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<title type="245">Further Design Features of the Nuclear Reactor at North Carolina State College</title>
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<author>Beck, Clifford; Menius, A. C., Jr.; Murray, R. L.; Underwood, Newton; Waltner, A. W.; Webb, George</author>
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<text id="NEfurther010052T">
<front><head rend="center">Further Design Features of the Nuclear Reactor at North Carolina State College
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<div2 type="titlepage" n="1">
<head>NCSC #46<lb/>
Copy <hi rend="underline">29</hi> of 50, Series A<lb/>
<title type="main">FURTHER DESIGN FEATURES<lb/>
OF THE<lb/>
NUCLEAR REACTOR<lb/>
AT<lb/>
NORTH CAROLINA STATE COLLEGE</title></head>

<p><name type="person">Clifford Beck</name><lb/>
<name type="person">A. C. Menius, Jr.</name><lb/>
<name type="person">R. L. Murray</name><lb/>
<name type="person">Newton Underwood</name><lb/>
<name type="person">A. W. Waltner</name><lb/>
<name type="">George Webb</name></p>

<p>PHYSICS DEPARTMENT<lb/>
<name type="corporate">SCHOOL OF ENGINEERING </name> <name type="corporate">NORTH CAROLINA STATE COLLEGE</name><lb/>
of the<lb/>
<name type="corporate">UNIVERSITY OF NORTH CAROLINA</name><lb/>
<name type="place">Raleigh North Carolina</name></p>

<p><date value="1952-01-00">January, 1952</date></p>

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</div2>
<div2 type="acknowledgement" n="1">

<p>The material presented in this report has<lb/>
resulted from the combined efforts of various<lb/>
members of the Physics Department. Almost<lb/>
all members of the department, in one way or<lb/>
another, have made noteworthy contributions<lb/>
to the reactor project. Members of the other<lb/>
departments in the School of Engineering,<lb/>
have also made significant contributions. The<lb/>
assistance of these men and the value of their<lb/>
contributions are gratefully acknowledged.</p>


<p>The Authors</p>
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</div2>
<div2 type="contents" n="1">
<head>TABLE OF CONTENTS</head>

<list>
<item>Introduction . . . . . . 1</item>
<item>I. The Reactor Building</item>
<item><list>
<item>A. General . . . . . . 2</item>
<item>B. Ventilation and Heating System for the Laboratories  . . . 3</item>
<item>C. Sewerage System for the Laboratories . . . . . . 4</item>
</list></item>
<item>II. Reactor Design</item>
<item><list>
<item>A. General . . . . . . 6</item>
<item>B. Concrete Shielding . . . . . . 6</item>
<item>C. Fissionable Fuel . . . . . . 8</item>
<item>D. The Fuel Cylinder and Reactor Envelope . . . . . . 9</item>
<item>E. Reflector, Thermal Column, Lead Shielding . . . . . . 10</item>
<item>F. Cooling System . . . . . . 11</item>
<item>G. Gas Disposal Unit . . . . . . 13</item>
<item><list>
<item>1. Hydrogen Oxygen Recombination System . . . . . . 13</item>
<item>2. Disposal to the Atmosphere . . . . . . 15</item>
</list></item>
<item>H. Instrumentation and Control . . . . . . 15</item>
<item><list>
<item>1. General . . . . . . 15</item>
<item>2. Fission Chambers . . . . . . 16</item>
<item>3. Neutron Flux Measurements on Linear Scales . . . . . . 16</item>
<item>4. Neutron Flux Measurements on Logarithmic Scales . . . . . . 18</item>
<item>5. Rate of Change of Neutron Flux: Period Measurements . . . . . . 18</item>
<item>6. Gamma Compensated Chamber . . . . . . 19</item>
<item>7. Measurement of the Gamma Ray Flux from the Reactor 19</item>
<item>8. Control Console and Recorder Rack . . . . . . 19</item>
<item>9. Control Safety and Shim Rods . . . . . . 21</item>
<item>10. Campus Monitoring . . . . . . 23</item>
<item>11. Miscellaneous Monitors . . . . . . 23</item>
</list></item>
</list></item>
<item>III. Reactor Characteristics</item>
<item><list>
<item>A. Safety Features . . . . . . 25</item>
<item>B. Reactivity and Nuclear Behavior . . . . . . 26</item>
<item>C. Power Level, Radiation Fluxes . . . . . . 28</item>
<item>D. Fission Products; Radioactivity . . . . . . 29</item>
</list></item>
<item>IV. Reactor Hazards and Safety <orig reg="Precautions">Preacautions</orig></item>
<item><list>
<item>A Normal Hazards . . . . . . 36</item>
<item>B. Minor Incidents . . . . . . 38</item>
<item>C. Major Catastrophe . . . . . . 41</item>
</list></item>
<item>V. Operation and Experimental Program</item>
<item><list>
<item>A. Start-Up . . . . . . 45</item>
<item>B. Initial Experiments . . . . . . . 45</item>
<item>C. Subsequent Experiments . . . . . . 46</item>
<item>D. Procedures and Policies . . . . . . 46</item>
</list></item>
</list>
</div2>

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<div2 type="figurelist" n="1">
<head>LIST OF FIGURES AND TABLES</head>

<p><list>
<item>Figure 1 Plan of Reactor Building</item>
<item>2 Elevation Plan of Reactor Building</item>
<item>3 External Appearance of Reactor Building</item>
<item>4 Laboratory Drainage System</item>
<item>5 Horizontal Cross-Section of Reactor Assembly</item>
<item>6 External View of Reactor Assembly</item>
<item>7 Photograph of Assembled Reactor Shield</item>
<item>8 Photograph of Partially Disassembled Reactor Shield</item>
<item>9 Photograph of Completely Disassembled Shield</item>
<item>10 Section Through Typical Exposure Port</item>
<item>11 The Reactor Cylinder</item>
<item>12 The Reactor Safety Envelope</item>
<item>13 Photograph of a Model of the Cooling Coils</item>
<item>14 Hydrogen-Oxygen Recombination-Recirculation System</item>
<item>15 Refrigerated Gas Cooler</item>
<item>16 Catalyst Chamber</item>
<item>17 Primary Condenser</item>
<item>18 Plan of the Gas Disposal System</item>
<item>19 Plan of the Control Room</item>
<item>20 Plan of Neutron Measuring Instrumentation: Linear Systems</item>
<item>21 Plan of Neutron Measuring Instrumentation: Logarithmic Systems</item>
<item>22 Control and Shim Rod Assembly</item>
<item>23 Reactor Behavior as the Control Rod is Withdrawn</item>
</list></p>

<p><list>
<item>Table 1 Characteristics of the Reactor Fuel 9</item>
<item>2 Data Relating to Fuel Cylinder 9</item>
<item>3 Data on Graphite Used in Reflector and Thermal<lb/>
Column 10</item>
<item>4 Activity Induced in the Reactor Cooling Water 12</item>
<item>5 Calculated Radiation Fluxes at 10 Kw Operation 28</item>
</list></p>

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<div2 type="introduction" n="1">
<head>FURTHER DESIGN FEATURES<lb/>
OF THE<lb/>
RALEIGH RESEARCH REACTOR<lb/>
AT<lb/>
NORTH CAROLINA STATE COLLEGE</head>

<p><hi rend="underline">INTRODUCTION</hi>
</p>
<p>A proposal to construct and operate a small nuclear reactor on the campus<lb/>
of the <name type="corporate">North Carolina State College</name>, at <name type="place">Raleigh, N. C.</name>, and the general design of<lb/>
a reactor which would be suitable for this purpose have been presented in previous<lb/>
reports.<ptr target="a1"/><ptr target="a2"/><ptr target="a3"/> The <name type="corporate">Atomic Energy Commission</name> has expressed approval of this<lb/>
project<ptr target="a4"/> and of the general design of the proposed reactor. It was recognized at<lb/>
the time of approval, of course, that a great deal of work yet remained to be done<lb/>
on the details of the design of the reactor before construction could begin.</p>

<p>Additional general plans of the reactor facility and further details of the <orig reg="reactor">re-<lb/>
actor</orig> design and of the auxiliary systems have now been completed. In <orig reg="accomplishing">accomplish-<lb/>
ing</orig> this, the staff at <name type="corporate">N. C. State College</name> have drawn heavily on the experience and<lb/>
ideas of the <name type="place">Los Alamos</name> and <name type="place">Oak Ridge</name> staffs. Designs of numerous component<lb/>
systems have been borrowed from the successful <name type="place">Los Alamos</name> water boiler and<lb/>
from the reports on reactor studies at <name type="place">Oak Ridge</name>, and have then been adapted to<lb/>
particular conditions and needs of the Raleigh Research Reactor. It has not been<lb/>
the intention of the <name type="corporate">State College</name> staff to produce a novel design of a reactor or to<lb/>
make original contributions to reactor technology. Rather, it has been the purpose<lb/>
to design and construct as simply and quickly as possible, a safe, flexible nuclear<lb/>
reactor with maximum adaptability to instructional and research purposes. The<lb/>
staff of <name type="corporate">N. C. State College</name> is therefore heavily indebted to the <name type="corporate"><abbr expan="Atomic Energy Commission">A. E. C.</abbr></name> and to the<lb/>
technical personnel of <name type="place">Los Alamos</name> and <name type="place">Oak Ridge</name> for the many suggestions and<lb/>
ideas which they have contributed to the Raleigh Research Reactor project with<lb/>
unfailing generosity and cooperation.
</p>
<p>The present report presents a general description of the Reactor Building,<lb/>
plans of the Reactor components, further discussion of potential hazards which<lb/>
may be involved, and the anticipated start-up procedures and operating policies.
</p>
</div2>
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</div2>

<div2 type="section" n="1">
<head><hi rend="underline">I. THE. REACTOR BUILDING</hi></head>

<div3 type="subsection" n="1">
<head>A. <hi rend="underline">General.</hi></head>

<p>The Raleigh Research Reactor is to be located in the southern half of the<lb/>
Court of Ceres, an open quadrangle near the center of the <name type="place">North Carolina State<lb/>
College</name> campus. The Court of Ceres lies between the buildings of the <orig reg="Engineering">Engineer-<lb/>
ing</orig> School and those of the Agricultural School. The location chosen for the <orig reg="reactor">re-<lb/>
actor</orig>, Site B as described in the report "Program Administration and <orig reg="Installation">Installa-<lb/>
tion</orig> Design of the Nuclear Reactor Project"<ptr target="a2"/> (p. 11 and Fig. 2), is one of the<lb/>
highest locations on the college campus and in the entire city of <name type="place">Raleigh</name>. The<lb/>
buildings housing Physics, Chemistry, and Engineering Research, whose <orig reg="activities">activi-<lb/>
ties</orig> particularly relate to the functioning of the reactor, are immediately <orig reg="adjacent">adja-<lb/>
cent</orig> to the quadrangle in which the reactor is being constructed. Thus, for<lb/>
several reasons the site chosen seems to be an advantageous one.</p>

<p>The plan of the Reactor Building is shown in Figures 1 and 2. A sketch of<lb/>
the external appearance is shown in Figure 3. The octagonally shaped reactor<lb/>
assembly is below ground level in the center of the 57 foot diameter Reactor<lb/>
Room. This room, in turn, is in the center of the building. On three sides of<lb/>
the room at ground level, are fourteen laboratory rooms to be used for <orig reg="instruction">instruc-<lb/>
tion</orig> and research. Underneath these laboratories, at the floor level of the<lb/>
Reactor Room, are five additional utility or laboratory rooms.
</p>
<p>On the fourth side of the Reactor Room are the Control Room and the <orig reg="Observation">Ob-<lb/>
servation</orig> Room, both being separated therefrom by <orig reg="masonry">masonary</orig> walls 12" thick<lb/>
and water-filled glass windows, 8" thick. In front of the Observation and <orig reg="Control">Con-<lb/>
trol</orig> Rooms is an entrance lobby and four offices.
</p>
<p>The photographic dark room, the counting laboratory and the Control<lb/>
Room are air conditioned. The entrance lobby and the offices are provided<lb/>
only with ordinary window ventilation. A ceiling exhaust fan furnishes <orig reg="ventilation">ventila-<lb/>
tion</orig> for the Observation Room. Except for the Control Room, these areas will<lb/>
be generally accessible to visitors and observers.
</p>
<p>It is not anticipated that radioactive contamination of these areas of the<lb/>
building will occur at any time. Plumbing facilities here are connected directly<lb/>
to the city system in the usual manner. The remaining areas of the building,<lb/>
i.e., the laboratories on upper and lower levels and the Reactor Room, may<lb/>
become contaminated with radioactive materials and therefore special <orig reg="ventilation">ventila-<lb/>
tion</orig> and sewer facilities are provided.
</p>
</div3>
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<div3 type="subsection" n="2">
<head>B. <hi rend="underline">Ventilation and Heating System for the Laboratories.</hi></head>

<p>
Separate systems are provided for supplying filtered air to and removing air<lb/>
from the laboratories. The intake air system is made up of two parts: one for<lb/>
the west side and one for the east side of the building. In each of the two parts,<lb/>
air is drawn through a bank of disposable paper filters located under the <orig reg="overhanging">overhang-<lb/>
ing</orig> eaves of the roof, near the front of the building. Intake blowers are mounted<lb/>
above the ceiling of the locker rooms and from these the air is distributed by ducts<lb/>
to each laboratory. The blowers in the supply system can be run either at full or<lb/>
at half capacity. In normal operation, each blower will operate at half capacity,<lb/>
which is 6,275 cfm. At full capacity, each system can supply 12,500 cfm, or a<lb/>
total of 25,000 cfm.
</p>
<p>The air is delivered to each laboratory through a control damper mounted<lb/>
on the inside wall of the room. In normal operation, the air is changed once every<lb/>
10 minutes.
</p>
<p>Providing comfortable temperature conditions in cold weather, with air <orig reg="flowing">flow-<lb/>
ing</orig> into and out the building at the above rate, would tax the capacity of usual <orig reg="building">build-<lb/>
ing</orig> heating systems. For this building, therefore, a dual system is used Heat<lb/>
exchangers in the main air supply duets insure a minimum air temperature of 65<hi rend="sup">o</hi>F.<lb/>
In addition, coils of hotwater pipes mounted in the ceiling or walls of each room<lb/>
provide radiant heat to the extent needed for comfort.
</p>
<p>The Exhaust Ventilation System withdraws the air from each laboratory<lb/>
through the hood in that laboratory and through the filter in the exhaust line under<lb/>
each hood, then through a system of ducts underneath the floor, to the filter room<lb/>
at the rear of the building. Air is supplied to and removed from the Reactor Room<lb/>
through louvered ventilators mounted in the wall of the room. Ducts from the <orig reg="exhaust">ex-<lb/>
haust</orig> ventilators of this room connect to the remainder of the Exhaust Ventilation<lb/>
System. Two 12,500 cfm centrifugal blowers, arranged in parallel, draw the air<lb/>
through the bank of filters and discharge it through a 48 inch diameter, 110 foot<lb/>
stack located at the rear of the building. In normal operation, only one of the two<lb/>
blowers is used. If desired, however, both blowers can be used simultaneously,<lb/>
in which case, 25,000 cfm are withdrawn through the exhaust system. At times<lb/>
it may be necessary to maintain the flow of air up the stack, when ventilation of<lb/>
the building is not desired. To permit this, a "by-pass" from the outside wall at<lb/>
the rear of the building to the blower intake is provided. If this by-pass is <orig reg="completely">com-<lb/>
pletely</orig> or partially open the full demand of the blowers can be satisfied with no<lb/>
air, or only part of the total, coming from the building itself. Operation of the<lb/>
by-pass can be either automatic or manual.
</p>
<p>The hoods in each room are of a special, downdraft design, having removable<lb/>
filters located in the exhaust duct under each hood.
</p>
</div3>
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</div3>
<div3 type="subsection" n="3">
<head>C. <hi rend="underline">Sewerage System for the Laboratories.</hi></head>

