From: Joel H. Schultz

To: Dale Meade, Phil Heitzenroeder

Subject: Update of Cryogenic Refrigerator Sizing and Costing for FIRE\*
2.14 m Reference with Self-Consistent Scenario

Date: August 11, 2003

NSO No WBS7_081103_UpdateCryoRefrigSizeCostFIRE-2003.doc

**Introduction**

The FIRE cryoplant and nitrogen distribution system provides liquid
nitrogen to the TF and PF magnet systems to recool the magnets after
pulses and for cooldown from room temperature. The magnet system is
flushed out with helium, immediately before each pulse, in order to
prevent the formation of radioactive N13. This memorandum describes the
magnet cooling circuit, the overall cryoplant topology, the cryogenic
loads, and the sizes of the cryoplant components. It has been updated
from previous refrigerator descriptions[^1] to be consistent with losses
in reference 2.14 m design and baseline and extended experimental plans
that are consistent with constraints on total fusion energy and recool
times[^2].

**I. Magnet Cooling Circuit**

The magnets are cooled by circulating liquid nitrogen through cooling
lines (TF), and radial flow through magnet interpancake space (CS and PF
coils). Liquid nitrogen is blown out and replaced by pressurized helium,
before pulses, in order to eliminate the creation of N13 through neutron
irradiation. A negligible amount of N13 is still formed in the shielded
nitrogen atmosphere of the nuclear island, but it is sufficiently low
that no nitrogen holdup system is now required.

The TF inside and outside legs are cooled separately by cooling lines
that are fed through adjacent gun-drilled holes in each of the TF coil
turns. One set of lines turns inwards and cools the TF inside leg and
the inner halves of the upper and lower legs, the other the outside leg
and the outer halves. The line inlet and outlet points are located at
the high and low points of the profile to facilitate draining of liquid
nitrogen prior to a pulse.

The central solenoid and poloidal field coils are cooled radially
between double pancakes. As in CIT, the flow direction is from the
outside to the inside to prevent outer layer heating and turn-turn
delamination. A can around the outside of the Central Solenoid acts as a
distribution header. The pancakes are individually insulated, but there
is no ground wrap around the entire coil, because of the need for radial
flow.

**II. Load Assessment**

Cryogenic loads, requiring the circulation of liquid nitrogen, include
the following:

> 1\) Radiation from the inner vacuum vessel warm surface to the inner
> magnet surface

2\) Radiation from the outer magnet surface to the cryostat walls and
the ducts

> 3\) Radiation from the transfer lines to its cryostat walls

4\) Conduction through cold mass supports

> 5\) Joule heating of the TF and PF coils
>
> 6\) Neutron and gamma heating of the TF and PF coils during pulses

7\) Heat conduction and Joule heating in the high-current leads

> 8\) Cold mass cooldown from room temperature
>
> 9\) Removal of nuclear after heat

The load parameters that are most relevant to assessing these loads are
accumulated in Table I. The dominant load is the ohmic dissipation of
the TF coil.

Table I- Key Cryogenic Load Parameters

(baseline/extended)

