REACTORS
e g * D
I0 ISOT 0P E S
RADIATION
I
W. R. TOMLINSON, Jr. The Johns Hopkins University, Operations Research Office, Bethesda, Md.
-
The Chemical Industry A Nuclear Future? Part 111. Nuclear Engineering With reactors we are familiar-nuclear reactors, another matter. HOW do you ride this new horse-what kind of saddle? Will he bite or kick?
IN
PART11, the critical reactor core was studied and equations were described for determining the critical radius and critical mass of fuel. I t is instructive to consider the core from a somewhat different point of view.-still concerned mainly with criticality. 4 s you remember, constancy in power level meant a constant number of fissions and constant number of neutrons of a given energy level; both from a time standpoint. Further, this signified that a neutron which caused a fission led, via this process, to another which also caused fission. Better. o n a statistical basis, x neutrons causing fission lead to x more which do the same. Thus, from one fission generation to the next the same number of fissioning neutrons are involved, and because the numbers of neutrons in each energy level interval were also fixed, the same total numbers of neutrons are involved from one generation to the next. This being the case it is possible to define a useful quantity called the effective multiplication factor, keff, relating the fission neutrons produced in one generation with those consumed in the next by all processes-i.e.? fission and capture (absorption) and losses or leakage. If k,ff is equal to 1, we have a chain G f successive generations of events, which is invariant, or a stationary and self-sustaining chain reaction. If on the other hand, kerf is less than 1, the chain
is convergent and not self-sustaining, and applies to a n assembly designated as subcritical; while if this quantity is more than one, the chain is divergent and the system is said to be supercritical. If were applied to a core of infinite size, but of the same make up, as the losses involved for a finite core disappear. the multiplication factor k (or k,) would increase as a result. Thus the ratio keff;k = P defines the so-called nonleakage probability for the finite core and P is a measure of the probability that neutrons will not leak out of the finite core. What has been done, of course, is equivalent to &if
=
kP
(1)
where P is always less than unity and applies to the system represented by keff. What determines k? As there are no losses due to leakage in the infinite core, if all neutrons which were absorbed led to fission, k would be equal to the average neutron yield per fission, v. However, even in the fuel itself, all absorptions do not lead to fission, the number 7, which defines k will be reduced by a t least the factor (neutrons causing fission)/(neutrons absorbed by fuel), or, in our cross section terminology 2,/3fuel.As other materials will also absorb neutrons, another factor must also be included (neutrons absorbed by fuel)/(total neutrons absorbed), or, Z:iuel lZa. T h e first factor is usually des-
ignated, 7, and is the neutron yield per neutron absorbed by the fuel. T h e second factor is denoted b y f , and called the thermal utilization. We have then k = tlf
(2)
and kerr
= VfP
(3)
In the case of thermal reactors, as it is assumed that the neutrons are thermalized before they cause fission-whereas, in fact, some fissions are actually caused by fast neutrons-and in a thermal reactor the uranium used is low in U235 content, and high in U23bcontent, a factor E is needed to account for these fast fissions which are predominantly in the UZ3*due to its relatively high concentration. Equation 3 then becomes kerf =
~tlfP
(4)
often referred to as the four factor formula. I t is rather convenient for rough analysis of thermal cores. .4s k is the number of neutrons produced in each generation of fissions per neutron absorbed and only one of these is required to maintain the chain, k - 1 is a measure of the relative neutron leakage in a finite core. T h e extent of leakage should depend on two things : the dimensions of the reactor, for a spherical reactor the radius, R; and the average distance a neutron travels from birth to absorption, M , known as the VOL. 51, NO. 12
0
DECEMBER 1959
1435
migration length. One might expect that k - 1 is proportional to some function of M / R . Remembering Equation 34 from Part I1
R2 = x 2 ( L 2
+
-
T ) / ( v ~
1)
(5)
we can rearrange to get
I n 6, v 2 , / Z a is the same thing as k = v ( 2 ~ / ~ f ~ ~ , ) ( ~We f ~ have ~ ~ / there~ ~ ) .