<p>It is not intended that any quantity of radioactivity above maximum <orig reg="concentration">concen-<lb/>
tration</orig> permitted by <name type="corporate"><abbr expan="Atomic Energy Commission">A.E.C.</abbr></name> regulations shall escape into the drain lines of the<lb/>
building. Short-lived radioactive materials above this concentration will be stored<lb/>
until sufficiently decayed, and long-lived materials above this concentration will be<lb/>
stored for disposal in other ways. Due to emergencies, accidental spillage or<lb/>
misoperation, however, above tolerance concentrations of activity may occasionally<lb/>
escape into the drain lines. For this reason, therefore, no drain lines from the<lb/>
work areas of the building connect to the city sewer system, except through a <orig reg="radiation">radia-<lb/>
tion</orig> monitored tank system.</p>

<p>All drain lines from the Reactor Room and the work rooms on the <hi rend="underline">lower level</hi><lb/>
discharge into a sump near the air filter room. A pump lifts the material from the<lb/>
sump to the drainage system of the laboratories above. The liquid at the sump is<lb/>
continuously monitored, and if excessive amounts of activity are found, the material<lb/>
is not pumped to the drainage system above. It should be necessary to use the drains<lb/>
on the lower level only seldomly and hence the sump pump will need to be used only at<lb/>
infrequent intervals.
</p>
<p>The drainage system from the ground level laboratories passes through<lb/>
system of monitors, holding tanks, and valves designed to prevent discharge of<lb/>
radioactive materials above concentrations permitted by <name type="corporate"><abbr expan="Atomic Energy Commission">A.E.C.</abbr></name> regulations to the<lb/>
city sewer system. (Fig. 4)
</p>
<p>In normal operation, laboratory drainage passes a radiation monitor and a<lb/>
cut-off valve into one of two 550 gallon tanks, arranged in parallel. The effluent<lb/>
line of this tank is halfway from top to bottom, so that the tank is always half full.<lb/>
As liquid leaves the tank it passes a second radiation monitor, located in the exit<lb/>
line, and then flows through an automatic, pneumatically operated valve to the city<lb/>
sewer system. When desired, the exit line from the midpoint of either tank can be<lb/>
closed and the tank becomes a holding tank with 275 additional gallons of capacity.
</p>
<p>In normal operation, the activity of materials discharged down the drains<lb/>
will be positively controlled within permissible limits before release. The <orig reg="radiation">radia-<lb/>
tion</orig> monitors and the hold-tanks serve as secondary defenses against unsafe<lb/>
amounts of radioactivity reaching the city sewer system in case activities of above<lb/>
tolerance levels are inadvertently released into the drains.
</p>
<p>The monitored holding tank system described above is intended to operate<lb/>
as nearly as possible as follows: If an amount of activity above the maximum<lb/>
permissible level goes down the drain, it passes the first radiation monitor, which<lb/>
sends a signal to the Control Room and also sends a signal to the pneumatically<lb/>
operated valve in the exit line of the hold-tank. The valve closes and the <orig reg="radioactive">radio-<lb/>
active</orig> material is caught in the tank. The operator then opens the valve to the<lb/>
second tank and this one is used in the drainage system while the decision is made<lb/>
as to the method of handling the material caught in the first tank. The radiation<lb/>
monitor in the exit line of the flow tank serves as a double check on the first <orig reg="monitor">moni-<lb/>
tor</orig>. It likewise acts to close the exit valve of the hold-tank if activity of excessive
</p>
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<p>level reaches that point.
</p>
<p>In actual practice, it may prove quite difficult to obtain radiation monitors<lb/>
capable of performing with reliability as described above, because the levels of<lb/>
activity intended to be discharged are extremely low. (Actually, the exact values<lb/>
of the maximum permissible concentrations have not yet been determined. <orig reg="further">Fur-<lb/>
ther</orig> conferences with the <name type="corporate"><abbr expan="Atomic Energy Commission">A.E.C.</abbr></name> on this matter will be necessary.) Therefore,<lb/>
in addition to the plan outlined above, in which the best monitoring procedures<lb/>
available will be used, spot checking of liquid samples withdrawn from various<lb/>
points in the system and other means as necessary will be instituted to insure<lb/>
that activities above safe levels are not discharged. If all possible methods of<lb/>
continuous operation of the system proves unsatisfactory, the two tanks can be<lb/>
used entirely as hold-tanks. That is, material can be discharged into one tank<lb/>
until it is full, and then the flow be diverted to the other. Meanwhile, sampling,<lb/>
monitoring and analysis of the material in the first tank should be made to <orig reg="determine">de-<lb/>
termine</orig> whether the material should be discharged to the sewer, held for <orig reg="radioactive">radio<lb/>
active</orig> decay, or pumped to storage tanks, etc.
</p>
<p>Each tank is provided with a gas vent line connected to the exhaust system<lb/>
of the building, a valved overflow line connecting to the city sewer system, a<lb/>
valved drain-line (normally closed) connecting to the city sewer system for <orig reg="completely">com-<lb/>
pletely</orig> draining the tank, and a vertical 4" pipe through which sampling or inside<lb/>
monitoring of the tank contents can be achieved.
</p>
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<div2 type="section" n="2">
<head><hi rend="underline">II. REACTOR DESIGN</hi></head>

<div3 type="subsection" n="1">
<head>A. <hi rend="underline">General.</hi></head>

<p>Since 1944, the <name type="corporate">Los Alamos Scientific Laboratory</name> has operated a low-power<lb/>
nuclear reactor of the "water-boiler" type.<ptr target="b4"/> At first the reactor was operated<lb/>
at a level below 1 kilowatt, then in step-wise changes in the design over a period<lb/>
of 6 years, at 5, 10, and now 25 kilowatts. Operation at each level has yielded<lb/>
knowledge and experience on the stability, behavior and use of a reactor of this<lb/>
type. With added experience, increased confidence and satisfaction with the basic<lb/>
principles on which the unit operates and its inherent safety, adaptability and <lb/>
utility have been gained.<ptr target="a5"/>
</p>
<p>The reactor being built by <name type="corporate">N. C. State College</name> is also of the homogeneous,<lb/>
water-boiler type, and its fundamental principles of operation are identical with<lb/>
those of the <name type="place">Los Alamos</name> unit. Such differences in details of design have been <orig reg="incorporated">in-<lb/>
corporated</orig> in the <name type="place">Raleigh</name> Research Reactor as would be expected to adapt it most<lb/>
satisfactorily to its proposed location on the college campus, and its proposed<lb/>
usage in research and instructional programs.
</p>
<p>The <name type="place">Raleigh</name> Research Reactor will contain on the order of 800 grams of<lb/>
U235, of 90% isotopic enrichment. The uranium will be in the form of uranyl<lb/>
sulfate in water solution, and will be contained in a stainless steel cylinder<lb/>
10-3/4 inches (i. d.) in diameter and 11 inches high (inside dimensions). The<lb/>
cylinder will be enclosed in 20 inches of purified graphite reflector and this, in<lb/>
turn, will be surrounded by six feet of a special, high density concrete. (Fig. 5)<lb/>
The graphite reflector is extended out in one horizontal direction to form a<lb/>
thermal column five feet square and five feet long. Four internal cooling coils<lb/>
in the fuel cylinder provide heat removing capacity to enable the unit to operate<lb/>
at a power level of 10 kilowatts. Besides the cooling system, instrumentation<lb/>
for operation and control and a "gas disposal system" for handling the gaseous<lb/>
by-products from the reactor, are the chief auxiliaries.
</p>
</div3>
<div3 type="subsection" n="2">
<head>B. <hi rend="underline">Concrete Shielding.</hi></head>

<p>The concrete shielding performs two essential functions: Absorption of<lb/>
radiation from the reactor and protection of the fissionable fuel from danger of<lb/>
theft or sabotage. The shielding must be arranged so that samples may be placed<lb/>
inside for irradiation, or radiation beams may be allowed to emerge for external<lb/>
</p>
<pb n="7"/>
<p><seg><xref id="NEfurther010052k.jpg" rend="new">
<figure entity="NEfurther010052k"></figure></xref></seg></p>

<p>use. Also, the shielding must permit convenient access to the internal components<lb/>
for repair and maintenance.
</p>
<p>For absorption of radiation, the concrete is made 6 feet thick, and is composed<lb/>
of special ingredients.<ptr target="a6"/> To increase the density above that of ordinary concrete and<lb/>
hence enhance its absorption of gamma rays, Barium Sulfate (Barytes Ore) is used<lb/>
as the coarse aggregate. A boron containing ingredient (finely ground colemanite<lb/>
ore) is used as the fine aggregate. The boron increases neutron absorption in the<lb/>
concrete and hence neutron activation of the shield is reduced. The boron content<lb/>
of the finished concrete is 1% by weight.</p>

<p>Final composition of the concrete, per cubic yard, is:</p>

<p><table>
<row>
<cell></cell><cell>4200 lbs. Barytes - </cell><cell>95% between 1/16" and 3/4" size<lb/>
5% smaller than 1/16"</cell>
</row>
<row>
<cell></cell><cell></cell><cell></cell>
</row>
<row>
<cell></cell><cell>423 lbs. Colemanite ore - </cell><cell>100% larger than 100 mesh sieve<lb/>
size and smaller than 20 mesh<lb/>
sieve size.</cell>
</row>
<row>
<cell></cell><cell></cell><cell></cell>
</row>
<row>
<cell></cell><cell>882 lbs. Portlant cement - </cell><cell>Type 3.</cell>
</row>
<row>
<cell></cell><cell></cell><cell></cell>
</row>
<row>
<cell></cell><cell>51.7 gallons water.</cell><cell></cell>
</row>
</table>
</p>
<p>The colemanite is soluble in water, hence considerable difficulty is encountered<lb/>
in its use. There appears to be a competition for the water between the dissolving<lb/>
action of the colemanite and the normal process of cement setting; the setting of the<lb/>
cement is delayed enormously. The barytes appears also to be sufficiently soluble<lb/>
to have some effect on the setting process. Two procedures<ptr target="a7"/> were found to be <orig reg="helpful">help-<lb/>
ful</orig>: (1) Using an absolute minimum of water, and (2) adding the colemanite in a<lb/>
second mixing process after some of the primary setting processes had commenced<lb/>
(40 to 45 minutes later). The concrete made in this way was found to have almost<lb/>
double the strength of normal concrete. An overall density of 3.4 g/cc was achieved<lb/>
in contrast to 2.4 g/cc for that of ordinary concrete.
</p>
<p>When assembled, the concrete shield is octagonally shaped in horizontal <orig reg="cross-section">cross-<lb/>
section</orig>, 17 feet across. A rectangular cavity in the center is provided for housing<lb/>
the reactor, the reflector and the auxiliary components. A 36" concrete slab covers<lb/>
the top of the assembly. (Figs. 6, 7) The shield can be partially disassembled by<lb/>
removal of various interlocking concrete blocks making up the assembly. The <orig reg="concrete">con-<lb/>
crete</orig> blocks range in weight up to about 6 tons. To disassemble the shield, the
</p>
<pb n="8"/>
<p><seg><xref id="NEfurther010052l.jpg" rend="new">
<figure entity="NEfurther010052l"></figure></xref></seg></p>

<p>"cap-stones" on top of the assembly must be removed first, and then the <orig reg="interlocking">inter-<lb/>
locking</orig> blocks underneath can be lifted out one by one. (Fig. 8)
</p>
<p>When all the portable concrete blocks are removed, there remain the two<lb/>
massive sides of the octagonal shield, separated by a five-foot gap. Thus, <orig reg="accessibility">access-<lb/>
ibility</orig> is provided for the initial assembly of components inside the shield and for<lb/>
subsequent maintenance and repair. (Fig. 9)
</p>
<p>There are 11 exposure ports extending through the shielding and reflector<lb/>
to the surface of the reactor or across the thermal column. All external <orig reg="opening">open-<lb/>
ings</orig> are so arranged that radiation leakage is prevented, and unauthorized access<lb/>
to the interior of the shield is prohibited. Each port (Fig. 10) is closed externally<lb/>
by a combination-lock safe door, the frame of which is imbedded in the shielding<lb/>
concrete. The outer 18" of the steel lined port is 7 inches in diameter. From<lb/>
this point to the inner end of the port the diameter is 6-1/2 inches. This one<lb/>
quarter inch annular offset in the port prevents escape of radiation through the<lb/>
crevices surrounding the concrete plugs which fill the port when it is not in use.
</p>
<p>One special port consists of a 1 inch vertical tube extending from the top<lb/>
center of the concrete shield, downward to the reactor and re-entrant into the<lb/>
center of the reactor. Small samples may thus be placed at the center of the <orig reg="reactor">re-<lb/>
actor</orig> for exposure to the highest possible flux.
</p>
<p>Attenuation of radiation by the shielding, and the levels of radiation <orig reg="expected">ex-<lb/>
pected</orig> on the outside surface of the shield during reactor operation, are shown<lb/>
in Table 5, in Section III, below.
</p>
</div3>
<div3 type="subsection" n="3">
<head>C. <hi rend="underline">The Fissionable Fuel.</hi></head>

<p>The reactor at <name type="place">Los Alamos</name> has, at different times, operated with water<lb/>
solutions of uranyl sulfate and of uranyl nitrate as the nuclear fuel. From the<lb/>
standpoint of neutron absorption, the sulfate has some advantage. From the<lb/>
standpoint of solubility and corrosion rate, the nitrate appears to have a slight<lb/>
advantage, particularly at high temperatures and pressures. It appears, <orig reg="however">how-<lb/>
ever</orig>, that either material would serve satisfactorily as the fuel for the proposed<lb/>
reactor, and there is at present no strong reason for choosing one instead of the<lb/>
other.
</p>
<p>Uncertainty in the exact chemical composition and geometry of the fuel <orig reg="container">con-<lb/>
tainer</orig>, and of the surrounding materials, the presence of a number of attached<lb/>
and re-entrant tubes, and other factors of uncertainty make it impossible to <orig reg="calculate">cal-<lb/>
culate</orig> the exact amount of U235 needed in the reactor. Calculating from the<lb/>
known critical mass of the <name type="place">Los Alamos</name> reactor, making allowance for the <orig reg="difference">differ-<lb/>
ence</orig> in geometry (sphere to cylinder), difference in size and arrangement of<lb/>
cooling coils and control rods, and estimating the effect of all other different<lb/>
features, it appears that 715 grams of U235 in uranium of 90% isotopic purity,<lb/>
as uranyl sulfate in water solution, are required to produce criticality at room<lb/>
</p>
<pb n="9"/>
<p><seg><xref id="NEfurther010052m.jpg" rend="new">
<figure entity="NEfurther010052m"></figure></xref></seg></p>

<p>temperature. To this must be added the amount required to overcome the negative<lb/>
temperature effect at operating temperature and the "working excess" needed in<lb/>
experimental procedures.
</p>
<p>A tabulation of various calculated quantities and characteristics relating to<lb/>
the nuclear fuel is presented in Table 1.
</p>
<p><hi rend="underline">TABLE 1 - CHARACTERISTICS OF THE REACTOR FUEL</hi></p>
<p><table>
<row>
<cell>Estimated critical mass at room temperature</cell><cell>715 gm U235</cell>
</row>
<row>
<cell>Added U235 for temperature coefficient</cell><cell>55 gm</cell>
</row>
<row>
<cell>"Experimental Excess"</cell><cell><hi rend="underline">20 gm</hi></cell>
</row>
<row>
<cell>Total U235 content</cell><cell>790 gm</cell>
</row>
<row>
<cell></cell><cell></cell>
</row>
<row>
<cell>Solution density (9% UO<hi rend="sub">2</hi>SO<hi rend="sub">4</hi> by weight)</cell><cell>1.08 gm/cm<hi rend="sup">3</hi></cell>
</row>
<row>
<cell>Hydrogen to U235 atom ratio</cell><cell>450</cell>
</row>
</table>
</p>
</div3>
<div3 type="subsection" n="4">
<head>D. <hi rend="underline">The Fuel Container and Reactor Envelope.</hi></head>