+----------------------------------------+-----------+----------------+
| Parameter                              | Units     | Value          |
+----------------------------------------+-----------+----------------+
| Ediss, TF                              | (GJ)      | 16.14          |
+----------------------------------------+-----------+----------------+
| Ediss, PF                              | (GJ)      | 6.84           |
+----------------------------------------+-----------+----------------+
| Ncircuits                              |           | 8              |
+----------------------------------------+-----------+----------------+
| ntransfer lines                        |           | 3              |
+----------------------------------------+-----------+----------------+
| L,xfer line                            | \(m\)     | 200            |
+----------------------------------------+-----------+----------------+
| tdwell, max                            | \(s\)     | 4500           |
+----------------------------------------+-----------+----------------+
| Npulses, full-power                    |           | 3000/6000      |
+----------------------------------------+-----------+----------------+
| Npulses, total                         |           | 30,000/        |
|                                        |           |                |
|                                        |           | 60,000         |
+----------------------------------------+-----------+----------------+
| Max pulses/storage                     |           | 40             |
+----------------------------------------+-----------+----------------+
| Max pulses/week                        |           | 100            |
+----------------------------------------+-----------+----------------+
| Max no. RT cooldowns                   |           | 50             |
+----------------------------------------+-----------+----------------+
| Storage tank drawdown                  |           | 0.8            |
+----------------------------------------+-----------+----------------+
| Storage tank boiloff                   |           | 0.1            |
+----------------------------------------+-----------+----------------+
| J/cooldown                             | (GJ)      | 110            |
+----------------------------------------+-----------+----------------+
| J/cooldowns, lifetime                  | (GJ)      | 5,500          |
+----------------------------------------+-----------+----------------+
| Pradiation, in                         | (kW)      | 59.0           |
+----------------------------------------+-----------+----------------+
| Pradiation, outside                    | (kW)      | 7.48           |
+----------------------------------------+-----------+----------------+
| Pconduction                            | (kW)      | 3.145          |
+----------------------------------------+-----------+----------------+
| P,xfer lines                           | (kW)      | 15             |
+----------------------------------------+-----------+----------------+
| Pleads, TF                             | (kW)      | 10.4           |
+----------------------------------------+-----------+----------------+
| Pleads, PF                             | (kW)      | 11.1           |
+----------------------------------------+-----------+----------------+
| Pdiss, TF                              | (MW)      | 3.59           |
+----------------------------------------+-----------+----------------+
| Pdiss, PF                              | (MW)      | 1.52           |
+----------------------------------------+-----------+----------------+
| Pdiss, total                           | (MW)      | 5.19           |
+----------------------------------------+-----------+----------------+
| Pleads, total                          | (kW)      | 21.52          |
+----------------------------------------+-----------+----------------+
| Pidle                                  | (kW)      | 95.4           |
+----------------------------------------+-----------+----------------+
| Ptotal, 1 recool                       | (MW)      | 5.21           |
+----------------------------------------+-----------+----------------+
| lN2 flow, full-power recool            | (kg/s)    | 26             |
+----------------------------------------+-----------+----------------+
| Volume, lifetime, total lN2            | (Mgal)    | 310/475        |
+----------------------------------------+-----------+----------------+
| lN2 usage/pulse, max                   | (kgal)    | 30.7           |
+----------------------------------------+-----------+----------------+
| lN2 Storage tank requirement           | (kgal)    | 881/1,087      |
+----------------------------------------+-----------+----------------+

The nitrogen storage tanks are sized for a two-day supply of nitrogen
for the worst case of DT, H-mode extended operation. The energy needed
for cooldown from room temperature was calculated to be equal to 13.4
days of idling losses. Therefore, the magnet system is kept cold
overnight and weekends and only warmed up to room temperature during
maintenance periods. There 50 room temperature cooldowns during the
machine life. Heaters are used on the vent lines to prevent condensation
plumes of liquid nitrogen.

**III.** **Cryoplant Topology**

The overall cryoplant design of FIRE was originally based on those of
CIT[^3] and BPX[^4]. Major design features include the following:

1.  Large liquid nitrogen storage tanks and fill stations are used,
    instead of a closed-cycle nitrogen refrigerator. However, in FY99,
    FIRE agreed with CIT, BPX, and Alcator that truck deliveries from a
    commercial air liquefaction plant must be most economical, because
    of the pulsed nature of the load. This was reviewed in FY00 and both
    BOC/AIRCO and Air Liquide recommended the construction of dedicated
    on-site or near-site nitrogen plants. The design still includes
    on-site liquid nitrogen storage.

2.  FIRE uses the Alcator C-Mod method of one pump and individual
    regulator valves for each flow circuit. This provides close to
    optimized cooldown and has proven to be very reliable.

3.  A subcooler is used, as in the BPX and CIT designs, in order to
    provide 80 K liquid nitrogen to the coils. The boiling temperature
    of nitrogen at 10 atmospheres is 105 K. The expensive secondary
    circuit of CIT is eliminated by BPX and FIRE.