fore the result that k - 1 is proportional , M 2 = La f r by definito ( M 2 / R 2 ) as tion, and is called the migration area. You will remember that E did not appear in Equation 34 as it was ignored. We took care of minor variations like this by making the equation fit the experimental facts by appropriate choice of neutron energy. You will also recall that R was not the actual critical radius, R,, but R, plus a small extrapolation distance from the surface of the core to a point of zero flux. Also, this extrapolated point of zero flux has no actual physical meaning but is merely a device for determining the radius. If the flux actually behaved this way, we would have no shielding problem; however, the flux falls off much less rapidly, and we do have a problem. Returning again to k e f f , while it is possible to have a self-sustaining chain reaction under these conditions-as the power at which the reactor operates is proportional to the neutral density and thus to the number of fissions per second say-we have to change the value of kerf to operate the reactor. Thus, to raise the power, the control rods are removed somewhat to raise k,ff above 1 , and then when the desired power level is reached, readjusted to bring k,ff to the value 1 again. T o reduce the power level or to shut the reactor off, the control rods are inserted further to bring kerf below unity and readjusted a t a lower power level or zero power. The power output of a reactor is not directly related to its size; power is proportional to the neutron density and thus to the number of fissions taking place per second. The relationship between power and size arises primarily from other than the basic physics considerations. For instance, it may be desired to produce a high power, but to do this a cooling system must be incorporated in the core to extract the heat a t the same rate at which it is generated by fission; the higher the power level, the higher the required rate of heat removal and the bulkier the coolant loop, for a given coolant system design. As power is produced, reactor products build up. These absorb neutrons which would otherwise be absorbed by the fuel. Naturally the longer it is desired that the reactor produce power at a given level, the larger the core must be to offset
1436
the effects of these accumulating poisons. I n simple terms, we use a larger core which, however, can only be criticalno explosions are desired-and thus must contain artificially added poisons (the control rods) which can be removed as the poisons build up. Xenon, for instance is a fission product and is very important in the operation of thermal cores as it has a very high cross section for absorption of thermal neutrons. How fast does the power level of a reactor change when the multiplication factor is varied from the equilibrium value: 1, for the steady state. Returning to k e f f , the effective multiplication factor, it is clear that if the neutron density is n at the end of a generation at the end of the next generation it will be nk,rf. The increase in this time, t o say. is naturally, nk,ff - nor n(k,ff - 1). The rate of increase per unit time is then this quantity divided by the time period of the increase, t o . T h e rate of increase is dn/dt. Stated mathematically this is d n l d t = n(k,if - l ) / t o = nkex/to
(7)
where k,, is defined as k e f { - 1, or the excess multiplication factor. The quantity k,, is thus a measure of the departure from equilibrium-i.e., from criticality. The simple integration of Equation 7 gives n =
determining, and, of course, t is in seconds. This can be approached by dividing k,, = kerf - 1 into two parts. If b is the fraction of neutrons which are prompt then k,, can be written k e f f (1 - b ) and k , f f b , where the first quantity applies to the prompt neutrons the latter to the delayed ones. If kerf (1 b ) is exactly 1, the reactor will be critical on prompt neutrons and strangely is referred to as prompt critical. For this case to is 0.001 and Equation 10 becomes n = n,e1000kext
and the rate of increase suddenly becomes extremely high. If then kerf (1 - 6) becomes any greater, the reactor becomes uncontrollable. This condition must, of course, be avoided in friendly territory. The reactivity of a reactor, p , is defined as P
= k., kefr
(kerf - l ) / k e i r
When kef!is near 1, k,, is small and p is nearly the same as kex. From what has just been discussed above, it is clear what the significance of reactivity is, at least in a general sort of way. Due to the special significance of the prompt critical condition a very interesting unit of reactivity has been defined: the dollar. Reactivity in dollars is defined as Reactivity = ke,jb, S