<p>Type 347 stainless steel is used throughout the reactor system wherever <orig reg="contact">con-<lb/>
tact</orig> with the fuel or its vapor is a possibility. Welding is used whenever possible<lb/>
in preference to other means of connection.
</p>
<p>A volume of 14 liters is provided in the reactor cylinder for the fuel solution.<lb/>
In addition to the fuel volume, the reactor cylinder (Fig. 11) contains numerous<lb/>
connecting and re-entrant tubes and an empty space at the top to allow for frothing<lb/>
and expansion of the fuel solution.
</p>
<p>Data relating to the fuel cylinder are contained in Table 2 below:
</p>
<p><hi rend="underline">TABLE 2 - DATA RELATING TO FUEL CYLINDER</hi>
</p>
<p>
<table>
<row>
<cell>(347 stainless steel)</cell><cell></cell>
</row>
<row>
<cell>Diameter o.d.</cell><cell>10-7/8 inches</cell>
</row>
<row>
<cell>i. d.</cell><cell>10-3/4 "</cell>
</row>
<row>
<cell>Height, outside</cell><cell>11-1/8 "</cell>
</row>
<row>
<cell>inside</cell><cell>11 "</cell>
</row>
<row>
<cell>Wall thickness</cell><cell>1/16 "</cell>
</row>
<row>
<cell>Weight of steel in walls</cell><cell>2.3 kg.</cell>
</row>
<row>
<cell>Total inside volume</cell><cell>15.6 liters</cell>
</row>
<row>
<cell>Inside volume occupied by re-entrant tubes</cell><cell>0.71 liters</cell>
</row>
<row>
<cell>Weight of steel in inside re-entrant tubes</cell><cell>1.9 Kg.</cell>
</row>
<row>
<cell>Liquid depth</cell><cell>9.92 inches</cell>
</row>
<row>
<cell>Liquid volume</cell><cell>14.0 liters</cell>
</row>
<row>
<cell>Depth of space above liquid</cell><cell>1.08 inches</cell>
</row>
<row>
<cell>Volume of space above liquid</cell><cell>0.90 liter</cell>
</row>
</table>
</p>
<pb n="10"/>
<p><seg><xref id="NEfurther010052n.jpg" rend="new">
<figure entity="NEfurther010052n"></figure></xref></seg></p>

<p>In case a leak should occur in the fuel cylinder, radioactive vapor or liquid,<lb/>
or perhaps both, depending on the location of the leak, would escape into the <orig reg="surrounding">sur-<lb/>
rounding</orig> space. To minimize exposure hazards resulting from an event of this kind,<lb/>
the reactor is enclosed in an envelope of 1/16" aluminum. (Fig. 12)
</p>
<p>All tubes, control rod sheaths, and thermocouple leads connect to the reactor<lb/>
on its top surface, and project vertically upward inside the reactor envelope. The<lb/>
motor drives and electromagnetic couplings of the control rods are located inside<lb/>
the top portion of the reactor envelope. Tubes and electrical wires leave the <orig reg="envelope">en-<lb/>
velope</orig> through seals in the walls.
</p>
</div3>
<div3 type="subsection" n="5">
<head>E. <hi rend="underline">Reflector, Thermal Column, Lead Shielding.</hi></head>

<p>The reactor envelope which is snugly fitted to the reactor is, in turn, <orig reg="enclosed">en-<lb/>
closed</orig> in 20 inches of high purity graphite which serves as a neutron reflector.<lb/>
Calculations show that a 20 inch layer of graphite around the reactor core is 90% as<lb/>
effective in reducing critical mass as an infinitely thick layer. Two to four inches<lb/>
of lead are placed around the graphite reflector, inside the concrete shielding, as<lb/>
a primary gamma ray shield. (See Section III for calculations of attenuation.)
</p>
<p>On one side of the reactor, outside the lead shielding, an additional 5 foot<lb/>
cube of graphite forms the thermal column. (Calculated values of thermal <orig reg="neutron">neu-<lb/>
tron</orig> fluxes are listed in Section III, C.) Several exposure ports penetrate into<lb/>
and across the thermal column to provide means of using the neutrons for <orig reg="experimental">ex-<lb/>
perimental</orig> purposes.
</p>
<p>A layer of lead four inches thick is placed across the end of the graphite<lb/>
column. This is followed by a layer of boron to absorb the neutrons reaching<lb/>
that point. The boron, in the form of finely. ground boron carbide, is impregnated<lb/>
into a layer of paraffin 3/4" thick, in sufficient concentration to form a boron<lb/>
layer of 3 gms/cm<hi rend="sup">2</hi> across the end of the column. A layer of concrete 12 inches<lb/>
thick is placed outside the boron layer.
</p>
<p>Specially prepared graphite, obtained from the <name type="corporate"><abbr expan="Atomic Energy Commission">A.E.C.</abbr></name> at <name type="place">Oak Ridge</name>, is used<lb/>
in the reflector and thermal column. Data relative to the graphite are presented<lb/>
in Table 3, below.
</p>
<p><hi rend="underline">TABLE 3 - DATA ON GRAPHITE USED IN REFLECTOR AND THERMAL<lb/>
COLUMN</hi>
</p>
<p>
<list>
<item>Volume of Reflector - 105 cu. ft.</item>
<item>Weight of graphite in Reflector - 5.4 tons</item>
<item>Volume of thermal column - 110 cu. ft.</item>
<item>Weight of graphite in thermal column - 5.7 tons</item>
<item>Density of graphite - 1.65 g/cc</item>
</list></p>
<pb n="11"/>
<p><seg><xref id="NEfurther010052o.jpg" rend="new">
<figure entity="NEfurther010052o"></figure></xref></seg></p>

<p>The graphite portions of the assembly are built up of successive layers of<lb/>
graphite bars 4 inches square in cross-section and in lengths up to 48". All joints<lb/>
are fitted to &#x00B1; 0.002".
</p>
</div3>
<div3 type="subsection" n="6">
<head>F. <hi rend="underline">Cooling System.</hi></head>

<p>Due to the negative temperature coefficient of nuclear reactivity of the <orig reg="reactor">re-<lb/>
actor</orig> system, the steady state power level at which the reactor will operate is<lb/>
limited by the rate of heat removal from the solution. If less heat is being <orig reg="removed">re-<lb/>
moved</orig> than is being released, the temperature rises and, as a result of the <orig reg="thermal">ther-<lb/>
mal</orig> expansion of the fuel and the creation of gas or vapor bubbles, the reactivity<lb/>
is reduced so that a heat balance is established.
</p>
<p>Dissipation of heat from the reactor through the external walls of the vessel<lb/>
will hardly exceed half a kilowatt. For operation at higher levels, therefore,<lb/>
auxiliary cooling of some sort must be provided. The system devised consists of<lb/>
four symmetrically arranged coils of 1/4" (i. d.) stainless steel tubing immersed<lb/>
in the reactor fuel. One gallon per minute of refrigerated water flows through<lb/>
each coil. A 7 foot length of each coil is immersed in the solution. The wall<lb/>
thickness is 1/32 inch.
</p>
<p>Water from the city mains flows through refrigerated coils in the air <orig reg="conditioned">con-<lb/>
ditioned</orig> system, through control valves in the Control Room, to a distribution<lb/>
manifold inside the reactor assembly and thence to the four reactor cooling coils<lb/>
(Fig. 13). The coils are adjusted for equal flow before installation, but after <orig reg="installation">in-<lb/>
stallation</orig>, flows in the individual coils are not measured or separately controlled.<lb/>
Temperatures are measured and recorded at the inlet manifold and at the exit of<lb/>
each coil.
</p>
<p>In its passage through the reactor, the cooling water becomes somewhat <orig reg="radioactive">radio-<lb/>
active</orig>. Calculations of the induced activity to be expected indicate that the total<lb/>
amount will not be large and most of this will be short-lived. (Table 4) The<lb/>
normal time required for the transit of an average water molecule through the <orig reg="reactor">re-<lb/>
actor</orig> is 1.1 seconds, and the average thermal neutrol flux is about 4 x 10<hi rend="sup">11</hi>. For<lb/>
calculation of the data presented in Table 4, a transit time of 2 seconds and a flux<lb/>
of 10<hi rend="sup">12</hi> thermal neutrons were conservatively assumed. Average analyses of<lb/>
water in the <name type="place">Raleigh</name> system were obtained from the City Public Utilities <orig reg="Department">Depart-<lb/>
ment</orig>.
</p>
<pb n="12"/>
<p><seg><xref id="NEfurther010052p.jpg" rend="new">
<figure entity="NEfurther010052p"></figure></xref></seg></p>

<p><hi rend="underline">TABLE 4 - ACTIVITY INDUCED IN THE REACTOR COOLING WATER</hi></p>
<p><table>
<row>
<cell>Target<lb/>Isotope</cell><cell>&#x2003;</cell><cell>Form of<lb/>the <orig reg="Impurity">Im-<lb/>purity</orig></cell><cell>&#x2003;</cell><cell>Avg.<lb/>Conc.<lb/>ppm</cell><cell>&#x2003;</cell><cell>Active<lb/>Isotope</cell><cell>&#x2003;</cell><cell>Half<lb/>Life</cell><cell>&#x2003;</cell><cell>&#x03BB;<lb/>sec<hi rend="sup">-1</hi></cell><cell>&#x2003;</cell><cell>&#x03C3;<hi rend="sub">a</hi><lb/>barns</cell><cell>&#x2003;</cell><cell>Abund. of<lb/>Target<lb/>Isotope<lb/>(%)</cell><cell>&#x2003;</cell><cell>N<lb/>cm<hi rend="sup">-3</hi></cell><cell>&#x2003;</cell><cell>Result.<lb/>Activity<lb/>d/sec/cm<hi rend="sup">3</hi></cell>
</row>
<row>
<cell>Si<hi rend="sup">30</hi></cell><cell>&#x2003;</cell><cell>SiO<hi rend="sub">2</hi></cell><cell>&#x2003;</cell><cell>9.8</cell><cell>&#x2003;</cell><cell>S<hi rend="sup">31</hi></cell><cell>&#x2003;</cell><cell>2.7h</cell><cell>&#x2003;</cell><cell>7.1 x 10<hi rend="sup">-5</hi></cell><cell>&#x2003;</cell><cell>0.12</cell><cell>&#x2003;</cell><cell>3.1</cell><cell>&#x2003;</cell><cell>1.0 x 10<hi rend="sup">16</hi></cell><cell>&#x2003;</cell><cell>0.017</cell>
</row>
<row>
<cell>Mg<hi rend="sup">26</hi></cell><cell>&#x2003;</cell><cell>Mg</cell><cell>&#x2003;</cell><cell>1.4</cell><cell>&#x2003;</cell><cell>Mg<hi rend="sup">27</hi></cell><cell>&#x2003;</cell><cell>9.58m</cell><cell>&#x2003;</cell><cell>1.2 x 10<hi rend="sup">-3</hi></cell><cell>&#x2003;</cell><cell>0.05</cell><cell>&#x2003;</cell><cell>11.3</cell><cell>&#x2003;</cell><cell>5.3 x 10<hi rend="sup">15</hi></cell><cell>&#x2003;</cell><cell>0.64</cell>
</row>
<row>
<cell>Na<hi rend="sup">23</hi></cell><cell>&#x2003;</cell><cell>Na+K</cell><cell>&#x2003;</cell><cell>4.2</cell><cell>&#x2003;</cell><cell>Na<hi rend="sup">24</hi></cell><cell>&#x2003;</cell><cell>14.9h</cell><cell>&#x2003;</cell><cell>1.3 x 10<hi rend="sup">-5</hi></cell><cell>&#x2003;</cell><cell>0.6</cell><cell>&#x2003;</cell><cell>100</cell><cell>&#x2003;</cell><cell>1.4 x 10<hi rend="sup">17</hi></cell><cell>&#x2003;</cell><cell>2.2</cell>
</row>
<row>
<cell>S<hi rend="sup">36</hi></cell><cell>&#x2003;</cell><cell>SO<hi rend="sub">4</hi></cell><cell>&#x2003;</cell><cell>11.0</cell><cell>&#x2003;</cell><cell>S<hi rend="sup">37</hi></cell><cell>&#x2003;</cell><cell>5.0m</cell><cell>&#x2003;</cell><cell>2.3 x 10<hi rend="sup">-3</hi></cell><cell>&#x2003;</cell><cell>0.14</cell><cell>&#x2003;</cell><cell>0.0136</cell><cell>&#x2003;</cell><cell>5.0 x 10<hi rend="sup">13</hi></cell><cell>&#x2003;</cell><cell>0.032</cell>
</row>
<row>
<cell>Cl<hi rend="sup">35</hi></cell><cell>&#x2003;</cell><cell>Cl</cell><cell>&#x2003;</cell><cell>4.9</cell><cell>&#x2003;</cell><cell>S<hi rend="sup">35</hi></cell><cell>&#x2003;</cell><cell>87.d</cell><cell>&#x2003;</cell><cell>9.2 x 10<hi rend="sup">-8</hi></cell><cell>&#x2003;</cell><cell>0.34</cell><cell>&#x2003;</cell><cell>75.4</cell><cell>&#x2003;</cell><cell>1.2 x 10<hi rend="sup">17</hi></cell><cell>&#x2003;</cell><cell>10<hi rend="sup">-2</hi></cell>
</row>
<row>
<cell>Cl<hi rend="sup">37</hi></cell><cell>&#x2003;</cell><cell>Cl</cell><cell>&#x2003;</cell><cell>4.9</cell><cell>&#x2003;</cell><cell>Cl<hi rend="sup">38</hi></cell><cell>&#x2003;</cell><cell>38.5m</cell><cell>&#x2003;</cell><cell>3.0 x 10<hi rend="sup">-4</hi></cell><cell>&#x2003;</cell><cell>0.6</cell><cell>&#x2003;</cell><cell>24.6</cell><cell>&#x2003;</cell><cell>4.0 x 10<hi rend="sup">16</hi></cell><cell>&#x2003;</cell><cell>14.</cell>
</row>
<row>
<cell>F<hi rend="sup">19</hi></cell><cell>&#x2003;</cell><cell>F</cell><cell>&#x2003;</cell><cell>0.1</cell><cell>&#x2003;</cell><cell>F<hi rend="sup">20</hi></cell><cell>&#x2003;</cell><cell>12s</cell><cell>&#x2003;</cell><cell>5.8 x 10<hi rend="sup">-2</hi></cell><cell>&#x2003;</cell><cell>0.009</cell><cell>&#x2003;</cell><cell>100</cell><cell>&#x2003;</cell><cell>3.35 x 10<hi rend="sup">15</hi></cell><cell>&#x2003;</cell><cell>3.5</cell>
</row>
<row>
<cell>O<hi rend="sup">18</hi></cell><cell>&#x2003;</cell><cell>H<hi rend="sub">2</hi>O</cell><cell>&#x2003;</cell><cell>10<hi rend="sup">6</hi></cell><cell>&#x2003;</cell><cell>O<hi rend="sup">19</hi></cell><cell>&#x2003;</cell><cell>29.4s</cell><cell>&#x2003;</cell><cell>2.4 x 10<hi rend="sup">-2</hi></cell><cell>&#x2003;</cell><cell>0.0002</cell><cell>&#x2003;</cell><cell>0.204</cell><cell>&#x2003;</cell><cell>6.8 x 10<hi rend="sup">19</hi></cell><cell>&#x2003;</cell><cell>653</cell>
</row>
</table></p>