4.  The amount of radioactive nitrogen-13 generated in FIRE is small,
    because of the smaller volume of unshielded nitrogen inventory. The
    FY99 cryogenic system provided one day's holdup for nitrogen-13,
    which has a half-life of ten minutes. Even without holdup, the
    discharge of nitrogen-13 would be within allowables[^5] for sites
    such as ORNL or Savannah River, with large distances to the site
    boundaries. The present design purges the coils with helium before
    operation, eliminating any need for nitrogen holdup.

####### Design Tradeoff

Five options were considered for the FIRE cryogenic refrigeration
system, as illustrated in Figures 1-4:

1)  Option 1a: Temporary Storage of all Irradiated Gas after Pulse with
    an Open Secondary

2)  Option 1b: Separate holdup streams for highly-irradiated nitrogen
    and recool gas after Pulse with Open Secondary

3)  Option 2: Open Nitrogen Loop with Helium Purge before a pulse

4)  Option 3: Magnet cooling by a closed-loop secondary nitrogen circuit

5)  Option 4: Magnet cooling by a closed-loop secondary helium circuit

The schematic of a sixth option, a helium refrigerator with closed-loop
primary and secondary circuits, has been developed, as shown in Figure
5, but not yet sized and costed. This option is the only one that avoids
the cost of replacing large amounts of nitrogen vented into the
atmosphere, but would also have the highest capital cost.

+-----------------------------------+-----------------------------------+
| ![](me                            | ![](media/image2.                 |
| dia/image1.wmf){width="3.30625in" | wmf){width="3.4916666666666667in" |
| height="3.84375in"}               | height="3.745833333333333in"}     |
|                                   |                                   |
| Figure 1: Option 1: Temporary     | Figure 2: Option 2: Open Nitrogen |
| Storage of Irradiated Gas after   | Loop with Helium Purge            |
| Pulse, Open Secondary             |                                   |
+-----------------------------------+-----------------------------------+
| ![](media/image3                  | ![](me                            |
| .wmf){width="3.282638888888889in" | dia/image4.wmf){width="3.45625in" |
| height="4.200694444444444in"}     | height="4.302083333333333in"}     |
|                                   |                                   |
| Figure 3: Option 3-Closed-loop    | Figure 4: Option 4: Closed-Loop   |
| Secondary N2 Circuit (BPX/CIT)    | Helium Secondary                  |
+-----------------------------------+-----------------------------------+

![](media/image5.wmf){width="6.355555555555555in"
height="8.395833333333334in"}

Figure 5: Fire Magnet Refrigerator with closed-cycle helium primary and
secondary circuits

The relative costs of the original five options are compared in Table
II:

Table II: Relative Costs of Five Refrigerator Topology Options

  ----------------- ----------------- ----------------- -----------------
  Refrigerator      PACE, min         PACE, max         Total
  Option                                                

  1a Open N2,       9.04              12.2              16.7
  Holdup all N2                                         

  1b Separate       5.51              8.64              11.8
  holdup streams                                        

  2 Open N2, He     5.46              8.59              11.8
  purge                                                 

  3 Closed-loop lN2 5.97              9.1               14.6
  Secondary                                             

  4 Closed-loop He  13                16.1              22.1
  Secondary                                             
  ----------------- ----------------- ----------------- -----------------

The performance tradeoffs are summarized as numerical rankings in Table
III:

Table III: Cost/Performance Rankings of five refrigeration system
options

  -------------------------- ------ ----------------------- -------------
  Refrigerator Option        Cost   N13 Generated/Released  Recool Time

  1a Open N2, Holdup all N2  4      3                       2

  1b Separate holdup streams 2      4                       5

  2 Open N2, He purge        1      2                       2

  3 Closed-loop lN2          3      5                       1
  Secondary                                                 

  4 Closed-loop He Secondary 5      1                       4
  -------------------------- ------ ----------------------- -------------

Option 2 was selected as the new reference design, because it had the
best overall combination of low cost, radioactivity, and recool time, as
shown in Table III. Parameters have been updated to correspond to the
CY2002 FIRE\* reference design at Ro=2.14 m and are reported in Section
V.