Tvhere n, is the initial neutron density (at t = 0) and n is that after time, t . The quantity t , / k , , is referred to as the reactor period and denoted by T , so that n = noellT
(9)
Equation 9 applies to either k,, positive or negative, and so provides information on the rapidity of decrease as well as increase of power level. T h e generation time, t o , is very important to reactor control. This is because the neutrons released in fission are released over a period o€ time. Over 99y0 of them are released within about 10-14 seconds of the instant of fission, called prompt neutrons, while the remainder are released in five major groups over a period of 0.6 to 80 seconds after fission, the delayed neutrons. The effective generation time is considerably increased by the delayed neutrons. The average elapsed time between release of a fission neutron and its capture is about 0.001second. The mean delay time for the delayed neutrons is about 0.1 second. Thus the average effective generation time is 0.001 0.1 or about 0.1 second. The value of to to be used in Equation 9 is about 0.1 and
+
(10)
Equation 10 then applies in the case when the delayed neutrons are rate
INDUSTRIAL AND ENGINEERING CHEMISTRY
(12)
(8)
n,etkex/to
n = n,elOkezl
(11)
(13)
When prompt critical, a reactor has a reactivity of 1 dollar. Thus a change in reactivity of 1 dollar will take a reactor from steady state operation, with k,, = 0 to prompt critical. Reactivity is also described in terms of the inverse hour, or “inhour” unit and designated Ih. T h e unit is defined as the reactivity which will make the reactor period (stable) equal to 1 hour or 3600 seconds (see Equation 9). As was mentioned earlier, the size of the reactor is not directly related to the desired power output by way of the physics of the fission process; rather other considerations determine this. For instance, it is clear that an 8.5-cm. radius sphere of L?’35 [actually so called oralloy = 93.57, L-235- 6.570 UZ3*,or relating to Oak Ridge, abbreviated Oy(93.5) J must be made somewhat larger to liberate heat at a practical rate, as cooling channels Lvould have to be provided. These actually reduce the average density of the fuel somewhat and in addition introduce an additional source of neutron loss by absorption. Thus the usable core must be somewhat bigger than this abstract model and contain somewhat more fuel. This abstraction has, however, becn built by the AEC and operated in bursts liberating about 100 watt-hour of energy in about 0.1 second-this critical assembly is named Godiva. Godiva was damaged
NUCLEAR ENGINEERING
Rising from the cluster of fuel rod tips are the control rods, x-shaped shafts which control the rate of nuclear reaction
not long ago by thermal shock resulting from the failure of a reflector to move freely which led to an abnormally large power pulse.
What Kind of Reactor? As mentioned above, a sphere of oralloy will produce power, but the level that could be maintained would be limited by heat conduction to a rate which would leabe the hot center in the solid state. T h e next step u p in improving the heat transfer picture would be to pass cooling coils through the sphere; the limiting factors here would be the number of channels, their size, the coolant selected and the ease with which it can be forced through the coils, and the thermal stresses set up in the core. Uranium melts a t 1133' C. (2072' F.) and is generally kept below the alphabeta transition temperature 662' C . (1224' F.). I n any case, depending on the design, there is a limit to the heat transfer capability that can be attained using cooling coils. The next step then is to shape the fuel (usually referred to as meat) in the form of pins and cover them with a cladding for protection against the coolant and to retain the fission products in the core. T h e pins are then set up in a parallel array, and the coolant is passed through the array. This design minimizes the distance over which heat conduction is controlling and thereby eases the thermal stress picture and makes it easier to avoid high temperatures in the fuel. This is, of course. a fast reactor. Without the cooling coils, the O y (93.5) sphere is about 8.5 cm. in radius and contains nearly 50 kg. of U235(8: 77). If delta plutonium were used (density 15.8), the critical bare sphere would weigh a little more than 16 kg.; using a IO-cm.