<p>Negligible activities were found for a number of additional elements likely to be<lb/>
present.  These are:</p>
<p>Fe<hi rend="sup">54</hi>, Fe<hi rend="sup">58</hi>, Ca<hi rend="sup">44</hi>, C<hi rend="sup">13</hi>, S<hi rend="sup">34</hi>, Cl<hi rend="sup">35</hi>, N<hi rend="sup">15</hi></p>
<pb n="13"/>
<p><seg><xref id="NEfurther010052q.jpg" rend="new">
<figure entity="NEfurther010052q"></figure></xref></seg></p>

<p>From this table, it is seen that the O<hi rend="sup">19</hi> activity (0.018 micro curies per ml),<lb/>
initially, is dominant. Since the half life is only 29.4 seconds, however, this<lb/>
activity will be reduced below 1 disintegration per ml/sec in 5 minutes, and thus<lb/>
no hazard would be anticipated.
</p>
<p>The next most significant activity is that of Cl<hi rend="sup">38</hi> (3.8 x 10<hi rend="sup">-4</hi> micro curies/ml)<lb/>
which is of the order of <orig reg="permissible">permissable</orig> concentration for drinking water, and hence no<lb/>
hazard would be expected to result from discharge of this material into the sewer.
</p>
<p>Inasmuch as the power at which the reactor operates is intimately associated<lb/>
with the rate of cooling, an interlock with the control rod system is provided<lb/>
which insures that the cooling water is flowing before the reactor can be operated.
</p>
<p>The exit line carrying the cooling water from the reactor passes through an<lb/>
underground, concrete shielded trench under the building to an underground tank<lb/>
of 250 gallon capacity located outside the building, and from there to the city sewer<lb/>
system. Radiation detectors continuously monitor the activity of the water as it<lb/>
enters and leaves the tank. The same plan of operation will be followed for this<lb/>
system as that described in Section I, C, for the laboratory drainage system.<lb/>
As in the drainage system, an attempt will be made to use a continuous flow method<lb/>
of discharging the reactor cooling water, through a monitored tank, to the city sewer<lb/>
system. But if the level of radiation proves too high, or if reliable monitors cannot<lb/>
be found for the low level, of radiation involved, then another tank will be installed<lb/>
and the two will be used alternately as hold tanks The cooling water will then be<lb/>
discharged batchwise to the city system after sampling and analyses of each batch.
</p>
</div3>
<div3 type="subsection" n="7">
<head>G. <hi rend="underline">Gas Disposal System.</hi></head>

<div4 type="part" n="1">
<head>1. <hi rend="underline">Hydrogen-Oxygen Recombination.</hi></head>

<p>When the reactor is operating at 10 Kw, from 1500 to 2000 cc of gas per<lb/>
minute are evolved. More than 99% of this gas volume will consist of gases <orig reg="resulting">result-<lb/>
ing</orig> from radiation decomposition of the fuel solution. A very small fraction of the<lb/>
gas volume will be fission product gases which, though negligible in volume,<lb/>
greatly complicate the disposal problem, because of their high radioactivity.
</p>
<p>Various possible methods of disposing of the gases were briefly outlined in<lb/>
the previous report, "Program Administration and Installation Design of the Nuclear<lb/>
Reactor Project at <name type="corporate">N. C. State College</name>." Since that time a great deal of study, at<lb/>
<name type="place">Oak Ridge</name> and <name type="place">Los Alamos</name>, as well as <name type="corporate">N. C. State College</name>, has been devoted to<lb/>
this problem.
</p>
<p>The scheme developed by Los Alamos and used thus far with complete <orig reg="satisfaction">satis-<lb/>
faction</orig> and success (over an operating period of 20,000 kw-hr) has been adopted<lb/>
for the <name type="place">Raleigh</name> Research Reactor. Modification in details of arrangements and<lb/>
components has been incorporated for adaptation to the new reactor but the <orig reg="fundamental">funda-<lb/>
mental</orig> principles of operation have remained unchanged. The <name type="place">Los Alamos</name> system
</p>
<pb n="14"/>
<p><seg><xref id="NEfurther010052r.jpg" rend="new">
<figure entity="NEfurther010052r"></figure></xref></seg></p>

<p>is based on a very ingenious combination of ideas and operating principles which<lb/>
achieves freedom from explosion hazard, simplicity of apparatus and mechanical<lb/>
components, low maintenance requirements, and satisfactory handling of <orig reg="radioactive">radio-<lb/>
active</orig> gases.
</p>
<p>The gas disposal apparatus as adapted for the <name type="place">Raleigh</name> Research Reactor<ptr target="c1"/><lb/>
consists of a closed circulating gas system, with a small exhaust gas bleed to the<lb/>
stack and a small inlet make-up flow. The flow path (Fig. 14) includes, in <orig reg="sequence">se-<lb/>
quence</orig>, the empty space in the reactor above the fuel surface, a condenser cooled<lb/>
with refrigerated water, a steel-wool-filled filter, a circulating blower, a<lb/>
platinized-alumina catalyst bed, a water cooled steam condenser, and a pipe <orig reg="connection">con-<lb/>
nection</orig> back to the top of the reactor. The system has a volume of 8000 cc, which<lb/>
is filled with air (94%), and gases from the reactor (6%). Fifty to one hundred ml<lb/>
per minute of mixed gases are bled from the circulating system through a series<lb/>
of hold-up tanks to the stack.
</p>
<p>A small volume of non-condensable gases from the reactor (SO, SO<hi rend="sub">2</hi>...)<lb/>
plus a small inflow of make-up air to the system is sufficient to maintain constant<lb/>
circulating inventory. The inbleed of make-up air occurs to some extent around<lb/>
the pump shaft, and the additional amount required is admitted through a small<lb/>
adjustable leak located on the inlet side of the pump.
</p>
<p>The essential features of this system are:
</p>
<p><list>
<item>1. The volume of the system and the rate of circulation are such that the<lb/>
hydrogen and oxygen content are maintained below the explosive limit (4% H<hi rend="sub">2</hi>) at<lb/>
all times and at all points, even within the reactor.
</item>
<item>2. A refrigerated condenser immediately above the reactor (gas <orig reg="temperatures">tempera-<lb/>
tures</orig> lowered to 13<hi rend="sup">o</hi>C) returns all vapors to the reactor as condensate. Many<lb/>
fission products such as I<hi rend="sub">2</hi> and Br<hi rend="sub">2</hi> which otherwise would escape, are kept in<lb/>
the reactor. This condenser also prevents liquid contamination of the <orig reg="remaining">remain-<lb/>
ing</orig> parts of the system, which is particularly important to the "longevity" of the<lb/>
catalyst.
</item>
<item>3. Recirculation of the gases through the catalyst provides increased <orig reg="opportunity">op-<lb/>
portunity</orig> for recombination of hydrogen and oxygen, and also provides a <orig reg="considerable">consider-<lb/>
able</orig> hold-up of radioactive inert gases, so that short-lived activities are <orig reg="considerably">con-<lb/>
siderably</orig> decayed before discharge.</item>
</list>
</p>
<p>The details of construction and arrangement of the chief components in the<lb/>
gas disposal system and other details are shown in Figures 15, 16. and 17.
</p>
</div4>
<pb n="15"/>
<div4 type="image">
<p><seg><xref id="NEfurther010052s.jpg" rend="new">
<figure entity="NEfurther010052s"></figure></xref></seg></p>

</div4>
<div4 type="part" n="2">
<head>2. <hi rend="underline">Disposal to the Atmosphere.</hi></head>

<p>About 50 to 100 ml per minute of gas are bled from the gas circulating-<lb/>
recombining system during periods when the reactor is in operation. The point<lb/>
of withdrawal (Fig 14) is located immediately downstream from the exit end of the<lb/>
steam condenser where the H<hi rend="sub">2</hi>-0<hi rend="sub">2</hi> content is lowest.
</p>
<p>The gas bled from the system cannot be discharged directly into the <orig reg="atmosphere">atmos-<lb/>
phere</orig>, because of its radioactivity. A hold-up system must be provided to delay<lb/>
discharge into the atmosphere sufficiently to permit radioactive decay to a safe<lb/>
level. Calculations showing amounts of gaseous fission products expected, their<lb/>
decay characteristics, and the adequacy of the proposed hold-up system are <orig reg="presented">pre-<lb/>
sented</orig> in Section III, C. Description of the system itself follows.
</p>
<p>The plan of the gas withdrawal system is shown in Fig. 18. A 1/4" <orig reg="stainless">stain-<lb/>
less</orig> steel tube leads from the bleed point of the circulating system downwards<lb/>
within the reactor shielding, then horizontally under the floor of the reactor room<lb/>
and out underneath the building to a series of gas-holding tanks immersed in an<lb/>
underground water tank (for shielding) outside the building The bleed gas is<lb/>
drawn through the holding tanks by a small pump, and is discharged from the<lb/>
pump into the 12,500 cfm ventilation exhaust stream from the Reactor Building.
</p>
<p>A constant flow of gas is maintained through the system by a suitably sized<lb/>
critical flow orifice located between the holding tanks and the exhaust pump. A<lb/>
water trap, through which the gas must bubble, is located between each holding<lb/>
tank. Eight-hold-up tanks in series, each having 100 gallon capacity, are, <orig reg="provided">pro-<lb/>
vided</orig>. It is estimated in Section III, C, that the attenuation achieved in a series<lb/>
of eight such tanks is on the order of 700 for Xenon<hi rend="sup">133</hi>, which is the most<lb/>
troublesome gaseous fission product. By-pass valves are arranged so that any<lb/>
tank can be removed from service without disrupting operation of the others.
</p>
</div4>
</div3>
<div3 type="subsection" n="8">
<head>H. <hi rend="underline">Instrumentation and Control.</hi></head>

<div4 type="part" n="1">
<head>1. <hi rend="underline">General.</hi></head>

<p>The instrumentation system of the reactor facility has four functions:<lb/>
(1) to indicate and record the level of radiation flux and the rate of increase or<lb/>
decrease of the neutron flux in the reactor; (2) to provide data for and means of<lb/>
safe manual and automatic control of the reactor; (3) to provide safety <orig reg="mechanisms">mechan-<lb/>
isms</orig> which insure reactor operation within predetermined limits; (4) to provide<lb/>
area and facilities monitoring to safeguard personnel from radioactivity<lb/>
hazards and to prevent inadvertent release of radioactive materials.
</p>
<p>The first three of these functions are performed by the instrumentation<lb/>
system provided for the reactor itself. In general plan, this reactor <orig reg="instrumentation">instrumen-<lb/>
tation</orig> system consists of fission - or ionization-chamber sensing elements<lb/>
located in the graphite reflector of the reactor assembly, which are connected
</p>
<pb n="16"/>
<p><seg><xref id="NEfurther010052t.jpg" rend="new">
<figure entity="NEfurther010052t"></figure></xref></seg></p>

<p>by coaxial cables and power lines to their respective power supplies, amplifiers,<lb/>
indicating meters, recorders, and control devices located in the Control Room.<lb/>
Operation and control of the reactor are handled entirely from the Control Room.<lb/>
Twenty feet of space and a wall of 12 inches of masonry or 8 inches of water <orig reg="between">be-<lb/>
tween</orig> the reactor and the Control Room (Fig. 19) provide protection for the<lb/>
operator from stray radiation. Viewing advantage is furnished the operator, and<lb/>
some added protection from stray radiation, by the floor of the Control Room <orig reg="being">be-<lb/>
ing</orig> at an elevation of 5 feet above that of the Reactor Room.
</p>
<p>Within the Control Room, there are two primary assemblies having to do<lb/>
with operation and control of the reactor: The Rack of Data Recorders and the<lb/>
Control Console (Fig. 19). In normal operating position, the operator sits at the<lb/>
central panel of the Control Console, with the water-window to the Reactor Room<lb/>
to his right. Directly in front of the operator, above and about 5 feet beyond the<lb/>
central panel of the Control Console, the 12 data recorders are in full view. The<lb/>
six central recorders, which handle data of primary importance, have illuminated<lb/>
scales. Along the wall to the left of the operator are instruments and recorders<lb/>
which indicate and collect data of secondary importance to the operation of the<lb/>
reactor.
</p>
</div4>
<div4 type="part" n="2">
<head>2. <hi rend="underline">Fission chambers.</hi></head>

<p>The fission chamber sensing elements of the instrumentation system are<lb/>
similar in design to chambers successfully used with the homogeneous reactor at<lb/>
<name type="place">Los Alamos</name>.<ptr target="d1"/> Three thin concentric cylindrical shells of lucite are covered with<lb/>
0.002" aluminum foils which, in turn, are coated with a layer of U235 (0.35 Mg/cm<hi rend="sup">2</hi>)<lb/>
of above 90% isotopic purity. The rate of fissioning is proportional to the neutron<lb/>
flux from the reactor, and hence the current from the fission chamber is directly<lb/>
related to the power level of reactor operation.
</p>
<p>It is anticipated, on the basis of <name type="place">Los Alamos</name> experience with similar <orig reg="chambers">cham-<lb/>
bers</orig>, that a current of 1 milliampere can be obtained when these chambers are in<lb/>
a neutron flux of 10<hi rend="sup">10</hi> neutrons/cm<hi rend="sup">2</hi>/sec.
</p>
</div4>
<div4 type="part" n="3">
<head>3. <hi rend="underline">Neutron Flux Measurements on Linear Scales.</hi></head>

<p>In the reactor instrumentation system, there are three independent<lb/>
channels having responses linearly related to the neutron flux. (Fig. 20).
</p>
<p>(a) In the first linear channel, the fission chamber is connected directly,<lb/>
without amplification, to a galvanometer located on the central operating panel of<lb/>
the Control Console. The galvanometer sensitivity is matched to the fission <orig reg="chamber">cham-<lb/>
ber</orig> so that operation at 10 Kw produces full scale deflection on the least sensitive
</p>
<pb n="17"/>
<p><seg><xref id="NEfurther010052u.jpg" rend="new">
<figure entity="NEfurther010052u"></figure></xref></seg></p>

<p>range, and operation at 1 watt level produces full scale deflection on the most<lb/>
sensitive range. There are 8 intermediate ranges.
</p>
<p>Four meters, in series with the galvanometer and with each other, are <orig reg="located">lo-<lb/>
cated</orig> on alternate faces of the reactor shield respectively, so that the level of<lb/>
reactor operation is visible to persons at any location in the Reactor Room.<lb/>
These four meters have only one sensitivity and indicate 10 Kw at full scale.
</p>
<p>(b) In the second channel with linear response, the fission chamber current<lb/>
is fed into a preamplifier and then into a Brown Recorder. The level of radiation<lb/>
flux is continually recorded. The sensitivity range of the recorder at any time is<lb/>
identical to that being displayed simultaneously on the galvanometer of channel (a).
</p>
<p>(c) The third channel with linear response is used in automatic control of<lb/>
the Reactor. The output of the fission chamber is amplified and balanced against<lb/>
the reference voltage from a Rubicon potentiometer. The latter voltage can be<lb/>
controlled at will by the operator. The difference between these two signals, if<lb/>
any, is amplified and applied to the motor which controls the motion of the reactor<lb/>
control rod. The motion of the motor is always in the direction which would <orig reg="decrease">de-<lb/>
crease</orig> the difference between the signals. For the benefit of the operator, this<lb/>
difference in signals is also displayed on a small cathode ray tube mounted on<lb/>
the Control Console.
</p>
<p>There are certain safety features common to each of the above systems. In<lb/>
each system, a safety interlock is provided such that, in case the neutron flux<lb/>
exceeds a pre-set level, the current to the electromagnets supporting the control<lb/>
and safety rods is turned off and the rods are dropped. In addition, between<lb/>
channels (b) and (c) there is a signal comparator which also causes the rods to<lb/>
drop in case the initially matched signals differ at any subsequent time by a <orig reg="pre-set">pre-<lb/>
set</orig> amount. This, precaution insures that one or the other of the systems does<lb/>
not fail without knowledge of the operator.
</p>
<p><list>
<head>Other features of these three channels are:</head>