##### IV.. Cost Algorithm

New pricing information was solicited on the cost of vacuum-jacketed
piping, unjacketed piping, elbows, and valves. A new set of cryogenic
equipment costing equations were derived on the basis of the data base
and are listed in Table IV. Although impressively large at first glance,
the data base is still not adequate. In particular, we haven\'t obtained
good recent pricing on large cold boxes, nitrogen gas bags, heaters or
blowers. However, because of the need to begin comparing different
design options, an interim set of costing equations was derived, based
on previous cost studies. This will be updated as new information
becomes available.

Table IV: Cryogenic Equipment Costing Equations

+-----------------+--------------------+------------------------------+
| Component       | Equation           | Notes                        |
+-----------------+--------------------+------------------------------+
| Pump/Compressor | \$273/gpm          | Liquid nitrogen,             |
|                 |                    | Barber-Nichols quote         |
+-----------------+--------------------+------------------------------+
| Cold Box        | \$4500/T~o~        | Slack formula, ratioed to    |
|                 | (Q)^0.7^           | BPX subcooler cost x 1.5 for |
|                 |                    | inflation, Q is in W; T~o~   |
|                 |                    | is the outlet temperature    |
+-----------------+--------------------+------------------------------+
| Vacuum jacketed | \$164 D~i~ (\$/m)  | Di=Inner diameter in         |
| pipe            |                    | inches,PHPK quote            |
+-----------------+--------------------+------------------------------+
| Unjacketed pipe | \$73/m (Dt)        | Dt=Inner diameter thickness  |
|                 |                    | product in inches, Stainless |
|                 |                    | Tubular Products             |
+-----------------+--------------------+------------------------------+
| Valves          | \$267 D~i~^2.27^   | PHPK quote; relative prices  |
|                 |                    | from BPX;                    |
| Throttle        | \$180 D~i~^2.27^   |                              |
|                 |                    | D~i~ in inches.              |
| Shutoff         | \$140D~i~^2.27^    |                              |
|                 |                    |                              |
| Relief          |                    |                              |
+-----------------+--------------------+------------------------------+
| Controller      | \$150 k-Hardware;  | 40 % deflation since BPX     |
|                 | \$250 k-Labor      |                              |
+-----------------+--------------------+------------------------------+
| Blower          | \$300/hp           | BPX x 1.5 for inflation      |
+-----------------+--------------------+------------------------------+
| Nitrogen        | \$250/kW           | Scaled from intepretation of |
| heaters         |                    | BPX, x 1.5 for inflation     |
+-----------------+--------------------+------------------------------+
| Filters         | \$500/gpm          | Scaled from BPX, x 1.5 for   |
|                 |                    | inflation                    |
+-----------------+--------------------+------------------------------+
| Storage Bag     | \$30/m^3^          | Robinson\'s eqn. x 1.5 for   |
|                 |                    | inflation                    |
+-----------------+--------------------+------------------------------+
| Storage Tank    | \$8/gal (250 MAWP) | Taylor-Wharton quotes        |
|                 |                    |                              |
| (vacuum         | \$5/gal (40 MAWP)  |                              |
| insulated)      |                    |                              |
+-----------------+--------------------+------------------------------+
| Local I&C       | \$400 k            | 40 % deflation since BPX     |
+-----------------+--------------------+------------------------------+
| Contingency     | 16 % of PACE       | Ratioed from BPX             |
|                 | subtotal           |                              |
+-----------------+--------------------+------------------------------+
| Assembly,       | 18 % of PACE       | Ratioed from BPX             |
| Installation &  | total +            |                              |
| Test            | contingency        |                              |
+-----------------+--------------------+------------------------------+

The cryogenic load for all options is summarized in Table I:

# V. Sizing of the Design Options

A sizing workbook was developed for the four design options with five
worksheets. The first (reference) option of storing the radioactive gas
after a shot for three hours between shots was subdivided into an Option
A, in which all of the nitrogen used in one shot, including that used
for recooling, is stored temporarily, and an Option B, in which the
magnets are purged both before and after a shot, and only the purged
gases are stored. Option 2, described below in more detail, is sized in
Worksheet 3 of the Workbook "Mag Refrig Design Extended Ops - 2.14
m.xls".