thick beryllium reflector, the plutonium weight could be cut to about 6 kg. (70). LVe could then build on fast cores such as these, after they had been engineered to get the energy out; follow u p with high density shielding, which would be quite expensive; and get a small reactor for cases where space limitations are important. If the reactor were to be used to manufacture isotopes however, there are two things wrong: T h e flux would be faster than optimum to get high probability of conversion, and we have limited the space in which we could put material for irradiation. Further, if it were desired to collect the fission products, it would be necessary to wait until the core was replaced and to extract them from the old core during the reprocessing operation. T o make the extraction of fission products easier, one could use a liquid core and circulate the fuel itself to remove the heat. For instance, plutonium melts a t 665' C. (2077' F.) and has a density of 16.5 a t the melting point (72). Plutonium, however, because of its toxicity is very dangerous. Liranium itself could be the basis for another high temperature system, for instance uranium-uranium dioxide but such systems have not been worked out from the corrosion and containment point of view. Bismuth with a melting point of 271' C. (520' F.) and lead a t 327' C. (621' F.) are interesting possibilities for liquid fuel bases; remember the attractive nature of the polonium \vhich is derived from bismuth by the addition of a neutron. Such systems have been studied; a study of small liquid metal fuel systems is given by Chernick (4, and Benedict and Pigford ( I ) examined the problem of continuous processing of fission products in a reactor. O n the other hand well moderated systems, such as those involving aqueous solutions of fuel have the very attractive feature of requiring very little fuel to achieve criticality. The minimum critical masses in water are 800 grams of P6, 588 grams of U233 and 509 grams Pu239( 3 ) . By using well moderated reactors-thermal reactorsit is simple to adjust to larger size and to provide the desired slow, thermal flux. Split cores might possess some virtue from this standpoint ( 9 ) and liquid metaluranium dioxide slurry reactors (5) deserve some study. For many operations where economics are of import and where there is no great need to conserve on space, the thermal type of reactor offers considerable advantage. Here one can use ordinary materials of construction like steel and concrete, and use sufficient quantities to gain the necessary physical strength and protection against radiation
which is required. A small fuel operating inventory is involved and moderators like graphite and hydrogenous materials are appropriate. I n addition, one can use a pressurized system and take advantage of the well known field of steam technology. Let us take a short look at the various reactor types and the abbreviated notation by which they are often referred to in the literature ( 2 ) . Reactors can be classified by application or by design. Classification by application involves such uses as central station power, small package units for remote inaccessible locations, process heat, central heat, isotope or fuel production (the latter are breeders), test, research, propulsion, irradiation, and the like. Classification by neutron energy would be thermal (slow), intermediate, and fast. T o the physicist, everything that is not slow or fast is intermediate. For instance, their sq. cross section unit is the barn, cm.-and to the nucleus this is as big as a barn-BNL 325, their neutron cross section manual, is adorned on the cover with a barn and silo. Anyway, slow neutrons run up to a few hundred electron volts, intermediate ones from here to 0.5 m.e.v., and fast ones above this point. From a design standpoint reactors are classified in accordance with neutron energy, geometry, fuel cycle (fertile material, fuel, and fuel regeneration), coolant, moderator (if present), structural material, and method of control. The geometry is referred to as homogeneous or heterogeneous ; the former is where the fuel, moderator (if present) and coolant are mixed intimately, often in liquid form, while the latter refers to component separation, usually in definite geometric arrangement. The system for designating reactors does not state the neutron energy or the geometry which is usually evident from the other components named. T h e most important design factors are usually the coolant, moderator and structural material, thus the system names first the coolant, then the moderator and then the structural material; these may be followed by the atomic weights of the fuel with enrichment in parentheses and the fertile material (material like U23s) capable of forming by neutron absorption more fuel-e.g., Pu239. If the coolant also serves as moderator, or if there is no moderator, this term is omitted. If the fuel serves as its own coolant, its state-e.g., pressurized water solution is substituted for coolant. If different structural materials are used, the fuel element cladding (if any) is named first. The control method is not stated-to date no designs have been eliminated by inability to devise control methods. VOL. 51, NO. 12
DECEMBER 1959
1437
-72'
Schematic shows relative position of essentials to each other