<item>(a) A Master Range Changing Switch permits simultaneous<lb/>
change from one range to another on all three of the<lb/>
above channels.</item>

<item>(b) Provision is made on the record to indicate the range<lb/>
being used so that there is no ambiguity as to the actual<lb/>
value recorded.</item>

<item>(c) The overall response time for these systems is of the<lb/>
order of 15 seconds for full scale response of the<lb/>
galvanometer and of the order of 4 seconds for the<lb/>
recorders.
</item>
<item>(d) The recorder is a curve-drawing Brown Recorder.</item></list>
</p>
<pb n="18"/>
<p><seg><xref id="NEfurther010052v.jpg" rend="new">
<figure entity="NEfurther010052v"></figure></xref></seg></p>
<p>
<list><item>(e) The indicating meters on the reactor shield are G.E. Type DB 18.</item>

<item>(f) A time delay and interlock are provided such that the control<lb/>
rods can not be raised until the linear systems are in operating<lb/>
condition.</item></list>
</p>
</div4>
<div4 type="part" n="4">
<head>4. <hi rend="underline">Neutron Flux Measurements on Logarithmic Scales.</hi></head>

<p>It is necessary to provide for the operator a set of instruments in which<lb/>
the flux over a very wide range of values can be shown. This is accomplished in<lb/>
duplicate channels by feeding the output current of ionization chambers into <orig reg="amplifiers">ampli-<lb/>
fiers</orig>, the outputs of which are proportional to the logarithm of the input currents.<lb/>
The logarithmic characteristic of a diode is used to obtain this logarithmic <orig reg="response">res-<lb/>
ponse</orig>. (Fig. 21).
</p>
<p>(a) In the first channel, the ionization chamber is logarithmically amplified<lb/>
and is then recorded on a Brown Recorder Safety features are described below.
</p>
<p>(b) The second channel is an exact duplicate of the first, except the current<lb/>
is not recorded.
</p>
<p>In either of these channels, if the neutron level exceeds a pre-set value,<lb/>
the current to the control and safety rods is interrupted and the rods are dropped.<lb/>
In addition, between these two channels there is a signal comparator which also<lb/>
causes the rods to drop in case the initially matched signals differ at any <orig reg="subsequent">subse-<lb/>
quent</orig> time by a pre-set amount.
</p>
<p>The currents from these two channels provide the input signals to the two<lb/>
respective channels described below.
</p>
</div4>
<div4 type="part" n="5">
<head>5. <hi rend="underline">Rate of Change of Neutron Flux: Period Measurement.</hi></head>

<p>The "period" of a nuclear reaction is the time required for the power<lb/>
level to increase or decrease by a factor of e. It is very important that the<lb/> <orig reg="operator">op-
erator</orig> know the rate at which the power level is changing, i.e., the length of the<lb/>
period.
</p>
<p>The logarithmically amplified currents from the two channels described<lb/>
above are fed into parallel electronic circuits respectively, where these <orig reg="logarithmic">logarith-<lb/>
mic</orig> currents are differentiated with respect to time, to furnish indications of the<lb/>
period of the reactor.
</p>
<p>(a) The period as measured by the first of these channels is indicated and<lb/>
recorded on a Brown Recorder. Safety features are described below.
</p>
<p>(b) The second channel is identical to the first, except the output is not<lb/>
recorded.
</p>
<p>In either of these two period-measuring circuits, if the period becomes
</p>
<pb n="19"/>
<p><seg><xref id="NEfurther010052w.jpg" rend="new">
<figure entity="NEfurther010052w"></figure></xref></seg></p>

<p>shorter than a pre-set value, a thyratron interlock causes the safety and control<lb/>
rods to drop. In addition, between these two period measuring circuits, there is<lb/>
a signal comparator which also causes the rods to drop in case the initially<lb/>
matched signals differ at any subsequent time by a pre-set value.
</p>
<p>A Master Range Changing Switch is provided for the logarithmic and period<lb/>
channels which permit simultaneous change from one range to another on these two<lb/>
systems.
</p>
</div4>
<div4 type="part" n="6">
<head>6. <hi rend="underline">Gamma Compensated Channel.</hi></head>

<p>In the U235 fission and boron ionization chambers used in the channels<lb/>
described above an indeterminate proportion of the current output is caused by<lb/>
ionization of the gas in the chamber by gamma rays from the reactor. The neutron<lb/>
fluxes indicated are therefore too high. To provide information on the magnitude of<lb/>
this effect, a gamma-compensated channel is included in the reactor instrument<lb/>
system. This channel consists of two identical "fission" chambers, except one<lb/>
chamber contains no U235. The difference in the signals from these two chambers,<lb/>
which is displayed on the Control Console, is a measure of the neutron flux <orig reg="essentially">essen-<lb/>
tially</orig> independent of the gamma ray ionization in the chamber. This system furnishes<lb/>
information only, and is not connected to automatic safety mechanisms of the reactor.
</p>
</div4>
<div4 type="part" n="7">
<head>7. <hi rend="underline">Measure of the Gamma Ray Flux from the Reactor.</hi></head>

<p>While a nuclear chain reaction is in progress in the reactor, the neutron<lb/>
detectors described above furnish adequate information on the level of radiation <orig reg="being">be-<lb/>
ing</orig> produced. When the chain reaction ceases, neutrons are no longer released by<lb/>
fission and the neutron detectors indicate cessation of activity. The gamma <orig reg="radiation">radia-<lb/>
tion</orig> from the reactor, however, which results from activity of the fission products,<lb/>
continues at a relatively high level. To follow the level of this activity after <orig reg="shut-down">shut-<lb/>
down</orig>, and during operation as well, a gamma ray monitor is included in the <orig reg="instrumentation">instru-<lb/>
mentation</orig> system. This monitor furnishes information only, and is not normally<lb/>
connected to automatic safety mechanisms of the reactor.
</p>
<p>This channel consists of an ionization chamber feeding through an amplifier<lb/>
to a recorder.
</p>
</div4>
<div4 type="part" n="8">
<head>8. <hi rend="underline">Control Console and Recorder Rack.</hi></head>

<p>The Control Console consists of a 3-section desk, each section being 24"<lb/>
wide and set at an angle of 135<hi rend="sup">o</hi> to its adjacent section (Fig. 19). The top of each<lb/>
section slopes toward the operator position at an angle of 30<hi rend="sup">o</hi> to the horizontal.<lb/>
The operator is thus able to view the apparatus on each panel with maximum con-<lb/>
venience and minimum parallax.
</p>
<p>The central panel contains apparatus of primary importance in the operation<lb/>
of the reactor. Included on this panel are:
</p>
<pb n="20"/>
<p><seg><xref id="NEfurther010052x.jpg" rend="new">
<figure entity="NEfurther010052x"></figure></xref></seg></p>

<p><list>
<item>(1) A galvanometer showing neutron flux (3 (a), above).
</item>
<item>(2) A meter showing the temperature of the Reactor solution.
</item>
<item>(3) Control and safety rod positioning switches.
</item>
<item>(4) The alternate manual-to-automatic control switch.
</item>
<item>(5) A button for manual release of the control and safety rods.
</item>
<item>(6) A cathode raytube for monitoring automatic control (3 (c), above).
</item>
<item>(7) Lights to indicate extreme positioning of control and safety rods.
</item>
<item>(8) Switches for master range-changing mechanism.
</item>
<item>(9) Emergency evacuation signal.
</item>
</list>
</p>
<p>The right hand panel contains the adjustment dials and galvanometer of the<lb/>
Rubicon potentiometer used in automatic operation, the shim rod positioning<lb/>
switches, shim rod extreme position indicating lights, and various meters <orig reg="indicating">indi-<lb/>
cating</orig> auxiliary operation data.
</p>
<p>The left hand panel contains pairs of red and green lights (red indicating<lb/>
non-operating and green indicating normal operating condition) for numerous<lb/>
auxiliary instrumentation systems; e.g.:
</p>
<p>
<table>
<row>
<cell>Stack radiation monitor</cell><cell>&#x2003;</cell><cell>Gas recombiner flow meter</cell>
</row>
<row>
<cell>Campus radiation monitors</cell><cell>&#x2003;</cell><cell>Recombiner coolant water flow meter</cell>
</row>
<row>
<cell>Coolant radiation monitor</cell><cell>&#x2003;</cell><cell>Reactor coolant flow meter</cell>
</row>
<row>
<cell>Stack flow meter</cell><cell>&#x2003;</cell><cell></cell>
</row>
</table>
</p>
<p>Also on the left hand panel are located the switches for trip-testing the<lb/>
automatic safety mechanisms in the neutron measuring channels, the meters<lb/>
indicating the recombiner gas circulation rate and the recombiner coolant <orig reg="temperature">tem-<lb/>
perature</orig>.
</p>
<p>The Recorder Rack contains 12 Brown Recorders. The data recorded on<lb/>
each are as follows: (Single channel, curve-drawing instruments used unless<lb/>
otherwise indicated.)
</p>
<p><list>
<item>(1) Temperature of reactor coolant (measured at 4 different points).</item>

<item>(2) Control Rod position.</item>

<item>(3) Reactor solution temperature.</item>

<item>(4) Neutron flux, linear.</item>
</list>
</p>
<pb n="21"/>
<p><seg><xref id="NEfurther010052y.jpg" rend="new">
<figure entity="NEfurther010052y"></figure></xref></seg></p>

<p><list>
<item>(5) Neutron flux, logarithmic.</item>

<item>(6) Period of the reactor.</item>

<item>(7) Campus radiation monitor (3 stations).</item>

<item>(8) Campus radiation monitor (3 stations).</item>

<item>(9) Recombiner temperatures (coolant, catalyst).</item>

<item>(10) Spare</item>

<item>(11) Spare</item>

<item>(12) Spare</item>
</list>
</p>
</div4>
<div4 type="part" n="9">
<head>9. <hi rend="underline">Control Safety and Shim Rods.</hi></head>

<p>Two vertical boron rods moving inside of sheath tubes which are re-entrant<lb/>
into the Reactor through the top surface, and two vertical cadmium strips located<lb/>
on the external periphery of the reactor cylinder, provide the means of controlling<lb/>
and adjusting the level of reactor operation (Fig. 22).
</p>
<p>The rods are of thin-walled stainless steel tubing filled with boron powder.<lb/>
The two rods and their remotely controlled actuating accessories are completely<lb/>
independent, but are identical in construction and in relative reactor location, so<lb/>
that the rods may be used interchangeably to perform respective functions as<lb/>
Safety and Control Rods. When fully lowered, the rods extend (inside of their<lb/>
re-entrant tubes) 9-1/2 inches into the reactor solution, to within 1/4 inch of the<lb/>
bottom of the reactor. When fully raised, the lower ends of the rods are 1-1/2<lb/>
inches above the top surface of the reactor. The length of travel is 12 inches.<lb/>
With the motor at maximum speed, the rate of rod movement is 5 inches/minute.<lb/>
This may be controlled at any lower rate desired.
</p>
<p>The boron rods are connected to their respective motor-driven elevating<lb/>
screws by a direct current electromagnetic coupling. If any one of the <orig reg="numerous">numer-<lb/>
ous</orig> potential safety signals interrupt the current to the electromagnets, the<lb/>
suspended rods are released and they fall by their own weight into the reactor.<lb/>
A shock-absorber slows the rate of fall over the last 1 inch of travel. The<lb/>
electronic safety circuits pre-set to release the rods and the electric circuit to<lb/>
the magnet are so adjusted that the rods are completely released by the magnet<lb/>
in 0.02 seconds after the initial signal appears, if the reactor is operating above<lb/>
the 100 watt level. At lower levels, the time of release is somewhat longer.
</p>
<p>The two boron rods are so connected by a micro-switch interlock that one<lb/>
rod must be completely poised at its upper limit of travel before the other rod<lb/>
can be raised. The excess reactivity in the reactor is so adjusted that either of<lb/>
these two rods alone, completely inserted, will stop the chain reaction. Thus<lb/>
one rod is always "cocked" in Safety Rod position before reactor operation can
</p>
<pb n="22"/>
<p><seg><xref id="NEfurther010052z.jpg" rend="new">
<figure entity="NEfurther010052z"></figure></xref></seg></p>

<p>be initiated by <orig reg="withdrawal">withdrawl</orig> of the second Control Rod.
</p>
<p>The boron rods are located on a diameter of the reactor cylinder on alternate<lb/>
sides of the center, each 2-11/16 inches (on center) from the center, with their<lb/>
axes parallel to that of the reactor cylinder. The rods are thus at position of <orig reg="approximately">ap-<lb/>
proximately</orig> maximum effectiveness. By calculation of the relative effectiveness<lb/>
of these rods, as compared to similar rods similarly placed in the spherical <name type="place">Los<lb/>
Alamos</name> Homogeneous Reactor<ptr target="e1"/>, it is estimated that either of the rods in the<lb/>
<name type="place">Raleigh</name> Research Reactor is "worth" 80 grams of U235. In actual operation, the<lb/>
excess uranium, above that required to produce criticality, will always be less<lb/>
than this amount.
</p>
<p>The Shim "rods", two in number, and likewise independent in operation<lb/>
and identical in construction, consist of 4" wide strips of 1/32" Cadmium, 10"<lb/>
long, are located on the periphery of the reactor cylinder in a vertical position<lb/>
(Fig. 22). The shim rods are positioned by a variable speed, motor driven<lb/>
mechanism exactly similar to that of the control rods, except no electromagnet<lb/>
coupling is provided between the motor driven screw and the shim.
</p>
<p>In lowered position, the lower ends of the cadmium shim "rods" are even<lb/>
with the bottom of the reactor cylinder. In fully raised position, the lower ends<lb/>
of the shims are 1 inch above the top of the reactor. The length of travel is<lb/>
12 inches; the maximum rate of travel is 5 inches per minute.
</p>
<p>The shims are positioned with their centers 5-3/8 inches apart, on one<lb/>
side of the diameter on which the control and safety rods are located, and<lb/>
symmetrically spaced with respect to the Control-Safety Rod diameter. The<lb/>
shims thus are each 64<hi rend="sup">o</hi> from the Control and Safety Rods, and 52<hi rend="sup">o</hi> from each<lb/>
other. The Control-Safety Rod diameter is perpendicular to the direction of the<lb/>
thermal column from the reactor, and the shims are on the opposite side of the<lb/>
Control-Safety diameter from the thermal column. The shims are thus in <orig reg="position">posi-<lb/>
tion</orig> (a) approximately maximum effectiveness, and (b) minimum effect on the<lb/>
flux entering the thermal column.
</p>
<p>It is calculated, again, by comparison with the somewhat similar shims of<lb/>
the <name type="place">Los Alamos</name> Reactor, that each of the shims of the <name type="place">Raleigh</name> Research Reactor<lb/>
is "worth" 25 grams of uranium.
</p>
<p>The shim rods are intended essentially to "normalize" the excess reactivity<lb/>
of the reactor so that the control rod operates at its position of maximum <orig reg="sensitivity">sensi-<lb/>
tivity</orig>. The procedure for use is on this wise: the safety rod is raised; the <orig reg="control">con-<lb/>
trol</orig> rod is (partially) withdrawn to the position approximately desired; then one<lb/>
or both shim rods (in succession) are withdrawn until a sustained reaction begins.
</p>
<pb n="23"/>
<p><seg><xref id="NEfurther010052a1.jpg" rend="new">
<figure entity="NEfurther010052a1"></figure></xref></seg></p>