## Sizing of Option2: Open Nitrogen Loop with a Helium Purge

If the liquid nitrogen were purged by helium before a pulse, then
essentially no radioactive gas would be generated by the pulse. Any
imperfectly shielded nitrogen atmosphere in the cell is not considered
here. There would then also be no need to purge the magnet vapor after a
shot and recool could begin immediately with no temporary storage. The
disadvantage is that pressurized helium storage and a helium-nitrogen
heat exchanger have to be added to the cryogenic system. There is also a
modest amount of helium that is vented and has to be purchased. Option 2
is illustrated by Figure 6 and sized in Table V.

![](media/image2.wmf){width="6.720833333333333in"
height="7.197222222222222in"}

Figure 6: Open Nitrogen Loop with Helium Purge

The sizes of the cryogenic refrigerator components in Option 2 are
listed in Table V.

Table V: Component Sizes of Option 2 with an Open Nitrogen Loop, Helium
Purge, and without Temporary Storage

+-----------------------------------------+-------+---------+----------+
| **Parameter**                           | **Un  | **Bas   | **Ex     |
|                                         | its** | eline** | tended** |
+-----------------------------------------+-------+---------+----------+
| **lN2 Storage tank requirement**        | (     | 880.7   | 1087.4   |
|                                         | kgal) |         |          |
+-----------------------------------------+-------+---------+----------+
| nstorage tank 12\" shutoff valves       |       | 4       | 4        |
+-----------------------------------------+-------+---------+----------+
| ### Nitrogen Supply to Magnets          |       |         |          |
+-----------------------------------------+-------+---------+----------+
| Lcold nitrogen piping                   | \(m\) | 200     | 200      |
+-----------------------------------------+-------+---------+----------+
| L 8\" lN2 vacuum-jacketed pipe          | \(m\) | 100     | 100      |
+-----------------------------------------+-------+---------+----------+
| Average nitrogen pumping reqmnt         | (     | 20.9    | 20.9     |
|                                         | kg/s) |         |          |
+-----------------------------------------+-------+---------+----------+
| Peak nitrogen pumping reqmnt            | (     | 30.3    | 41.7     |
|                                         | kg/s) |         |          |
+-----------------------------------------+-------+---------+----------+
| nRegulator valves to magnets            |       | 3       | 3        |
+-----------------------------------------+-------+---------+----------+
| Dregulator valves to magnets            | (in)  | 10      | 10       |
+-----------------------------------------+-------+---------+----------+
| nfilters                                |       | 4       | 4        |
+-----------------------------------------+-------+---------+----------+
| Total gpm, premagnet filters            | (gpm) | 819     | 819      |
+-----------------------------------------+-------+---------+----------+
| no 12\" shutoff valves                  |       | 6       | 6        |
+-----------------------------------------+-------+---------+----------+
| ## Purge Requirements                   |       |         |          |
+-----------------------------------------+-------+---------+----------+
| Flush cycles                            |       | 20      | 22       |
+-----------------------------------------+-------+---------+----------+
| Flush length                            | \(m\) | 50      | 50       |
+-----------------------------------------+-------+---------+----------+
| Di, flushed pipes                       | (in)  | 12      | 12       |
+-----------------------------------------+-------+---------+----------+
| V, total flushed volume                 | (     | 4.65    | 4.65     |
|                                         | m\^3) |         |          |
+-----------------------------------------+-------+---------+----------+
| M, He gas purges                        | (kg)  | 985     | 985      |
+-----------------------------------------+-------+---------+----------+
| nshots/Pressurized He tank capacity     |       | 20      | 20       |
+-----------------------------------------+-------+---------+----------+
| Volume, 18 atm pressure vessel,supply   | (     | 6800    | 6800     |
|                                         | m\^3) |         |          |
+-----------------------------------------+-------+---------+----------+
| Di, shutoff valve, He purge stream      | (in)  | 12      | 12       |
+-----------------------------------------+-------+---------+----------+
| L,addit\'l pipe, separate flush exhaust | \(m\) | 100     | 100      |
+-----------------------------------------+-------+---------+----------+
| Di, regulator valve, He purge stream    | (in)  | 12      | 12       |
+-----------------------------------------+-------+---------+----------+
| Total flush time                        | \(s\) | 600     | 600      |
+-----------------------------------------+-------+---------+----------+
| Average mass flow, flush stream         | (     | 1.642   | 1.642    |
|                                         | kg/s) |         |          |
+-----------------------------------------+-------+---------+----------+
| Q,He-lN2 heat exchanger                 | \(W\) | 1908    | 1908     |
+-----------------------------------------+-------+---------+----------+
| Blower capacity                         | (     | 156.5   | 156.5    |
|                                         | kg/s) |         |          |
+-----------------------------------------+-------+---------+----------+
| Blower power                            | (hp)  | 1795    | 1795     |
+-----------------------------------------+-------+---------+----------+
| Lexhaust pipes                          | \(m\) | 200     | 200      |
+-----------------------------------------+-------+---------+----------+
| Di, exhaust pipe                        | (in)  | 16      | 16       |
+-----------------------------------------+-------+---------+----------+
| no x Di,vent valves                     | (in)  | 2 x 12  | 2 x 12   |
+-----------------------------------------+-------+---------+----------+
| Peak mass flow through gas storage line | (     | 41.72   | 41.72    |
|                                         | kg/s) |         |          |
+-----------------------------------------+-------+---------+----------+
| Heater power                            | (kW)  | 8915    | 8915     |
+-----------------------------------------+-------+---------+----------+

