### 6.2.2 VLHC-2 Cryogenic System Concept[^1]

#### 6.2.2.1 Introduction. 

This study of possible high field VLHC cryogenic systems relies heavily
on previous reports about VLHC cryogenics, especially "Cryogenic Systems
for the High Field RLHC Study Cases," by M. McAshan and P. O. Mazur, and
"Cryogenic Systems for the Low Field RLHC Study Cases," by the same
authors \[1,2\]. Comparisons are frequently made with LHC parameters not
only because it is the most recent large accelerator cryogenic system
design, but because the thorough analyses done in support of the LHC
cryogenic system provide an excellent baseline for comparison. One of
the most extensively used LHC documents was "LHC sector heat loads and
their conversion to LHC refrigerator capacities," by L. Tavian and U.
Wagner \[3\].

#### 6.2.2.2 System layout. 

The high field VLHC design effort will use 12 cryogenic plant locations
as the working assumption for the cryogenic system layout. Such an
arrangement creates 24 cryogenic strings of approximately 10 km length
each.

![](media/image1.wmf){width="5.998611111111111in"
height="4.269444444444445in"}

Figure 1. VLHC high field cryogenic schematic for one cell

Shown above in Figure 1 is a concept for a flow and electrical bus
schematic for one cell of the high field VLHC. We avoid the use of
recoolers or two-phase helium by allowing a 1 K rise in the helium flow
through the magnet cold mass. Magnets are cooled by a large flow rate of
supercritical, 4.5 K helium.

A nominally 80 K to 110 K helium stream cools the thermal shields and
beam screens. High pressure (20 bar) helium is selected for the shield
and beam screen since the higher pressure and density permit more mass
flow in a given pipe size. Nevertheless, pressure drops for the 80 K to
110 K flow should be small so that most of the pressure remains
available for expander work upon returning to the cold box.

This flow scheme provides four parallel beam screen cooling flow paths
in each cell, two in each 135 meter long half-cell. A crossover is shown
in each half-cell. The alternative to the crossover is balancing valves
controlled by temperature sensors in the spool piece. Depending on how
the beam screen passes through the interconnect, valves might be less
costly than the crossover, but for now we will show the crossover.

This scheme puts all the large cold pipes and most of the electrical bus
in a separate transfer line, so one does not have to deal with them at
each magnet interconnect. It requires one jumper from the transfer line
to the magnet string every 270 m for helium pipe connections, and one
jumper every half-cell, or every 135 m, for electrical bus connections.
Jumper connections containing electrical bus will require flow plugs to
prevent helium flow short-circuits. The helium pipe containing four 25
kA bus may be cooled with a fraction of the 5.5 K, 1.8 bar return flow
or with a parallel supply flow of 4.5 K, 4 bar helium. A 300 K helium
gas return pipe is shown for lead flows and relief valve flow
collection. A 300 K, 20 bar, helium gas line (not shown in Figure 2)
might be required for inventory management.

The quench valve spacing of one every 270 meters appears to be adequate
based on an analysis of quenching in 25 kA Nb~3~Sn magnets \[4\]. Large
quench valves would be required, with a port size of at least 60 cm, but
quench pressures would remain under 20 bar.

All of the lines utilize helium as the coolant. Our initial decision is
not to use nitrogen in the tunnel, but one might make good use of it
above ground for cool-down and load leveling. Although it presents
safety problems for the tunnel, one might reconsider the use of nitrogen
in the tunnel in the thermal shields and/or for recooling helium from
the beam screens, in order to reduce the huge helium inventory of this
system.

#### 6.2.2.3 Estimated heat loads. 

The heat load numbers in Table 1 (below) are scaled from LHC heat loads
as reported in reference \[3\]. A thermal model \[5,6,7\] scales static
heat loads to the thermal shields and cold mass for VLHC based on LHC
experience. Synchrotron radiation comes from beam dynamics studies
\[8\]. An analysis finding optimum beam screen temperature is also
reported in \[8\].

The heat load to the thermal shield of the arc magnets in LHC at
nominally 60 K is 3.7 W/m. Scaling to our high-field Nb3Sn magnet
concept, we find 4.2 W/m as the predicted static heat load to the VLHC
magnet thermal shield. To the LHC transfer line at 60 K, the heat load
is 2.7 W/m. Our VLHC transfer line is smaller in diameter than the LHC
transfer line by 0.80, so we use 0.80x2.7 = 2.2 W/m.

For the magnet cold mass heat load estimate, static and dynamic heat
loads for LHC scale up with our higher current and higher luminosity in
VLHC, adding 0.15 W/m to the 0.35 W/m LHC number, yielding 0.50 W/m for
VLHC. In addition, we have a warmer beam screen than LHC, adding about
another 0.14 W/m (total for two beams), for a total of 0.64 W/m.

To the beam screen we estimate 10 W/m total for both beams due primarily
to synchrotron radiation. Image current heating and multipacting are
negligible compared to the 5 W/m/beam synchrotron radiation. As
indicated in Figure 2 and in Table 1, the beam screen operational
temperature in this flow scheme is between 90-110 K, at the predicted
optimum range. Studies \[7\] have shown the optimal magnet thermal
shield temperature (in terms of minimizing overall refrigeration power)
to be about 65 K, consistent with the LHC selection of thermal shield
temperature. In order to reduce the number of pipes through this VLHC
system, the thermal shield and beam screen are placed in series with the
thermal shield first. The high heat load on the beam screen results in
its optimum temperature dominating that for the screen and thermal
shield combined. Thus, the optimum thermal shield average temperature
when in series with the beam screen is 83 K.