<p>The reaction is thus achieved with the control rod at the desired position.
</p>
<p>The shim rods are necessary because the excess reactivity of the reactor may<lb/>
change from day to day as exposure samples are inserted or withdrawn, as <orig reg="reflector">reflec-<lb/>
tor</orig> in exposure ports is removed or returned, etc. If the shim rods were not used,<lb/>
frequent additions or removals of nuclear fuel might be necessary to keep the excess<lb/>
reactivity adjusted to safe and workable limits.
</p>
</div4>
<div4 type="part" n="10">
<head>10. <hi rend="underline">Campus Monitoring.</hi></head>

<p>It is not anticipated that enough radioactivity will be released from the<lb/>
reactor facility to cause significant increase in the normal level of background<lb/>
activity. To insure positively that this is the case, a series of instruments designed<lb/>
to measure continuously the level of radioactivity at various locations on the campus<lb/>
are provided. Part of this system was placed into operation in September, 1951, in<lb/>
order that a continuous record of normal background radiation might be obtained<lb/>
over a period of several months before the reactor is placed in operation.
</p>
<p>Beta and gamma monitoring stations are located at 5 positions on the campus.<lb/>
A mobile monitoring station will be used in making periodic check of the area. The<lb/>
stationary positions are in a deliberately chosen pattern with respect to the reactor<lb/>
location: Four positions are each about 550 feet from the reactor, in northeast,<lb/>
northwest, southwest, and southeast directions, respectively. The fifth station is<lb/>
1200 feet northwest of the reactor. The prevailing wind in this area is toward the<lb/>
northwest; therefore there are two monitoring stations in the direction of the <orig reg="prevailinig">pre-<lb/>
vailing</orig> winds and one each in directions opposite and perpendicular to this, <orig reg="respectively">res-<lb/>
pectively</orig>.
</p>
<p>Two types of monitoring instruments have been chosen: A G-M tube <orig reg="rate-meter">rate-<lb/>
meter</orig>, recorder combination and an ionization-chamber, dynamic condenser, recorder<lb/>
electrometer system. Two monitoring stations are equipped with one type and two<lb/>
with the other. The fifth station, namely; the near station in the direction of the <orig reg="prevailing">pre-<lb/>
vailing</orig> <orig reg="winds">wids</orig>, is equipped with one of each type.
</p>
<p>Each electrometer is provided with an automatic zero drift <orig reg="indication">indiciation</orig> and an<lb/>
automatic calibrating device which operate at regular intervals. The latter consists<lb/>
of a clock mechanism arranged to withdraw a known radioactive source from a<lb/>
shielded position and place it in a pre-determined position near the detector. A<lb/>
similar calibrating mechanism is provided for the G-M units. Thus, on the recorded<lb/>
chart of the background radioactivity measured by each monitor, there also appears<lb/>
an hourly check of the sensitivity of the instrument and a zero recalibration if any<lb/>
drift has occurred. The recording apparatus for all monitoring stations is located<lb/>
in the Control Room of the Reactor Building. Signals are sent from each outlying<lb/>
station to central recorders so that the operator can be informed at all times of any<lb/>
change in the level of radioactivity at any of the monitoring stations.
</p>
</div4>
<div4 type="part" n="11">
<head>11. <hi rend="underline">Miscellaneous Monitors.</hi></head>

<p>A number of radiation detecting and measuring instruments, in addition to
</p>
<pb n="24"/>
<p><seg><xref id="NEfurther010052b1.jpg" rend="new">
<figure entity="NEfurther010052b1"></figure></xref></seg></p>

<p>those described above, will be provided in the reactor facility. The following are<lb/>
included;
</p>
<p><list>
<item>A Stack Monitor, to measure the level of activity in the gases being<lb/>
discharged to the atmosphere.</item>

<item>A Liquid Monitor at the Sump, to measure the activity in liquids collecting<lb/>
from the Reactor Room drains.</item>

<item>Two Liquid Monitors in the drainage system of the laboratories.</item>

<item>Two Liquid Monitors in the waste line carrying the effluent reactor<lb/>
cooling water.</item>

<item>A Hand and Foot monitor for laboratory personnel.</item>

<item>Personnel electroscopes and film badges</item>
</list></p>
</div4>
</div3>
</div2>
<pb n="25"/>
<div2 type="image">
<p><seg><xref id="NEfurther010052c1.jpg" rend="new">
<figure entity="NEfurther010052c1"></figure></xref></seg></p>
</div2>
<div2 type="section" n="3">
<head>III. <hi rend="underline">REACTOR CHARACTERISTICS</hi></head>

<div3 type="subsection" n="">
<head>A. <hi rend="underline">Safety Features.</hi></head>

<p>When the reactor is fully assembled, at room temperature, with graphite<lb/>
reflector in position, only removal of a shimor control rod) addition of nuclear<lb/>
fuel, or substitution of Be or heavy water for some of the graphite reflector could<lb/>
cause an increase in the reactivity. All other changes which could occur would<lb/>
reduce the potential reactivity of the reactor. An increase in temperature, <orig reg="insertion">in-<lb/>
sertion</orig> of a non-fissionable absorber for irradiation, opening of a channel to <orig reg="permit">per-<lb/>
mit</orig> escape of a neutron beam, and addition or removal of water from the reactor<lb/>
are all factors which would reduce the potential reactivity of the reactor.
</p>
<p>The decrease in reactivity as the temperature increases is one of the most<lb/>
important features. There are four factors which contribute to this overall effect:<lb/>
(1) As the temperature increases, the fuel solution expands, the density decreases,<lb/>
and the reactivity is reduced. (2) As the temperature increases, the average<lb/>
energy of the neutrons, most of which are in thermal equilibrium with the atoms<lb/>
of the solution, also increases. Increasing the average neutron velocity causes a<lb/>
larger percentage to be captured (without resultant fission) by the U238 atoms<lb/>
present, because of the large resonant absorption cross-section in U238 at 7 ev.<lb/>
This tends to reduce the reactivity, though for small temperature increases and<lb/>
for high U235 enrichment this effect is small. (3) If the temperature increases<lb/>
due to an increased rate of energy release by fission, the total radioactivity in the<lb/>
fuel solution increases and, a proportionally larger amount of decomposition<lb/>
gases--mostly H<hi rend="sub">2</hi> and 0<hi rend="sub">2</hi>--are released throughout the volume of the solution.<lb/>
The bubbles of these gases rise rapidly to the top, but their presence in the <orig reg="solution">solu-<lb/>
tion</orig> causes an overall reduction in density, and hence tends to decrease the <orig reg="reactivity">re-<lb/>
activity</orig>. (4) As the temperature increases to a value near the boiling point of the<lb/>
solution, vapor bubbles of the solution are formed. These bubbles also lower the<lb/>
solution density and decrease the reactivity. A steady state temperature in excess<lb/>
of the boiling point of the solution cannot be achieved, since the pressure is <orig reg="maintained">main-<lb/>
tained</orig> essentially at atmospheric pressure. The negative temperature coefficient<lb/>
observed for the Los Alamos Homogeneous Reactor<ptr target="f1"/> varies from 0.7 gm U235/<hi rend="sup">o</hi>C<lb/>
at low temperature and low power to about 1.25 gm U235/<hi rend="sup">o</hi>C at higher powers and at<lb/>
temperatures near the, boiling point. The temperature coefficient for the Raleigh<lb/>
Research Reactor is expected to have similar values.
</p>
<p>As water is removed from the reactor, by evaporation, entrainment, or <orig reg="decomposition">de-<lb/>
composition</orig>, two effects occur which tend to lower the reactivity: (1) the ratio<lb/>
of hydrogen atoms to uranium atoms, initially adjusted to optimum, deviates from
</p>
<pb n="26"/>
<p><seg><xref id="NEfurther010052d1.jpg" rend="new">
<figure entity="NEfurther010052d1"></figure></xref></seg></p>

<p>optimum, decreasing the reactivity. In fact, whether water is added or removed,<lb/>
the reactivity tends to decrease. The optimum <hi rend="sup">H</hi>/<hi rend="sub">U235</hi> ratio is not a sharply <orig reg="defined">de-<lb/>
fined</orig> number, however, may vary over a relatively large range of values, say<lb/>
from <hi rend="sup">H</hi>/<hi rend="sub">U235</hi> = 300 to <hi rend="sup">H</hi>/<hi rend="sub">U235</hi> = 500, without great effect on reactivity. Hence,<lb/>
rather large amounts of water must be added or removed before this factor <orig reg="decreases">de-<lb/>
creases</orig> reactivity by a significant amount. (2) As water is removed, the dissolved<lb/>
uranyl sulfate tends to precipitate out of solution. This changes the homogeneous<lb/>
distribution of U235 in the solution, and any such change causes a decrease in <orig reg="reactivity">re-<lb/>
activity</orig>.
</p>
<p>A change in the acidity of the fuel solution resulting from radiation <orig reg="decomposition">decom-<lb/>
position</orig> of some of the acid molecules in the solution, is more likely to cause<lb/>
precipitation than is the removal of a small amount of water. Hence, the acidity<lb/>
of the solution is checked frequently and adjusted as necessary.
</p>
</div3>
<div3 type="subsection" n="2">
<head>B. <hi rend="underline">Reactivity and Nuclear Behavior.</hi></head>

<p>It is estimated that 715 grams of U235 at 90% isotopic purity are required<lb/>
for criticality at 20<hi rend="sup">o</hi>C. About 770 grams are required at 80<hi rend="sup">o</hi>C, the normal <orig reg="operating">op-<lb/>
erating</orig> temperature. (Both figures with all control, safety, and shim rods <orig reg="removed">re-<lb/>
moved</orig>.) The reactor will contain 790 grams. Thus, there is in the reactor 75<lb/>
grams in excess of the critical amount at room temperature and 20 grams excess<lb/>
at operating temperature. The control, and safety rods are each "worth" 80<lb/>
grams of U235, and the shims 25 grams each: a total of 210 grams. Thus either<lb/>
control rod alone can control the total excess reactivity with the reactor at room<lb/>
temperature, and any shim or control rod alone can absorb the excess with the<lb/>
reactor at operating temperature.
</p>
<p>It is of interest to explore the behavior of the reactor if all interlocks and<lb/>
instrumental safety devices should fail as the control rod is being removed.<lb/>
Consider first the case in which the reactor is at room temperature and the rod<lb/>
is removed slowly, so that nuclear and thermal equilibrium are maintained.
</p>
<p><hi rend="underline">Case 1. Slow removal of control rod.</hi>
</p>
<p>As the rod is removed, the nuclear reaction begins, heat is released, and<lb/>
the solution temperature increases. The negative temperature coefficient tends<lb/>
to reduce reactivity, but as the rod continues to be removed, this effect is <orig reg="over-ridden">over-<lb/>
ridden</orig>, and the temperature continues to increase. Some of the heat released<lb/>
will be removed by the cooling system of the reactor, but if sufficient excess<lb/>
uranium is present, the amount of heat released as the rod removal continues<lb/>
will eventually be more than the cooling system can remove, and the <orig reg="temperature">tempera-<lb/>
ture</orig> will increase.
</p>
<p>If enough excess uranium is present in the reactor to permit the reaction
</p>
<pb n="27"/>
<p><seg><xref id="NEfurther010052e1.jpg" rend="new">
<figure entity="NEfurther010052e1"></figure></xref></seg></p>

<p>to continue, despite the negative temperature coefficient, at the boiling point of<lb/>
the solution, then, as the rod is removed, the temperature will increase until the<lb/>
liquid boils. If the rod is removed further, more vigorous boiling will <orig reg="ensue">insue</orig>.<lb/>
Eventually, due to "evaporation" of water or decomposition of acid, the reaction<lb/>
would cease. Vigorous boiling would probably result in large fluctuations in <orig reg="reactivity">re-<lb/>
activity</orig> as vapor bubbles formed and collapsed.
</p>
<p>If the excess uranium present in the reactor is not sufficient to over-ride<lb/>
the negative temperature coefficient up to the boiling point, as will be the usual<lb/>
situation, then, as removal of the rod causes release of more heat than the <orig reg="cooling">cool-<lb/>
ing</orig> system can remove, the temperature will increase to some value, at which<lb/>
the k of the reactor drops below 1. As the reactor cools slightly, the reaction<lb/>
recommences, the temperature increases and k again drops below 1. Thus,<lb/>
the temperature oscillates around the critical value with reactor operating at<lb/>
such level that the rate of heat released is just equal to that removed.
</p>
<p>It is thus clear that the steady state amount of power released by the <name type="reactor">re-<lb/>
actor</name> is directly related to the rate at which heat can be removed. It is estimated<lb/>
that about 0.5 Kw of heat can be dissipated from the <name type="place">Raleigh</name> Research Reactor by<lb/>
conductivity and radiation into the reflector, with no auxiliary cooling. The <orig reg="cooling">cool-<lb/>
ing</orig> system described in Section II, F is designed to remove about 10 Kw of heat<lb/>
when the reactor is at 80<hi rend="sup">o</hi>C.
</p>
<p><hi rend="underline">Case 2. Fast Removal of the Rods.</hi>
</p>
<p>If the rods and shims are removed instantaneously from the reactor, while<lb/>
the temperature is at 20<hi rend="sup">o</hi>C; an excess reactivity of 0.016 results. With this <orig reg="excess">ex-<lb/>
cess</orig>, the reactor will flash to a power peak of about 170 megawatts, with an<lb/>
e-folding time of about 0.02 seconds (and a total elapsed time of about 3-1/2<lb/>
seconds) before the negative temperature coefficient can begin to control the<lb/>
power downward. Another 1-1/2 seconds are required to reduce the excess <orig reg="reactivity">re-<lb/>
activity</orig> to zero.
</p>
<p>In making these estimates, a constant negative temperature coefficient of<lb/>
2.0 x 10<hi rend="sup">-4</hi>/<hi rend="sup">o</hi>C is assumed, and no consideration is given to the effect of bubble<lb/>
formation in the solution. It is known that bubbles will be formed, and that more<lb/>
favorable temperature coefficients will exist over a portion of the event. Both<lb/>
of these factors would tend to slow the rate of rise, lower the value of peak<lb/>
power achieved, and hasten the return of the power level to nominal values.
</p>
<p>The net results of an event of this kind would be (1) the temperature of the<lb/>
solution would be increased, probably to boiling, and (2) the levels at the outer<lb/>
surface of the reactor shield would flash to a few thousand times continuous <orig reg="exposure">ex-<lb/>
posure</orig> tolerance levels for about 3 seconds. An explosion would almost <orig reg="certainly">cer-<lb/>
tainly</orig> not occur.
</p>
<p>If all the rods and shims are removed from the cold reactor (20<hi rend="sup">o</hi>C) at a<lb/>
uniform rate in a total of 5 second, (the normal time required is 2 minutes) a<lb/>
flash up to a power level of 14 megawatts results. (Fig. 23). As above, a
</p>
<pb n="28"/>
<p><seg><xref id="NEfurther010052f1.jpg" rend="new">
<figure entity="NEfurther010052f1"></figure></xref></seg></p>

<p>conservative value of the temperature coefficient and no effects of bubbling are<lb/>
assumed. The flash up and return to normal levels again occurs within three or<lb/>
four seconds. As shown earlier, with slow rate of rod removal (i.e., in times<lb/>
longer than 15 or 20 seconds) the power rises smoothly to equilibrium value with<lb/>
no flash up.
</p>
</div3>
<div3 type="subsection" n="3">
<head>C. <hi rend="underline">Power Level, Radiation Fluxes.</hi></head>

<p>It is anticipated that the normal maximum power level of operation of the<lb/>
reactor will be about 10 Kw. Calculations have been made of the radiation fluxes<lb/>
to be anticipated at various points in and around the core, when the reactor is <orig reg="operating">op-<lb/>
erating</orig> at this level. The calculated values are shown in Table 5.
</p>