**VI. Costing of the Design Options**

Having sized the individual components and proposed a set of costing
equations, it is now possible to compare the costs of the five design
options. Each option was costed according to the costing rules in Table
IV. The cost of Option 2 is given in Table VI, below.

Table VI: Cost of Option 2 with an Open Nitrogen Loop, Helium Purge, and
without Temporary Storage

  -------------------------------- ------- ------------- ---------- ----------
  Parameter                        Units   2.0 m Design  Baseline   Extended

                                                                    

  Subcooler                        (k\$)   1007.7        2008.7     2013.4

  lN2 Storage tank                 (k\$)   4211.8        4403.6     5437.2

  Dstorage tank shutoff valves     (k\$)   202.8         202.8      202.8

  L 8\" lN2 vacuum-jacketed pipe   (k\$)   196.8         196.8      196.8

  Nitrogen pump                    (k\$)   96.4          223.7      228.6

  Regulator valves to magnets      (k\$)   149.2         149.2      149.2

  Presubcooler filter              (k\$)   176.5         409.7      418.7

  Premagnet filter                 (k\$)   176.5         409.7      418.7

  Dmisc shutoff valves             (k\$)   304.2         304.2      304.2

  18 atm pressure vessel           (k\$)   89.8          448.8      471.2

  Shutoff valve, He purge stream   (k\$)   50.7          50.7       50.7

  Addit\'l pipe, separate flush    (k\$)   32.9          32.9       32.9
  exhaust                                                           

  Regulator valve, He purge stream (k\$)   75.2          75.2       75.2

  He-lN2 heat exchanger            (k\$)   24.7          40.2       40.2

  Blower                           (k\$)   556.7         538.4      538.1

  Cold exhaust pipe                (k\$)   58.4          58.4       58.4

  Warm exhaust pipe                (k\$)   58.4          58.4       58.4

  Vent valves                      (k\$)   101.4         101.4      101.4

  Nitrogen exhaust heater          (k\$)   1920.1        3462.2     3515.4

  Instrumentation and Control              759.2         1054.0     1144.9

  PACE, subtotal                   (M\$)   10.25         14.23      15.46

  Contingency                      (M\$)   1.64          2.28       2.47

  PACE+Contingency                 (M\$)   11.89         16.51      17.93

  Assembly, Installation & Test    (M\$)   2.14          2.97       3.23

  Grand Total                      (M\$)   14.03         19.48      21.16
  -------------------------------- ------- ------------- ---------- ----------

Although the total nitrogen consumption in the present baseline is
actually less than in the 2.00 m design, the refrigerator is more
expensive, because recool has been accelerated from 3 hours to ¼ -1¼
hours, depending on pulse length. The incremental cost of extended
operation is surprisingly similar to that of baseline operations. The
main reason for this is that recool ability "clamps" the refrigerator
power over a single shot, day, or week. The operations are extended
primarily by increasing the operating weeks, which increases nitrogen
consumption, but not refrigerator power or even local storage
requirements. Idling losses are also the same for baseline and extended
operations.