4 Here is a typical exchanger tube which carries coolant through the core
Reactor Control There are many different ways in which the value of the effective multiplication factor, k e f f , may be varied to permit operation of the reactor. The addition of fuel or moderator, or their removal, is a particularly easy way to modify the reactivity of homogeneous or slurry fuel reactors. As a last ditch safety measure the reactor may be shut down by dumping-of course dumping the charge into another container of the same shape and size would accomplish little. One must change the shape of the charge radically to increase neutron losses and thus obtain a subcritical mass or divide it into two or more portions. This same change of shape just mentioned can be applied to the core as a method of control. The reactor structure can be divided up into parts which can be moved relative to each other, or reflector elements incorporated in the design which when moved will alter the neutron density in the core to achieve control. The core can be so designed that an elevation in temperature will increase the volume which automatically reduces reactivity; this type approach can be used to improve the control exerted by other methods and, in addition the coolant flow can be modified to enhance the effect. The insertion of solid rods which have high absorption cross sections for neutrons, however, seems to be the most generally used method to achieve control. Xenon poisoning is an important factor in the operation of a thermal reactor. Xenon is formed as the reactor operates, but builds up to a steady concentration gradually at constant power. As some of the xenon is destroyed by its own radioactive decay, and also by interaction with neutrons, when the reactor is shut down the latter removal mechanism disappears, and the concentration of xenon can build u p to several times the steady state operating level-the
1438
so-called override. This build up must be allowed for in terms of sufficient excess reactivity to permit reactor start up after a shut down.
Heat Transfer Considerations Although only about 5% of the total heat produced is liberated in the reflector and the shield, including the pressure vessel-if there is one-the cooling of these components may be a serious problem, especially for operation at high power levels. The calculation of the effect is quite difficult as it requires a fairly detailed knowledge of the gamma-ray spectrum as a function of the gamma-ray energies and an estimate of the neutron leakage from the core. Gammas are produced not only in the fissions but also by the radioactive decay of the fission products and by capture of neutrons in structural materials. As would be expected from the exponential nature of the absorption processes themselves, the heat generation in general falls off exponentially with distance from the core, so cooling is more necessary in the inner than in the outer portions of the shield. It is most important to know something about the amount of energy liberated in the core and to consider the heat that must be removed to permit operation of the reactor for any purpose. For instance, while the interest in a particular evaluation may be in the rate of production of radioisotopes, it must be realized that along with the desired materials comes so much heat that it would be utterly ridiculous to throw it away. Here we are working the energy mass relation the wrong way, or in other words, just as the consumption of 1 pound of fissionable material releases 3.6 X 101o B.t.u., so a similar amount of energy will be liberated in the production of 1 pound of fission
INDUSTRIAL AND ENGINEERING CHEMISTRY
products. Toirradiate bismuthwith neutrons to produce polonium in a reactor will involve the production of somewhat more than this amount of energy as all the neutrons produced will not be applicable to the manufacture, nor will all of them react. Thus, except for the tracer amount uses, the desire to manufacture materials like radioisotopes in a reactor must contemplate a power industry as well. A large chemical complex might find it very attractive to satisfy its energy and power requirements in the nuclear way and develop a very attractive radioactivity cperation as part of its output. The power industry considers the radioactive output of its contemplated nuclear plants as a headache; here is a good place for us to fit in. Let us not allow conditions to force the power company into this business by our default. To return to the heat transfer business, a reactor generates about 191 m.e.v. per fission plus an amount due to various parasitic capture processes which raises this to a total near 200 m.e.v. per fission. The rate of heat liberation from this is in the neighborhood 180 m.e.v. A good source term for heat generation, Q, is then 180 m.e.v. per fission. Heat transfer coefficients, h, for this usage are: For gas or water h
=
5k 0.023),(Dvp
0.8
(y) cPp
0.4
(14)
For liquid metals h = k[ 7
+ 0.025
(9)0'8 (15)
where h = heat transfer coefficient of the coolant, B.t.u./(hr. sq. ft.-" F.) p = coolant density, lb./cu. ft. u = coolant velocity, ft./hr. p = coolant viscosity, lb./(hr. ft.) c p = coolant specific heat, B.t.u./ (1b.-" F.) k = coolant thermal conductivity, B.t.u./(hr. sq. ft.-" F./ft.) D = coolant channel diameter, ft.