Table 1. Predicted heat loads and power requirements

![](media/image2.wmf)

#### 6.2.2.4 Current leads. 

There are one 25 kA dipole circuit per 10 km string and two 25 kA
quadrupole circuits per 20 km. The 25 kA dipole circuit requires a pair
of current leads at each end of the 10 km string. Thus, each cryo plant
location has eight 25 kA leads and each 10 km turnaround point has 4
leads. We assume six 100 amp corrector leads per beam per spool piece,
with about 150 spools in one 10 km sector, so 900 corrector leads per
sector. LHC current lead test data \[9\] and Fermilab HTS lead test data
\[10\] were used to scale cooling requirements for VLHC-2 current leads.
The relatively low number of high-current leads and the use of HTS leads
make the total cooling power for the current leads only about 4% of the
cryogenic system power.

#### 6.2.2.5 Cooling power requirements and plant sizing. 

Table 1 shows that the heat load estimates and the 240 km circumference
of the VLHC give rise to a system requiring about 105 MW of installed
cooling power, equivalent to about two large cryoplants at each of the
12 locations. Such a system would total about 3.3 times the cooling
capacity of the LHC cryogenic system. Note the applied factors: the
uncertainty factor of 1.25 on heat loads other than the beam screen, the
carnot efficiency of 0.30 which is high but achievable with today's
technology (LHC reports 0.3 for their helium systems), and the
overcapacity factor of 1.3. Overcapacity is the cooling capacity reserve
required for maintenance, control, and non-optimal operation. LHC uses a
factor of 1.5. We have reduced that to 1.3 in light of the large
proportion of heat load due to synchrotron radiation, over which we have
control.

#### 6.2.2.6 Cool-down and warm-up.

Cool-down times are estimated to be on the order of two months using
liquefier capacity. Each 20 km of high field VLHC has roughly 35000 tons
of cold mass (about equal to LHC), requiring the removal of about
3x10\^12 Joules to cool to 80 K. Some reduction in time can be gained
with the use of above-ground LN2 precooling, but extremely large amounts
of LN2 storage would be required. The extremely large cold mass will
force long cool-down and warm-up times.

#### 6.2.2.7 Helium inventory. 

The inventory for the entire machine is estimated to be 0.65 million kg
or 5 million liquid liters equivalent. This is about 85 times the
Tevatron inventory, 7 times the LHC inventory, and about 0.056 of the
annual U.S. production of helium, costing about \$12 million. One of the
problems with reducing the number of cryogenic plant sites from 12 to
six is that doubling the lengths of cryogenic loops, along with doubling
the mass flow to maintain the same exit temperature, requires
significantly larger diameter pipes. As a result, the helium inventory
for such a system is approximately twice this one, about 10 million
liquid liters instead of 5 million liquid liters.

#### 6.2.2.8 Conclusions and recommendations. 

While a high field VLHC cryogenic system as described here is feasible,
at \$0.114/kWh, power would cost \$1.00 per Watt-year, so the "installed
power" shown in MW could be approximately the annual power bill in M\$.
Thus, one can see that it would be very desirable to reduce the
installed power to significantly less than the presently estimated 105
MW. The heat load with the biggest potential for reduction by some
innovative method is probably the synchrotron radiation. Developing
methods for removing some significant fraction of the synchrotron
radiation at room temperature could permit a dramatic reduction in
cryogenic system size for a high field VLHC.

In order to make cool-down and warm-up times reasonable, one would like
to significantly reduce the amount of cold mass, perhaps with warm-iron
magnets.

Other recommendations for cryogenic system R&D may be found in (THE R&D
SECTION).

#### References.  {#references. .Reference-heading}

\[1\] M. McAshan and P. O. Mazur, "Cryogenic Systems for the High Field
RLHC Study Cases," 1996 Snowmass Study.

\[2\] M. McAshan and P. O. Mazur, "Cryogenic Systems for the Low Field
RLHC Study Cases," 1996 Snowmass Study.

\[3\] L. Tavian and U. Wagner, "LHC sector heat loads and their
conversion to LHC refrigerator capacities," LHC Project Note 140 (1998).

\[4\] Roger Rabehl, VLHC quench study, personal communication.

\[5\] C. Darve, A. Poncet, D. Willems, "Technical Note 98-19, CTM3, the
latest evolution of the cryostat thermal model: thermal performance
measurements of the first run from March to May 1998," 03/1999.

\[6\] C. Darve, G. Ferlin, M. Gautier, L.R, Williams,
LHC-Project-Note-112, "Thermal performance measurements for a 10 meter
LHC dipole prototype (Cryostat Thermal Model 2)," 11/1997.

\[7\] Christine Darve, et. al., "VLHC Thermal Shield Cooling," to be
published as a TD note or VLHC note.

\[8\] Pierre Bauer, et. al., "VLHC Beam Screen Cooling," to be published
as a TD note or VLHC note.

\[9\] Amalia Ballarino and Albert Ijspeert, "Design and Tests on the 30
to 600 A HTS Current Leads for the Large Hadron Collider",
CERN-LHC-Project-Report-78, 24 Oct 1996.

\[10\] G. Citver, et. al., "Thermal tests of 6-kA HTS current leads for
the Tevatron," Advances in Cryogenic Engineering, Vol. 45B, (2000), pp.
1549 -- 1556. (Also FERMILAB-Conf-99-284)

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