Although Option 2 requires a helium cold box and temporary helium
storage, their cost is relatively low, since the helium isn\'t needed
for magnet heat removal, but merely for purging the nitrogen volume.

.

The closed-loop helium secondary is the most expensive of the five
options considered, because of the requirement for a cold box,
compressor, and helium storage tank that is adequate for magnet
cooldown.

**VII. Cost of Nitrogen**

The cost of the cryogenic refrigeration system remains small in
comparison with the cost of nitrogen over the course of the project. The
energy dissipation in the TF coils was calculated by P. Titus over a
range of fields and flat-top times, while PF energy was scaled from the
6.0 GJ dissipation in a single simulation. The lifetime ohmic
dissipation is based on self-consistent experimental plan with 3,000
full-field and current shots, 30,000 lifetime shots and 6500 GJ of
fusion power for baseline operation and double these numbers for
extended operation. Titus has shown a broad range of tradeoffs between
nitrogen and power supply requirements vs. cooldown time. We adopted the
minimum power consumption scenario, starting each pulse at 80 K. This
study calculates the change in cost, due to increasing the size of FIRE
from Ro=2.0 m to Ro=2.14 m and using a self-consistent scenario.

In 2001, BOC gave pricing for a 10 year lease and a 15 year lease. This
was then updated in 2003 for nitrogen use up to four times that of the
previous design, an overly conservative intepretation of the extended
operations needs for the larger, 2.14 m machine. The quotes were scaled
to the self-consistent design, and an interpretation of the nitrogen
cost estimates is listed in Table VII:

Table VII: Nitrogen Cost Estimates

+----------------+-----+---------+-----------------+------------------+
| Total Cost     | Un  | P       | 2.14 m FIRE     | 2.14 m FIRE      |
|                | its | revious |                 |                  |
|                |     |         | Self-Consistent | Self-Consistent  |
|                |     |         | Baseline        | Extended         |
+----------------+-----+---------+-----------------+------------------+
| 10 Year        | (M  | 143     | 57.7            | 88.4             |
| Commitment     | \$) |         |                 |                  |
+----------------+-----+---------+-----------------+------------------+
| 15 Year        | (M  | 10      | 43.3            | 66.3             |
| Commitment     | \$) | 7/118.5 |                 |                  |
+----------------+-----+---------+-----------------+------------------+

The penalty for purchasing more nitrogen/year over 10 years seems high,
but is based on a quote of 20 cents/100 cu ft of liquid nitrogen for a
10 year lease and 15 cents/100 cubic feet for 15 years. In 2003, I
received a new quote from BOC. It remained at 20 cents/100 cu ft for a
10 year lease and 15 cents/100 cubic feet for 15 years. The explanation
was that inflation was exactly balanced by a quantity discount.
Unfortunately, the specifications were given to them when it was
believed that extended operation would consume four times as much
nitrogen as baseline, 2.0 m. It, therefore, seems probable that the most
recent quotation is too optimistic. If the cost were 25 cents/100 cu ft,
then nitrogen for the baseline would cost \$72 M over the life the
machine, while extended operations would cost \$110.5 M. I expressed
incredulity that the price for the same amount of nitrogen over 10 years
should be higher than that over 15 years to two different BOC
representatives, both Marc Berlinger, the interface, and Jim Flaherty,
who prepared the estimate. They insisted that this was the case and
Berlinger actually cited "return on investment" and "mortgage rates." I
tried to explain that getting less money in a longer period of time
can't be as good as getting more money in a shorter period and that one
actually pays more on a 15 year mortgage than a 10 year mortgage, even
if the monthly payments or even the interest rate are less, but to no
avail. So while I remain suspicious, I have to assume that this is the
actual result from BOC's costing spreadsheets. The reason for the second
cost for the 15 year lease/2.0 m FIRE is that the price/100 cubic feet
is a constant, down to 75 % of nominal usage. After that it would be
flat, so that BOC/AIRCO would collect \$8.5 M/year, even if the facility
never ran. Presumably, since the nitrogen requirements are now smaller,
the minimum cost would be less than \$8.5 M/year, but it may still be
the cost driver, increasing the lifetime nitrogen cost to something
above \$100 M over the actual sixteen year experimental plan.