As the most common type of reactor design involves regularly distributed fuel elements cooled by parallel channels of ccolant, let us imagine a cylindrical coolant channel traversing the length of a core. Associated with this coolant channel will be a certain volume of fuel -we will design it simply so that if there are 10 channels, 10% of the fuel will be associated with each channel for the purpose of heat removal. At a given point along the channel the fluid temperature will be defined as follows: mean mixed fluid temperature surface temperature of the coolant channel-i.e., fuel-coolant interface to = tf a t the end of the channel-Le., the entrance end
t, = ts =
NUC LE AR E N G I N E ERIN 8 and
I n addition: = fuel cross section (perpendicular
A
t o the channel) from which
L = AL = Q
=
Qo = Qao
=
Ah = A,
=
w
=
the particular coolant channel removes heat length of the coolant channel volume of fuel from which the coolant channel removes heat = V a local average heat source per unit volume applies to its maximum value at the center of the channel average value of Q associated with the channel heat transfer area minus the area of the inner surface of the coolant channel cross sectional area of the coolant channel mass rate of flow of the coolant = ~ p A j
I n the steady state the heat generated by the fuel associated with the coolant channel is, of course, QBYV. This turns out to be QavV = 2 Q 0 V / ~
Heat removed wcpAt,, where
by
the
= (t,)L
(16)
coolant
- to
is (17)
and (t,)L refers to the exit end of the channel. From Equation 16 and 17, Atc is At, = 2 Q 0 1 ~ * / ( ~ t e c=p )QavV/(wcp) (18)
T h e factor T 2 = Qo, Q a Y = P,,x/J‘sv (where P is power density) is for a flat radial flux. In practice this ratio can be related to the reactor geometry as follows: Core Geometry Sphexe, bare Rectangular parallelepiped, bare Cylinder, bare Cylinder, flat radial flux (reflected) Swimming pool type (water reflected)
Pln,xlPav 3.29 3.87 3.64 1.57 = 7r/2 2.6
A reflector flattens out the radial flux of a cylinder, as indicated in the table. The quantities t, and to are related as f0llOW~S: 1 - cos
7)
=z
TX -, L
+
amax=
where all these max’s refer to the point where the surface temperature, f,, is a maximum. Then
+
&Y (1 - cos TWCP
y)
(22)
need anything else. T o make tht. bargain more binding, as Gordon Dean states (7) Glasstone is an outstanding scientist and author in chemistry and related fields-as a matter of fact, in the writer’s humble opinion, Glasstone has. in the field of scientific writing, no peer. Nuclear Safety
Of course, as you remember from trig: sec2amhX= 1
+ tan2
amax
(24)
How do we use these equations? First set the quantities (to)man: t o and u (thus w). In other words you can set the maximum surface temperature of the cladding for some reason, or to keep the temperature in the fuel below some maximum value (a formula for this for the simple case of a fuel pin will be given shortly), and you can pick a reasonable coolant inlet temperature and rate of flow. The QoV is obtained from Equation 23, using 21 to get tan a!,,,? and then sec amexfrom 24. Then QoV provides QevV from 16, using the proper power density factor as a divisor, if the geometry is not compatible with a/2. At, comes from Qav, the heat removed by the coolant in the steady state via Equation 18. To get the number of channels required for a given core, one divides the power output one wants by QavVj which then sets the reactor size for these chosen conditions. We will probably want to set a maximum temperature in the fuel and/or a maximum temperature gradient. T o get at this, we must work back from (tE)mBX> or t, or alternatively set the fuel temperature and derive t, from it. Actually t , and t, are both involved. Image a fuel pin in cylindrical shape, with radius a, and add a thin layer of cladding so the total radius is 6. Then if t , is the temperature at the center of the pin’s cross section, t , the temperature a t the fuel cladding interface, tr. the temperature at the cladding outer surface-Le., t,-k, and k , the thermal conductivities of the fuel and cladding, respectively, then t,