<p><hi rend="underline">TABLE 5 - CALCULATED RADIATION FLUXES AT 10 Kw. OPERATION</hi>
</p>
<p><table>
<row>
<cell></cell><cell>&#x2003;</cell><cell><hi rend="underline">Fast n</hi></cell><cell>&#x2003;</cell><cell><hi rend="underline">Slow n</hi></cell><cell>&#x2003;</cell><cell><hi rend="underline">Gamma</hi></cell>
</row>
<row>
<cell></cell><cell>&#x2003;</cell><cell>(n/cm<hi rend="sup">2</hi>/sec)</cell><cell></cell><cell>(n/cm<hi rend="sup">2</hi>/sec)</cell><cell></cell><cell>(&#x03B3;/cm<hi rend="sup">2</hi>/sec)</cell>
</row>
<row>
<cell>Inside Core</cell><cell>&#x2003;</cell><cell>2 x 10<hi rend="sup">11</hi></cell><cell></cell><cell>5 x 10<hi rend="sup">11</hi></cell><cell></cell><cell>6.7 x 10<hi rend="sup">11</hi></cell>
</row>
<row>
<cell>Surface of Reactor Envelope</cell><cell>&#x2003;</cell><cell>7 x 10<hi rend="sup">10</hi></cell><cell></cell><cell>3 x 10<hi rend="sup">11</hi></cell><cell></cell><cell>4.5 x 10<hi rend="sup">11</hi></cell>
</row>
<row>
<cell>Surface of Reflector (20" from<lb/>reactor)</cell><cell>&#x2003;</cell><cell>8 x 10<hi rend="sup">9</hi></cell><cell></cell><cell>8 x 10<hi rend="sup">10</hi></cell><cell></cell><cell>1.8 x 10<hi rend="sup">10</hi></cell>
</row>
<row>
<cell>Outside 4" lead shielding</cell><cell>&#x2003;</cell><cell>"</cell><cell></cell><cell>"</cell><cell></cell><cell>1.1 x 10<hi rend="sup">8</hi></cell>
</row>
<row>
<cell>Four feet from center of<lb/>
reactor on axis of thermal<lb/>
column</cell><cell>&#x2003;</cell><cell>2.5 x 10<hi rend="sup">7</hi></cell><cell></cell><cell>1.4 x 10<hi rend="sup">10</hi></cell><cell></cell><cell>6.0 x 10<hi rend="sup">7</hi></cell>
</row>
<row>
<cell>One foot from end of thermal<lb/>
column (on axis)</cell><cell>&#x2003;</cell><cell>2.0 x 10<hi rend="sup">5</hi></cell><cell></cell><cell>1.5 x 10<hi rend="sup">9</hi></cell><cell></cell><cell>1.2 x 10<hi rend="sup">6</hi></cell>
</row>
<row>
<cell>Outer surface of concrete at<lb/>
end of column</cell><cell>&#x2003;</cell><cell></cell><cell></cell><cell></cell><cell></cell><cell>70</cell>
</row>
<row>
<cell>Average radiation over outer<lb/>
surface of concrete shield</cell><cell>&#x2003;</cell><cell>0.8</cell><cell></cell><cell>negligible</cell><cell></cell><cell>0.15</cell>
</row>
</table>
</p>

<pb n="29"/>
<p><seg><xref id="NEfurther010052g1.jpg" rend="new">
<figure entity="NEfurther010052g1"></figure></xref></seg></p>

</div3>
<div3 type="subsection" n="4">
<head>D. <hi rend="underline">Fission Products; Radioactivity.</hi></head>

<p>After the reactor has been in operation for some time, the solution will<lb/>
possess a considerable amount of radioactivity, due to the build up of fission <orig reg="products">pro-<lb/>
ducts</orig>. It is necessary to know how much activity accumulates in the solution and<lb/>
how much radioactive gas is evolved.
</p>
<p>If the reactor were operated for a known time at a known power level, <orig reg="calculation">cal-<lb/>
culation</orig> of the resulting fission products would be a relatively simple matter.<lb/>
For intermittent operation at random levels and for various lengths of times,<lb/>
calculation of the composite accumulation of non-volatile and gaseous products<lb/>
becomes impossible. To determine the upper limit of activity to be expected,<lb/>
a schedule of operation was postulated which results in a build up of activity not<lb/>
expected to be exceeded by any actual schedule of reactor operation. The <orig reg="postulated">pos-<lb/>
tulated</orig> "worst case" of reactor operation is:
</p>
<p>(1) The reactor is operated at 10 Kw for the first 6 hours of every <orig reg="successive">suc-<lb/>
cessive</orig> 24 hour period, and is not operated over the remaining 18 hours of the<lb/>
period. (At times, the reactor may be operated continuously for periods <orig reg="considerably">con-<lb/>
siderably</orig> longer than 6 hours. Such periods would be preceded and followed<lb/>
by correspondingly longer "down" periods, however, so that the average <orig reg="result">re-<lb/>
sult</orig>, say at the end of' the week, would produce no more activity than that<lb/>
produced by the schedule described.)
</p>
<p>(2) Assume that the gas disposal system operates as described in Section<lb/>
II G for the 6 hours that the reactor is in operation, plus 1 additional hour after<lb/>
shut down, and then does not operate over the remaining 17 hours of each 24<lb/>
hour period. The' gases which accumulate in the reactor during the 17 hour<lb/>
"down" period, however, are withdrawn during the subsequent operating period<lb/>
along with those produced during the period.
</p>
<p>(3) The refrigerated condenser of the gas disposal system lowers the gas<lb/>
temperature to 13<hi rend="sup">o</hi>C, and only those fission products remaining volatile at this<lb/>
and lower temperatures escape from the reactor.
</p>
<p>Two questions are asked: After the reactor has operated for many days<lb/>
on this schedule, so that equilibrium has been reached, (a.) what is the level of<lb/>
the radioactivity in the reactor solution, and (b) what is the quantity of <orig reg="radioactive">radio-<lb/>
active</orig> gas to be disposed of in the 7 hour operating period of each 24 hour<lb/>
period?
</p>
<p>(a) <hi rend="underline">Radioactivity of the Fuel Solution.</hi></p>

<p>According to information presented in an article by K. Way,<ptr target="a8"/> the amount
</p>
<pb n="30"/>
<p><seg><xref id="NEfurther010052h1.jpg" rend="new">
<figure entity="NEfurther010052h1"></figure></xref></seg></p>

<p>of radioactive energy released by the fission products in a reactor immediately<lb/>
after shutdown, after the reactor had been operating for an extended period at a<lb/>
10 Kw power level would be 2.6 x 10<hi rend="sup">15</hi> mev/sec. It is difficult to interpret<lb/>
this in terms of curies. A rough approximation may be made by assuming that<lb/>
one beta and one gamma, each of 1 mev energy are given off in each "<orig reg="disintegration">disintegra-<lb/>
tion</orig>". There are then 1.3 x 10<hi rend="sup">15</hi> disintegration/see; or 35,000 curies
</p>
<p>It may be shown by rather simple calculations that the fission product activity<lb/>
of shutdown in a reactor operating on a regular schedule of 6 hours per day at a<lb/>
10 Kw level is about 75% of the activity at shutdown in a reactor operated <orig reg="continuously">contin-<lb/>
uously</orig> at a 10 Kw level. Thus the maximum activity expected in the Raleigh<lb/>
Reactor is about 2. x 10<hi rend="sup">15</hi> mev/sec., or about 26,000 curies. The decay in<lb/>
activity after shutdown is rapid. After 18 hours, the normal down time in the<lb/>
postulated daily schedule, the activity would be only about 2.6 curies.
</p>
<p>It is of interest to note the thermal effects of the fission product activity<lb/>
after the reactor is shut down. If the reactor cooling water should cease to<lb/>
circulate when the reactor should be closed down, low much increase in <orig reg="temperature">temper-<lb/>
ature</orig> might be expected?
</p>
<p>For data presented in the above mentioned article,<ptr target="a8"/> it may be shown that<lb/>
the thermal energy resulting from the beta and gamma activity of fission <orig reg="products">pro-<lb/>
ducts</orig> in a 10 Kw reactor after shut down is given approximately by the equation:
</p>
<p><seg rend="left"><figure entity="NEfurther010052form1"></figure></seg>

<formula notation="mathml"><hi rend="suppress"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <mi>E</mi>
      <mi>&thinsp;</mi>
      <mrow>
        <mo>(</mo>
        <mi>w</mi>
        <mi>a</mi>
        <mi>t</mi>
        <mi>t</mi>
        <mi>s</mi>
        <mo>)</mo>
        <mi>&thinsp;</mi>
        <mo>=</mo>
        <mi>&thinsp;</mi>
        <mn>6</mn>
        <mn>3</mn>
        <mn>8</mn>
        <mi>&thinsp;</mi>
        <mo>[</mo>
        <mfrac>
          <mrow>
            <mn>1</mn>
          </mrow>
          <mrow>
            <msup>
              <mrow>
                <mi>t</mi>
              </mrow>
              <mrow>
                <mn>0</mn>
                <mn>.</mn>
                <mn>2</mn>
              </mrow>
            </msup>
          </mrow>
        </mfrac>
        <mi>&thinsp;</mi>
        <mo>-</mo>
        <mfrac>
          <mrow>
            <mn>1</mn>
          </mrow>
          <mrow>
            <mrow>
              <msup>
                <mrow>
                  <mrow>
                    <mo>(</mo>
                    <msub>
                      <mrow>
                        <mi>T</mi>
                      </mrow>
                      <mrow>
                        <mi>o</mi>
                      </mrow>
                    </msub>
                    <mo>+</mo>
                    <mi>t</mi>
                    <mo>)</mo>
                  </mrow>
                </mrow>
                <mrow>
                  <mn>0</mn>
                  <mn>.</mn>
                  <mn>2</mn>
                </mrow>
              </msup>
            </mrow>
          </mrow>
        </mfrac>
        <mo>]</mo>
      </mrow>
    </mrow>
  </mrow>
</m:math>
-->
</hi></formula></p>
<p>where t is the time in seconds after shutdown, and T<hi rend="sub">o</hi> is the time<lb/>
in seconds the reactor had operated prior to shutdown.
</p>
<p>By application of Way's relation for activities at various times after <orig reg="shut-down">shut-<lb/>
down</orig>, and assuming that all betas and gammas are completely absorbed in the<lb/>
reactor, the rate at which thermal energy is imparted to the fuel is
</p>
<p><list>
<item>At the end of 10 seconds, 402 watts</item>
<item>At the end of 100 seconds, 253 watts</item>
<item>At the end of 1 hour, 124 watts</item></list>
</p>
<p>If the reactor should be at 80<hi rend="sup">o</hi>C, 500 watts for about 15 minutes (<orig reg="assuming">assum-<lb/>
ing</orig> no heat loss) would be required to raise the temperature to boiling. It is<lb/>
estimated, on the other hand, that about 500 watts of power will be lost from the<lb/>
reactor by <hi rend="strike">condensation</hi> <hi rend="italics">conduction</hi> when the temperature is at 80<hi rend="sup">o</hi>C. Therefore, heat<lb/>
from the fission products would hardly cause any increase in temperature, and<lb/>
certainly would not cause the solution to boil.
</p>
<p>(b) <hi rend="underline">Daily Gaseous Radioactivity Produced.</hi>
</p>
<p>Most of the primary and the daughter elements produced in the fission
</p>
<pb n="31"/>
<p><seg><xref id="NEfurther010052i1.jpg" rend="new">
<figure entity="NEfurther010052i1"></figure></xref></seg></p>

<p>process are neither gases nor vapors at the temperatures prevailing in the reactor.<lb/>
A few, however, are sufficiently volatile to escape from the 80<hi rend="sup">o</hi>C fuel solution in<lb/>
the reactor. A careful examination of the, list of product elements leads to the <orig reg="conclusion">con-<lb/>
clusion</orig> that two such elements, iodine and Xe<hi rend="sup">133</hi>, the daughter of I<hi rend="sup">133</hi>, contain<lb/>
many times more activity than all others. Without the use of the refrigerated <orig reg="condenser">con-<lb/>
denser</orig> in the Recirculation-Recombination system,(Section II G), it is possible that<lb/>
a considerable portion of the iodine might find its way out of the reactor solution,<lb/>
through the disposal system, and out into the atmosphere. This would probably<lb/>
necessitate a revision of the disposal system, for the tolerance concentration of<lb/>
radioactive iodine in the atmosphere is very low. (10<hi rend="sup">-7</hi> micro curies/cc)<lb/>
Available evidence indicates, however, that the iodine will be returned to the <orig reg="reactor">re-<lb/>
actor</orig> by the refrigerated condenser, even if it escapes into the Recombination<lb/>
system.
</p>
<p>This leaves the daughter product, Xe<hi rend="sup">133</hi>, to be handled in the gas disposal<lb/>
system, for all xenon produced would be expected to escape from the reactor. The<lb/>
calculation of the amount of Xe<hi rend="sup">133</hi> produced by the intermittent reactor operation<lb/>
schedule described above is performed by essentially standard methods. The<lb/>
growth-decay equation<lb/>

<seg rend="left"><figure entity="NEfurther010052form2"></figure></seg>

<formula notation="mathml"><hi rend="suppress"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <mfrac>
        <mrow>
          <mi>d</mi>
          <mi>N</mi>
        </mrow>
        <mrow>
          <mi>d</mi>
          <mi>t</mi>
        </mrow>
      </mfrac>
      <mo>=</mo>
      <mi>&thinsp;</mi>
      <mi>g</mi>
      <mi>&thinsp;</mi>
      <mo>-</mo>
      <mi>&lambda;</mi>
      <mi>N</mi>
    </mrow>
  </mrow>
</m:math>
-->
</hi></formula><lb/>
is solved for the number of atoms of the principal primary source (I<hi rend="sup">133</hi>, having a<lb/>
22 hr. half-life) resulting from a single 6 hour operating period. Here g, the rate<lb/>
of generation by fission, is proportional to the power level. The contribution of<lb/>
all previous days is added by a series method, with the effect of decay accounted<lb/>
for, to yield the equilibrium level of iodine. The gaseous Xe<hi rend="sup">133</hi> (5.3 day half-life)<lb/>
that is produced by the iodine over a 24 hour period may then be determined. No<lb/>
account is taken of the distribution of fission products by atomic number, and the<lb/>
predecessors of I are taken to have effectively zero half-life. An outline of the<lb/>
calculation is given below. For a given operating period, say from time zero to<lb/>
time <hi rend="italics">&#x03C4;</hi>, the solution of the above equation is<lb/>
<seg rend="left"><figure entity="NEfurther010052form3"></figure></seg>

<formula notation="mathml"><hi rend="suppress"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <msub>
        <mrow>
          <mi>N</mi>
        </mrow>
        <mrow>
          <mn>1</mn>
        </mrow>
      </msub>
      <mo>=</mo>
      <mi>g</mi>
      <mo>/</mo>
      <msub>
        <mrow>
          <mi>&lambda;</mi>
        </mrow>
        <mrow>
          <mn>1</mn>
        </mrow>
      </msub>
      <mrow>
        <mo>(</mo>
        <mn>1</mn>
        <mo>-</mo>
        <msup>
          <mrow>
            <mi>e</mi>
          </mrow>
          <mrow>
            <msub>
              <mrow>
                <mo>-</mo>
                <mi>&lambda;</mi>
              </mrow>
              <mrow>
                <mn>1</mn>
              </mrow>
            </msub>
            <mi>t</mi>
          </mrow>
        </msup>
        <mo>)</mo>
      </mrow>
    </mrow>
  </mrow>
</m:math>
-->
</hi></formula></p>
<p>For the down-time between <hi rend="italics">&#x03C4;</hi> and 1 day, the equation reduces to
<lb/>
<seg rend="left"><figure entity="NEfurther010052form4"></figure></seg>