A second estimate is (hopefully) being prepared by Air Products. They
have questioned me extensively about the actual operating plan, so
hopefully the fluctuations in load will be taken correctly into account
in the costing. They also have the latest, lower estimates of lifetime
nitrogen usage.

**VII. Conclusions**

Sizing and costing of the reference option, an open lN2 system with a
helium purge, has been updated to include a more extensive inventory of
losses in the 2.14 m machine and more self-consistent experimental plan
for both baseline and extended operations.

A methodology was developed for comparing different refrigerator design
options. Three of the five options were relatively inexpensive and
difference between their costs within the uncertainties of the costing
exercise. These were 1) Open N2 system with a helium purge, 2) Open N2
with a nitrogen purge and two exhaust lines, and 3) Closed-loop lN2
Secondary.

The open N2 system with a helium purge also had high-rankings in low
generation and release of N13 and recool time, although the difference
between all of the sytems may be relatively small in both categories.

The closed-loop lN2 secondary costing is probably optimistic, since it
doesn\'t include an emergency nitrogen holdup system. A more expensive
closed-loop helium refrigerator concept has been developed, but not
sized or costed. It's main advantage would be that of eliminating high
nitrogen costs. It would also eliminate any generation of radioactive
N13 and permit "IGNITOR-style" subcooling.

Option 2 was selected, Open N2 with a helium purge. If the relatively
low liquid nitrogen costs from a dedicated plant can't be confirmed for
nonsteady-state operation, the closed-cycle helium system is being
developed as a backup design.

Costs of the cryogenic refrigeration system were updated for the FIRE\*
Option, the CY2002 reference design, and the CY2003 baseline and
extended operations experimental plans. The overall cost of the
cryogenic system increased from to \$14 M to \$19.5 M for baseline
operation and \$21.2 M for extended operation. Recool time constraints
prevented extended operation from being significantly more expensive
than baseline.

The cost of liquid nitrogen has been reconfirmed by a new budgetary
estimate, albeit with identifiable sources of possible error. We are
attempting to obtain a second, independent estimate. The cost of
nitrogen has decreased, because of the fixed number of pulses in the
baseline and the reduced average power, integrated over all discharges.

[^1]: NSO No WBS7_000526\_ Sizing and Costing of Cryogenic Refrigerator
    Options.doc, Joel H. Schultz, \"Sizing and Costing of Cryogenic
    Refrigerator Options,\" May 26, 2000; NSO No
    WBS7_121401_UpdateCryoRefrigSizeCostFIRE\*.doc, Joel H. Schultz,
    "Update of Cryogenic Refrigerator Sizing and Costing for FIRE\* 2.14
    m Reference Machine," December 14, 2001

[^2]: NSO No WBS7_0709_Extended\_ Operations_Plan_Rev3, Joel H. Schultz,
    "Schedule and Shot-counts for FIRE Baseline and Extended Operations,
    Rev. 3," July 9, 2003

[^3]: R.B. Fleming and G.D. Martin, \"Liquid nitrogen cooling for the
    Compact Ignition Tokamak,\" Knoxville, SOFE 13, 1989

[^4]: R.B. Fleming and G.D. Martin, "System Description, Cryogenic
    System, WBS Q: BPX Design Description Document," Feb 13, 1991

[^5]: H. Khater, Sec. 5.8, FIRE FY 01 Engineering Report Update