(19)
where x refers to the distance from the channel entrance to the point in question. Putting x = L gives AtC--i.e., Equation 18. T o determine (t,),,,, define 01
t,, = to
Q V . TX -C sin hAh L
- t,
= Qa2/(4k,>
This aspect of the subject can scarcely be overlooked by anyone regarding the field with more than a passing interest. It will not be necessary to discuss the subject of safety at any length. however, as there is plenty of literature availablethere is a particularly interesting introduction to the subject ( 7 4 ) and a good bibliographv (73). It might be appropriate, however, to quote from the foreword to the former to indicate its contents and those to whom it will be of interest. “The recommendations in the Guide are intentionally conservative, and may, therefore, be applied directly and safely provided the appropriate restricting conditions are met. I n this usage, it is believed that the Guide will be of value to organizations whose activities with fissionable materials are not extensive. The Guide is also expected to be a point of departure for members of established nuclear safety teams, experienced in the field, who can judiciously extend the specifications to their particular problems. The references in this report will be of especial value to them since reference to the experimental results will aid in guided extrapolations.”
(25)
and t, - t/ = Q a 2 / ( 4 k U )-k 0.5 Qa*(k,-‘ In b / a -k b-lh-’)
(26)
As before, t i is the coolant mean mixed temperature and h its heat transfer coefficient. The surface temperature of the pin, t. or tb, comes from Equation 22. We are going to stop here, the interested reader should follow Glasstone (6) further; although his book is beamed mainly a i thermal reactors, he covers intermediate and fast reactors in a t least an introductory fashion-as a matter of fact his coverage of the entire field is so good that for our purposes, you hardly
Some idea of the extent of protective shielding can b e had from the arrangement shown here. The reactor sets at the bottom of the tank which i s filled with water. The thick concrete casing forms the outer protective ring VOL. 51,
NO. 12
DECEMBER 1959
1439
Further Interesting and Useful References Sheet No.
Month/Year Month/Year
Data tabulations or graphs or nomograms, all termed Data Sheets, published in AVucleonics 1 March 1955 X-ray critical absorption and emission energies in k.e.v. 2 April 1955 Nomogram for radioisotope buildup and decay May 1955 3 Gamma rays from thermal neutron capture 4 June 1955 Beta emitters by energy and half life July 1955 5 Tenth-value thickness for gammaray absorption 6 Aug. 1955 Dosimetry with commercial film 7
Oct. 1955
8
Xov. 1955
9
Dec. 1955
Simple spot tests for aluminum contaminants Fission-neutron reaction cross sections Weight change in cylindrical shields
10
Jan. 1956
Gamma-ray attenuation
11
Feb. 1956
Slow-neutron capture radioisotopes arranged by half life 12 March 1956 Stress-strain curves for reactorirradiated plastics 13 June 1956 Locating Compton edges and backscatter peaks in scintillation spectra 14 July 1956 Gamma-ray scattering from thin scatterers Aug. 1956 Nomogram for radioactivity in15 duced in irradiation Nov. 1956 16 Gamma-ray streaming through an annulus Dec. 1956 17 Gamma dose rates in cylindrical sources Jan. 1957 18 Gamma attenuation with build-uD in lead and iron April 1957 Radiation from neutron activated 19 slabs and cylinders 20 July 1957 Gamma-ray streaming through a duct 21 Gamma detection efficiency o Oct. 1957 organic phosphors 22 Feb. 1958 Radionuclides arranged by gamma-ray energy 23 Thermal neutron data for the March 1958 elements 24 April 1958 Fission product yields from U, Th, and Pu June 1958 Attenuation of gamma-rays from 25 a n infinite plane Gamma-ray attenuation with 26 July 58 build-up in water a Volume and page number.
