure and 4.5 K. This is expanded in a J-T process (Joule
    Thomson) to saturated helium at 4.5 K. The saturated gas is returned
    to the refrigeration plant.

2)  4.5 K liquefaction is provided from the 3 bar, 4.5 K stream
    returning at 1 bar and 300 K.

3)  Shield cooling is provided by a stream delivered from the
    refrigeration plant at 19 bar and 40 K and returned at 16 bar and 60
    K.

4)  40 K liquefaction is provided from the 19 bar, 40 K stream also
    returning at the standard state.

## Cryogenic System Components

At the level of abstraction of this report, the cryogenic system of the
Neutrino Factory consists of three kinds of components: Refrigeration
plant; transfer line; and boxes. These will be described below.

### Refrigeration Plant

Anticipating the results of the capacity requirement roll up and from
the discussion below, the capacity required in this plant for the
Neutrino Factory is 80 kW equivalent at 4.5 K. This is equal to two
LHC-size refrigeration stations. LHC is installing four stations each
with two cold boxes of 20 kW equivalent capacity at 4.5 K \[1\]. This
experience makes the specification and procurement of a refrigeration
plant for the Neutrino Factory a straightforward engineering task with
low risk.

The Neutrino Factory plant will contain approximately twenty helium
screw compressors, oil removal, and inventory management equipment. This
system will require about 24,000 square feet of medium rise floor space
isolated for noise control and ventilated for about 2 MW of heat
dissipation. The cold boxes will require about 15,000 square feet of
space. In addition 1,500 square feet of air-conditioned space would be
needed for control system electronics and local control room.

The total installed power in this plant will be about 25 MW with a
nominal operating power of about 18 MW. Heat rejection of 25 MW with
redundancy will be needed.

### Transfer Line

The transfer line system includes four cold lines and two warm lines.
The cold lines carry the supply and return streams listed in Table 1.
The sizes required for these lines will be different for the different
transfer lines, but typical sizes are: 2 and 3.5 inch ips sch 5 for the
4.5 K supply and return: and 2.5 inch ips, sch 5 for the 40 - 60 K
shield system supply and return. The transfer line will contain a shield
thermally connected to the 60 K return line. The outside diameter of the
vacuum jacket of the cold line assembly will approximately 18 inches.

The two warm lines are warm helium gas supply and return - the supply
for module purging and warm-up and the return for the liquefaction load
and for module cool-down. The sizes of these lines might be 2 and 4 inch
ips.

The transfer line system will include other components such as supports,
periodic vacuum barriers in the cold line, and an insulating vacuum
system with monitoring.

### Boxes

The variety of requirements for modules that must operate in this
cryogenic system can best be satisfied by providing a minimum set of
components in each connection box. These components are needed for
connecting an individual module to the transfer line. Each module will
contain the special equipment required in addition to the minimum set.
Examples of special situations are modules that have saturated helium
baths or current leads. The saturated bath would need a liquid level
gauge and the current leads would need flow control for the liquefaction
flow.

In general the boxes will require four cold shut-off valves, two cold
control valves, and valves for the warm gas lines. In addition there
will be a vacuum barrier between the transfer line and the module and
some means of disconnecting the module - U-tubes or field joints. Some
instrumentation and some relief devices will be standard in the boxes as
well.

## Module and Component Heat Loads

Cryogenic system heat loads in each of the four categories for modules
in the Neutrino Factory subsystems are given in Table 2 below with
discussion following. These are divided into static and dynamic
components. The static heat load is that which is present when the beam
and all power supplies are not operating.

### Current Leads

The Neutrino Factory is assumed to use HTC current leads throughout. The
HTC bottom ends of the leads are to operate up to 60 K and are to be
conduction cooled. The top ends are to be cooled by a flow of 40 K from
the shield circuit returned to the refrigeration plant at 300 K. This is
high-pressure gas regulated by a valve at room temperature, and the
circuit will probably have to have a cold shut-off valve. In the heat
load estimate the requirement is taken to be 0.1 g/s at 40 K and 1 Watt
at 4.5 K both per kA-pair. The 40 K liquefaction load is divided equally
into static and dynamic.

### Target Solenoid and Channels

Heat load estimates for the target solenoid were made at the National
High Magnetic Field Laboratory \[1\]\[2\]. The heat load estimates for
the solenoid channels appear in chapter 9. It is assumed that each
channel will have one pair of 6 kA current leads.