<formula notation="mathml"><hi rend="suppress"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <mfrac>
        <mrow>
          <msub>
            <mrow>
              <mi>d</mi>
              <mi>N</mi>
            </mrow>
            <mrow>
              <mn>1</mn>
            </mrow>
          </msub>
        </mrow>
        <mrow>
          <mi>d</mi>
          <mi>t</mi>
        </mrow>
      </mfrac>
      <mo>=</mo>
      <mi>&thinsp;</mi>
      <mo>-</mo>
      <msub>
        <mrow>
          <mi>&lambda;</mi>
        </mrow>
        <mrow>
          <mn>1</mn>
        </mrow>
      </msub>
      <mi>N</mi>
    </mrow>
  </mrow>
</m:math>
-->
</hi></formula>, having a solution, 
<seg rend="left"><figure entity="NEfurther010052form5"></figure></seg>

<formula notation="mathml"><hi rend="suppress"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <msub>
        <mrow>
          <mi>N</mi>
        </mrow>
        <mrow>
          <mn>1</mn>
        </mrow>
      </msub>
      <msub>
        <mrow>
          <mo>)</mo>
        </mrow>
        <mrow>
          <mi>&tau;</mi>
        </mrow>
      </msub>
      <mi>&thinsp;</mi>
      <msup>
        <mrow>
          <mi>e</mi>
        </mrow>
        <mrow>
          <msub>
            <mrow>
              <mo>-</mo>
              <mi>&lambda;</mi>
            </mrow>
            <mrow>
              <mn>1</mn>
            </mrow>
          </msub>
          <mrow>
            <mo>(</mo>
            <mi>t</mi>
            <mo>-</mo>
            <mi>&tau;</mi>
            <mo>)</mo>
          </mrow>
        </mrow>
      </msup>
    </mrow>
  </mrow>
</m:math>
-->
</hi></formula>
</p>
<p>Since the contribution to the number of previous days' operation is given by the latter<lb/>
expression with time t - <hi rend="italics">&#x03C4;</hi> + 1, t - <hi rend="italics">&#x03C4;</hi> + 2, etc. inserted, a geometric series
<lb/>
<seg rend="left"><figure entity="NEfurther010052form6"></figure></seg>

<formula notation="mathml"><hi rend="suppress"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <munderover>
        <mrow>
          <mo>&sum;</mo>
        </mrow>
        <mrow>
          <mi>i</mi>
          <mi>&thinsp;</mi>
          <mo>=</mo>
          <mi>&thinsp;</mi>
          <mi>o</mi>
        </mrow>
        <mrow>
          <mi>&infty;</mi>
        </mrow>
      </munderover>
      <msub>
        <mrow>
          <mi>N</mi>
        </mrow>
        <mrow>
          <mn>1</mn>
        </mrow>
      </msub>
      <mo>)</mo>
      <mi>&thinsp;</mi>
      <mi>&thinsp;</mi>
      <msup>
        <mrow>
          <mi>e</mi>
        </mrow>
        <mrow>
          <msub>
            <mrow>
              <mo>-</mo>
              <mi>&lambda;</mi>
            </mrow>
            <mrow>
              <mn>1</mn>
            </mrow>
          </msub>
          <mrow>
            <mo>(</mo>
            <mi>t</mi>
            <mo>-</mo>
            <mi>&tau;</mi>
            <mo>+</mo>
            <mi>i</mi>
            <mo>)</mo>
          </mrow>
        </mrow>
      </msup>
    </mrow>
  </mrow>
</m:math>
-->
</hi></formula>
</p>
<pb n="32"/><p><seg><xref id="NEfurther010052j1.jpg" rend="new">
<figure entity="NEfurther010052j1"></figure></xref></seg></p>

<p>maybe written. This is summed by the relation l + x + x<hi rend="sup">2</hi> + ---- = <hi rend="sup">1</hi>/<hi rend="sub">1-x</hi>.
</p>
<p>During the period of reactor operation, an additional growth term must be added<lb/>
to this solution.
</p>
<p>The equilibrium iodine level is different from that for continuous operation<lb/>
N<hi rend="sub">1</hi> = g/&#x03BB;<hi rend="sub">1</hi> by a factor 
<seg rend="left"><figure entity="NEfurther010052form7"></figure></seg>

<formula notation="mathml"><hi rend="suppress"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <mi>B</mi>
      <mi>&thinsp;</mi>
      <mo>=</mo>
      <mi>&thinsp;</mi>
      <mfrac>
        <mrow>
          <mn>1</mn>
          <mo>-</mo>
          <msup>
            <mrow>
              <mi>e</mi>
            </mrow>
            <mrow>
              <msub>
                <mrow>
                  <mo>-</mo>
                  <mi>&lambda;</mi>
                </mrow>
                <mrow>
                  <mn>1</mn>
                </mrow>
              </msub>
              <mi>&tau;</mi>
            </mrow>
          </msup>
        </mrow>
        <mrow>
          <mn>1</mn>
          <mi>&thinsp;</mi>
          <mo>-</mo>
          <mi>&thinsp;</mi>
          <msup>
            <mrow>
              <mi>e</mi>
            </mrow>
            <mrow>
              <msub>
                <mrow>
                  <mo>-</mo>
                  <mi>&lambda;</mi>
                </mrow>
                <mrow>
                  <mn>1</mn>
                </mrow>
              </msub>
            </mrow>
          </msup>
        </mrow>
      </mfrac>
    </mrow>
  </mrow>
</m:math>
-->
</hi></formula>, with relatively small periodic <orig reg="variations">varia-<lb/>
tions</orig> reflecting the nature of the operation. The Xe accumulation per day is then<lb/>
derived from the solution of the equation
<lb/>

<seg rend="left"><figure entity="NEfurther010052form8"></figure></seg>

<formula notation="mathml"><hi rend="suppress"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <mfrac>
        <mrow>
          <msub>
            <mrow>
              <mi>d</mi>
              <mi>N</mi>
            </mrow>
            <mrow>
              <mn>2</mn>
            </mrow>
          </msub>
        </mrow>
        <mrow>
          <mi>d</mi>
          <mi>t</mi>
        </mrow>
      </mfrac>
      <mi>&thinsp;</mi>
      <mo>=</mo>
      <mi>&thinsp;</mi>
      <msub>
        <mrow>
          <mo>-</mo>
          <mi>&lambda;</mi>
        </mrow>
        <mrow>
          <mn>2</mn>
        </mrow>
      </msub>
      <msub>
        <mrow>
          <mi>N</mi>
        </mrow>
        <mrow>
          <mn>2</mn>
        </mrow>
      </msub>
      <mi>&thinsp;</mi>
      <mo>+</mo>
      <mrow>
        <msub>
          <mrow>
            <mi>&lambda;</mi>
          </mrow>
          <mrow>
            <mn>1</mn>
          </mrow>
        </msub>
        <msub>
          <mrow>
            <mi>N</mi>
          </mrow>
          <mrow>
            <mn>1</mn>
          </mrow>
        </msub>
      </mrow>
    </mrow>
  </mrow>
</m:math>
-->
</hi></formula><lb/>
where the last term is the fluctuating supply from iodine decay.
</p>
<p>For the chosen pattern of reactor operation, i.e., 6 hours on and 18 hours<lb/>
off in each 24, the equilibrium level of I<hi rend="sup">133</hi> is computed to be around 365 curies,<lb/>
and, hence, the daily Xe production is 11 curies. To reduce the 11 curies of<lb/>
Xenon activity to a value below 1 curie, a hold up of about 4 half-lives, or 21 days,<lb/>
is necessary. The system designed to accomplish the desired hold-up of the Xenon<lb/>
actually achieves reduction of the activity to a value many times lower than this.<lb/>
In this system, the gas from the recombination unit is bubbled through a water<lb/>
trap to the first of several holding tanks arranged in series. A water trap is <orig reg="located">lo-<lb/>
cated</orig> between each tank so that the gas bubbles from one tank to another through<lb/>
these traps. The delay of the gas in reaching the stack after traversing this system<lb/>
of hold-up tanks is calculated according to the analysis below.
</p>
<p>Three types of holding systems are considered: (1) a single long continuous<lb/>
tube, (2) a single large tank, (3) a sequence of small tanks.
</p>
<p>Since the effectiveness of a given holding volume can be shown to be dependent<lb/>
on the degree with which mixing is prevented, it follows that the long tube is the<lb/>
most favorable system, and the large tank is the least favorable. The analysis of<lb/>
the relative merits of the three arrangements was made on the basis of continuous<lb/>
flow; the extension to intermittent flow introduces only a correction factor.
</p>
<p><hi rend="underline">Case 1.</hi> Regardless of the dimensions of the system, the time t for a given<lb/>
sample of a fluid flowing without turbulence or friction through a vessel is given by<lb/>
V/v where V is the total volume of the vessel and v is the volume flow rate. The<lb/>
radioactive attenuation factor is thus
<lb/>
<seg rend="left"><figure entity="NEfurther010052form9"></figure></seg>

<formula notation="mathml"><hi rend="suppress"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <msup>
        <mrow>
          <mi>e</mi>
        </mrow>
        <mrow>
          <mo>-</mo>
          <mi>&lambda;</mi>
          <mi>V</mi>
          <mo>/</mo>
          <mi>v</mi>
        </mrow>
      </msup>
      <mo>=</mo>
      <mrow>
        <mo>(</mo>
        <mfrac>
          <mrow>
            <mn>1</mn>
          </mrow>
          <mrow>
            <mn>2</mn>
          </mrow>
        </mfrac>
        <mo>)</mo>
        <mfrac>
          <mrow>
            <mi>V</mi>
            <mo>/</mo>
            <mi>v</mi>
          </mrow>
          <mrow>
            <msub>
              <mrow>
                <mi>t</mi>
              </mrow>
              <mrow>
                <mi>H</mi>
              </mrow>
            </msub>
          </mrow>
        </mfrac>
      </mrow>
    </mrow>
  </mrow>
</m:math>
-->
</hi></formula>
<lb/>
where &#x03BB; is the decay constant and t<hi rend="sub">H</hi> is the half-life of the radioactive <orig reg="constituent">consti-<lb/>
tuent</orig>. This situation would most nearly be approached by a long tube.
</p>
<pb n="33"/>
<p><seg><xref id="NEfurther010052k1.jpg" rend="new">
<figure entity="NEfurther010052k1"></figure></xref></seg></p>

<p><hi rend="underline">Case 2.</hi> The rate at which molecules (radioactive or not) will be exhausted<lb/>
from the large tank is given by
<lb/>
<seg rend="left"><figure entity="NEfurther010052form10"></figure></seg>

<formula notation="mathml"><hi rend="suppress"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <mfrac>
        <mrow>
          <mi>d</mi>
          <mi>N</mi>
        </mrow>
        <mrow>
          <mi>d</mi>
          <mi>t</mi>
        </mrow>
      </mfrac>
      <mo>=</mo>
      <mi>&thinsp;</mi>
      <mo>-</mo>
      <mi>N</mi>
      <mfrac>
        <mrow>
          <mi>v</mi>
        </mrow>
        <mrow>
          <mi>V</mi>
        </mrow>
      </mfrac>
    </mrow>
  </mrow>
</m:math>
-->
</hi></formula>
</p>

<p>Letting v/V = f, the solution if the initial number introduced at time zero is N<hi rend="sub">0</hi>,<lb/>
N = N<hi rend="sub">0</hi>e<hi rend="sup">-ft</hi>. Complete mixing of the contents are assumed. The total of the<lb/>
particles that escape as radioactive over all subsequent time is given by
<lb/>

<seg rend="left"><figure entity="NEfurther010052form11"></figure></seg>
<formula notation="mathml"><hi rend="suppress"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <msub>
        <mrow>
          <mi>N</mi>
        </mrow>
        <mrow>
          <mi>r</mi>
        </mrow>
      </msub>
      <mo>=</mo>
      <mrow>
        <msubsup>
          <mo>&int;</mo>
          <mrow>
            <mn>0</mn>
          </mrow>
          <mrow>
            <mi>&infty;</mi>
          </mrow>
        </msubsup>
        <msup>
          <mrow>
            <mi>d</mi>
            <mi>N</mi>
            <mi>e</mi>
          </mrow>
          <mrow>
            <mo>-</mo>
            <mi>&lambda;</mi>
            <mi>t</mi>
          </mrow>
        </msup>
      </mrow>
      <mo>=</mo>
      <mrow>
        <msubsup>
          <mo>&int;</mo>
          <mrow>
            <mn>0</mn>
          </mrow>
          <mrow>
            <mi>&infty;</mi>
          </mrow>
        </msubsup>
        <msub>
          <mrow>
            <mi>N</mi>
          </mrow>
          <mrow>
            <mi>o</mi>
          </mrow>
        </msub>
        <mi>f</mi>
        <msup>
          <mrow>
            <mi>e</mi>
          </mrow>
          <mrow>
            <mo>-</mo>
            <mi>f</mi>
            <mi>t</mi>
            <mo>-</mo>
            <mi>&lambda;</mi>
            <mi>t</mi>
          </mrow>
        </msup>
      </mrow>
      <mi>&thinsp;</mi>
      <mi>d</mi>
      <mi>t</mi>
      <mi>&thinsp;</mi>
      <mo>=</mo>
      <mfrac>
        <mrow>
          <mi>f</mi>
        </mrow>
        <mrow>
          <mi>f</mi>
          <mo>+</mo>
          <mi>&lambda;</mi>
        </mrow>
      </mfrac>
      <msub>
        <mrow>
          <mi>N</mi>
        </mrow>
        <mrow>
          <mi>o</mi>
          <mi>&thinsp;</mi>
        </mrow>
      </msub>
      <mo>=</mo>
      <mfrac>
        <mrow>
          <mn>1</mn>
        </mrow>
        <mrow>
          <mn>1</mn>
          <mi>&thinsp;</mi>
          <mo>+</mo>
          <mi>&thinsp;</mi>
          <mi>&lambda;</mi>
          <mo>/</mo>
          <mi>f</mi>
        </mrow>
      </mfrac>
      <msub>
        <mrow>
          <mi>N</mi>
        </mrow>
        <mrow>
          <mi>o</mi>
        </mrow>
      </msub>
    </mrow>
  </mrow>
</m:math>
-->
</hi></formula>

<lb/>so that the attenuation factor is <seg rend="left"><figure entity="NEfurther010052form11a"></figure></seg>.
<formula notation="mathml"><hi rend="suppress"><!--
<m:math xmlns='http://www.w3.org/1998/Math/MathML' xmlns:m='http://www.w3.org/1998/Math/MathML' >
  <mrow>
    <mrow fontstyle='normal'>
      <mfrac>
        <mrow>
          <mn>1</mn>
        </mrow>
        <mrow>
          <mn>1</mn>
          <mo>+</mo>
          <mfrac>
            <mrow>
              <mi>&lambda;</mi>
              <mi>V</mi>
            </mrow>
            <mrow>
              <mi>v</mi>
            </mrow>
          </mfrac>
        </mrow>
      </mfrac>
    </mrow>
  </mrow>
</m:math>
--></hi></formula></p>
<p>
<hi rend="underline">Case 3</hi>. If the volume V is made up of n tanks of volume V/n, the above form<lb/>
for the attenuation factor may be applied successively, giving the result
</p>
<p><table>
<row>
<cell><seg rend="left"><figure entity="NEfurther010052form12"></figure></seg>
<formula notation="mathml"><hi rend="suppress"><!--
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  <mrow>
    <mrow fontstyle='normal'>
      <msup>
        <mrow>
          <mrow>
            <mo>(</mo>
            <mfrac>
              <mrow>