literature Cited (1) Benedict, M., Pigford, T. H., “Nuclear Chemical Engineering,” pp. 49-58, McGraw-Hill, New York, 1957. (2) Bonilla, C. F. (ed.), “Nuclear Engineering,” Chap. 14, McGraw-Hill, New York, 1957. (3) Charpie, R. A., Horowitz, J., others (eds.), “Progress in Nuclear PhysicsSeries 1: Physics and Mathematics,” McGraw-Hill, New York, 1956. (4) Chernick, J., ix’uclear Sci. and Eng. 1, 135-55 (1956).
1440
Subject
Subject Articles of general interest in Nucleonics Properties of beryllium (compreMay 1953 hensive) Compressive (and tensile) properJune 1954 ties of uranium Radiation effects on reactor maSept. 1954 terials Producing radioisotopes in very Jan. 1955 low power reactors Nomogram for estimating nuclear Feb. 1955 reaction energies Energy spectrum of gammas from May 1955 gross fission products Data on fissionable elements Sept. 1955 Graphical method speeds producOct. 1955 tion scheduling of radioisotopes Fission product build-up in longDec. 1955 burning thermal reactors Fast breeder power reactors; also April 1957 neutron spectra of fast and thermal reactors Resolving complex decay curves June 1957 Calculation of gamma-ray heating Oct. 1957 in reactor structures Nuclear power costs Jan. 1958 Fast breeder power reactors: where March 1958 does U S . program stand (reactor constants giyen) Fuel symposium (general-availAug. 1958 ability) Articles in h’uclear Science and Engineering Processing of power reactor fuels 1, 409-19‘ Heat transfer and economics us. 2, 14-23a core size and geometry Fission product decay and energy 3, 726-45a release Articles in Xuclear Engineerinp. (British) Properties of graphite June 1956 Uranium and its alloys Sept. 1957 Thorium-properties and characOct. 1957 teristics Plutonium and its alloys Nov. 1957 Magnesium and its alloys Feb. 1958 Zirconium and its alloys March 1958 Niobium and its alloys May 1958 Molybdenum and tungsten June 1958 Aluminum and its alloys July 1958 Graphite: its properties and beNov. 1958 havior, Part I Graphite: its properties and beDec. 1958 havior, Part 2 Boron and boron-containing maJan. 1959 tprinlq -. . . . . .
Feb. 1959
(5) Davidson, J. K., Robb, W. L., Salmon, 0. N., Sampson, J. B., Ibzd.: 5, 227-36 (1959). (6) Glasstone, S., “Principles of Nuclear Reactor Engineering,” Van Nostrand. New York, 1955. (7) Glasstone, S., “Sourcebook on Atomic Energy,” 1st ed., Van Nostrand, New York, 1950. Foreword. (8) Groves, G. A., Paxton, H. C., S u cleonics 15, 90-2 (1957). (9) Jablonski? F. E., Carter, R. S., ,Vucleur Sci. and Eng. 5, 257-63 (1959).
INDUSTRIAL AND ENGINEERING CHEMISTRY
Liquid metals (data)
(10) Kloverstrom, F. A , , U. S. !tomic Energy Comm., UCRL-4957, Criticality Studies,” TID-4500, September 1957. (11) Paxton, H. C., A-ucleonics 13, 48-50 (1955). (12) Reactor Handbook, U. S. Atomic Energy Comm., Vol. 3, Sect. 1, p. 237, AECD-3647, March 1955. (13) Smith, R. J., “Reactor Safety,” TID3073, May 1958. A bibliography. (14) U. S. Dept. Commerce, Washington 25, D. C., OTS, TID-7016, 1956.