### Superconducting Linac Modules

The average heat load of the 10 m cryomodules of the 350 MHz LEP SRF
system is 80 watts at 4.5 K. This system does not have intermediate
temperature shielding, but it does have a 4.5 K liquefaction load of
0.25 to 0.05 g/s per cavity from gas cooling on HOM cables, beam tubes,
tuners and power couplers \[4\]\[5\]. The KEKB coupler also uses gas
cooling \[6\], and in the design of SNS 0.05 g/s static and 0.025 g/s
dynamic is allowed for each coupler\[7\]. The cryomodules for both CEBAF
and the TESLA TTF have heat loads of about 1 W/m average for the parts
of the system at 4 K and below.

It is somewhat difficult to directly extrapolate values for the 200 MHz
10 m long modules from this disparate set of previous designs. However,
it would probably safe but not extravagant to estimate 5 W/m for the 4.5
K refrigeration load for these modules. Also we can take the 80 W load
mentioned above as the shield load for the long modules, applying one
factor of two for the larger size and a second factor of two rounded
down to reflect the fact that we will not want the shield to be a
critical item. Including 0.05 g/s of 4.5 K liquefaction for each cavity,
the total static cryogenic load of the 200 MHz 10 m module is estimated
to be 50 Watts at 4.5 K, 300 Watts at 40-60 K and 0.2 g/s liquefaction
at 4.5 K.

To get a similar estimate for the static loads 200 MHz short module and
the 400 MHz module we take 2/3 of the load for the 200 MHz long module.
The dynamic loads of the linacs are discussed in Chapter 7 of this
Report. The values taken in Table 2 are the baseline values chosen in
the Superconducting Study Meeting \[11\]\[12\]:  these are for the
Preaccelerator, 2090 W;   for RLA1, 1337 W;  and for RLA2, 12,034 W.
This is approximately a factor of three more than what has been
presented in chapter 7, which assumed an ideal case with all the
cavities achieving the specified Q0 and no contributions to the dynamic
load from other sources (field emission, higher order modes, couplers
etc). The number presented here is certainly conservative in that sense
and should become smaller as the R&D progresses.

### Half-Arcs of the Storage Ring

The arcs of superconducting magnets in the muon storage ring are
illustrated and discussed in Chapter 8 of this report. Each of the two
arcs is divided into two half-arc cryogenic modules each about 86 m in
length. For the purposes of estimation of the cryogenic performance,
each of the half-arcs contains 9 cells: a total of 18 dipoles and 18
quadrupoles; and each operates as a magnet string with a feed box at one
end and an end box at the other. The magnet string operates with a flow
of 40 g/s of single-phase helium, which passes down the length of the
string in alternating half-cells and recoolers, and returns down the
string again in alternating half-cells and recoolers. After passing
through all of the magnets in the string, the single phase flow is
flashed into the shell side of the recoolers. The two-phase sides of the
recoolers are connected in series.

The heat loads are estimated in Chapter 8: the static load is 5 W per
half-cell at 4.5 K and 30 W at 40-60 K. The dynamic loads are due to
particle heating of the magnet iron and of the tungsten liner inside the
magnet bore which is cooled by a flow of 40-60 K helium. The total lead
current is 50 kA for each arc of the storage ring. It has been assumed
that the half-arcs will have a transfer line connection box at both
ends.

Issues in the storage ring cryogenic system are first, the large tilt of
the ring, and second, the deep location of the west arc of the ring. The
tilt requires that the magnet strings of the arcs operate on a slope
that varies from about 20 % at the end of the arc to level at the apex
of the ring. This presents problems in controlling the flow of the
two-phase helium in the recoolers mentioned above. Each of the 4 strings
of magnets will have to be operated so that the two-phase flow is down
hill, and the recoolers will have to be equipped with wiers to
distribute the two-phase fluid on the heat exchange surfaces. CERN has
had to take similar measures in the LHC which has a slope much smaller
than here. The 200 meter depth of the west arc in the storage ring
presents problems with head pressure in the distribution of cryogens.
For example, a 200 m head of saturated liquid helium is a pressure of
2.3 bar and of saturated gas, 0.43 bar. These are significant pressures
compared to the saturation pressure of 1.3 bar, at it is clear that the
depth places requirements on the cryogenic system. At LHC this problem
is dealt with by dividing the refrigeration plant cold boxes at the 20 K
level, putting the cold end down in the tunnel. This would be
appropriate for the storage ring if it proves to be cost effective to
have a local plant rather than distributed refrigeration for the deep
end. An alternative to this is to put a cold compressor at the deep end
to provide the head pressure. This was the choice made in the SSC
cryogenic system design and it will work here also.

### Solenoids of the Pre-Accelerator and Splitters and Arcs of RLA2

At the time of the Superconducting Study Meeting \[11\]\[12\] there was
no engineering design for the magnetic elements in the Pre-accelerator
or the arcs of RLA2. For the purposes of cryogenic load estimation we
take the static loads in the arcs of RLA2 to be the same as those in the
arcs of the storage ring. The dynamic load due to particle loss in the
last arc of RLA2 is estimated to be 2 W/m \[12\]. We therefore choose
half this peak value or 80 W per half-arc for the dynamic load. Likewise
we use half of the magnet current of the storage ring for an average in
the RLA2 arc.

Proceeding in the same way to choose static and loads for the pre
accelerator solenoids and the splitters in RLA2 we take the same values
as for the short 200 MHz module, recognizing that this may, at least in
the case of the solenoids, be an over-estimate.

### Transfer Lines and Boxes

The heat load of the transfer lines are taken be taken to be roughly the
same as the LHC Cryogenic Distribution Line \[1\]. This includes
functions of both the Neutrino Factory transfer lines and boxes and does
not include shut-off valves for all circuits or disconnect devices such
as u-tubes. The heat load values for the lines and boxes in Table 2
includes allowances for the valves, and for module connection piping.

## Cryogenic Load of the Neutrino Factory Subsystems

In Table 3 the component and module heat loads are added up and
displayed by category for each of the five cryogenic subsystems. The
transfer line lengths and boxes have been distributed among the
subsystems, so that the table gives the connected load for each
subsystem.

## 4.5 K Equivalent Cryogenic Loads

In order to get a feeling for what is implied in terms of hardware by
the cryogenic loads presented in Table 1, and to be able compare and
combine loads in different categories to get an estimate of total
refrigeration plant requirement, it is convenient to reduce all of the
loads to a common basis in thermodynamic ideal power. The ideal power is
familiar as the power required to reversibly move heat from a
temperature T to a higher temperature T~o~. According to Carnot\'s
formula this is (T~o~ - T)/T. For refrigeration at 4.5 K with heat
rejection at T~o~ = 300 K the ideal work is 65.7 Ideal watts per watt of
refrigeration. This is given also in the second line of Table 1 above.
Ideal work or power can be determined for all of the categories of
refrigeration plant load, and these are given in Table 1 also. For
example, refrigeration with a supply and return at 4.5 K as indicated in
lines 3 and 4 of the table requires 71.8 w/w and refrigeration at 40-60
requires 6.14 w/w. The ideal power of a refrigeration process is given
in terms of J/g, that is ideal power per g/s of flow.

The ideal power equivalents in Table 1 are used to express the loads in
Table 3 in terms of equivalent power at 4.5 K. These are given in Table
4 below together with the percentage distribution of the equivalent
power over the five cryogenic subsystems.

This table presents the start of a second law analysis of the Neutrino
Factory cryogenic system. It is interesting to note that 70% of the
equivalent load is in the static and dynamic loads at 4.5 K., about 20%
in the shielding loads; and only 10% in liquefaction. This suggests that
as the engineering design of the components gets started, trying to
intercept more heat on the shields and in liquefaction streams could
reduce the operating cost and the size of the cryogenic plant

The total equivalent load is approximately 60 kW. This gives an
understanding of both the size and cost of cryogenic plant for the
Neutrino Factory. The CERN cryogenics group gives scaling methods
\[2\]\[3\] by which plant equipment cost can be scaled from equivalent
load. Also we can say that the equivalent load here requires a plant
capacity approximately half that of LHC for high-availability operation.

REEFERENCES

1.  *The Large Hadron Collider* - Conceptual Design, (The Yellow Book)
    CERN/AC/95-05(LHC) October 1995

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    p735-739 CEA/Saclay/96 080/1

7.  Superconducting Radio Frequency Linac for the Spallation Neutron
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8.  W. Schneider et. al., \"Thermal Performance of the CEBAF
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9.  F. Alessandria et. al., \"Design, Manufacture and Test of the
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10. G. Horlitz, T. Peterson, and D. Trines \"The TESLA 500 Cryogenic
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11. Superconducting RF Study Meeting, Held at Fermilab February 17 -
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12. Private communication from M. Harrison, BNL