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Examples for Pressure Drop Calculations in Parallel Flow Helium Cooling: Pressure drop calculations are shown for He cooled power plants ranging from 400,000 kw to 30,000 kw.
Interaction of Be with Fission Neutrons: To determine whether or not the (n,2n) reaction in Be would produce a net increase in fission neutrons in a power plant, the distribution of In resonance neutrons slowed down from fission energies in a graphite block was measured with and without a 2" of Be in front of a U3O8 slab undergoing fission. The thermal neutrons producing the fissions were obtained by slowing down neutrons from a cyclotron source. The observed distribution without Be was well represented by a Gaussian source range 36 cm. (corresponding to an initial fission energy of 3 MeV) and a similar sink of range 7.8 cm. The total In resonance intensity with Be was 5% less than without Be. On the assumption that the effect of the Be is entirely due to its different mean free path and moderating power, the In distribution with Be was calculated. Since the m.f.p. as a function of energy is not known for Be, two separate calculations were made using the highest (2.9 cm.) and the lowest (1.80 cm.) possible values for the effective Be m.f.p. Both calculated curves were found to be higher than the observed Be distribution, indicating that at least 10% of the fission neutrons are removed by the Be. Since there are uncertainties in the values of the constants used, the present conclusions are not entirely unambiguous. Improvement in the experimental techniques to remove these uncertainties are suggested.
Chain Reaction of Pure Fissionable Materials in Solution: The critical mass of 94-239 and the corresponding critical dimensions of homogeneous mixtures of 94-239 with various moderating media been calculated as a function of the concentration of 94. A simple transformation makes the figures applicated to92-235. the results are in essential agreement with the preliminary estimated made independently by Oppenheimer and Serber. The problem of the stability of a chain reaction in solution and questions of protection are discussed.
Poisoning and Production in a Power Plant: The yield of 49, the efficiency of production of 49, and poisoning in a power plant are discussed. Only the crudest of estimates of the poisoning are possible: these indicated that production will probably not be hampered by poisoning. In this case the yield of 49 could be as high as 3 kg/ton but only about 2 kg/ton is compatible with a fairly high efficiency. In the case that production is stopped by poisoning, smaller yields, proportional to the tolerable loss in k, are obtained. In this case the yield will be improved by a factor of 2 or 3 if only the most poisoned parts are extracted and replaced by new uranium.
Low-Density UO2 Pile: The multiplication factor and minimum pile size for a multiplying pile using UO2 powder of density 1 have been computed. It appears that a k of 1.0177 is possible for a volume ration of V/V001=3.33.
Effective Temperature of Neutrons in a Lattice: The average energies of neutrons emitted from a graphite column at 22 degrees C were compared by measurement of the cross section of boron for neutrons which are stopped by cadmium. At a distance from the neutron source great enough to insure that the neutrons were in thermal equilibrium the average energies of the emerging neutrons were found to be proportional to the temperature within the limits of the experimental error. A measurement made with boron absorbers which had been thus standardized in the graphite column indicated neutrons emerging from the chain reacting pile to have an average temperature approximate 60 +- 50 degrees above that of thermal neutrons emerging from the graphite column at 22 degrees C. Such a measurement made inside the chain reacting pile indicated the average temperature of neutrons therein to be about 65 degrees +- 15 degrees above the average temperature of neutrons in the graphite column.
Radioactivity of the Cooling Water: The most important source of radioactivity at the exit manifold of the pile will be due to O19, formed by neutron absorption of O18. A recent measurement of Fermi and Weil permits to estimate that it will be safe to stay about 80 minutes daily close to the exit manifolds without any shield. Estimates are given for the radioactivities from other sources -- both in the neighborhood and farther away from the pile.
Temperature Coefficient of the Reproduction Factor for Different Lattice Arrangements: The temperature coefficient is calculated for various lattice arrangements, taking into account the variation of [formula], suggested by Fermi. Four contributions are included: leakage, levelling of the dip in thermal neutron density in the lump, resonance absorption, and hardening of the neutrons as they penetrate a metal lump. The departure of neutron temperature from lattice temperature decreases the total coefficient. Values are given for 3 typical piles; in general, the larger the uranium elements, the less stable the pile. A rod lattice tends to be more stable. A pile with metal lumps over 50 lbs. will be unstable.
Effect of Temperature on the Resonance Absorption of Neutrons by Uranium: The resonance absorption of uranium for neutrons has been investigated between 20 degree C and 1000 degree C. Experiments were caried out on both UO2, density 4.63, and metal. The resonance activity was measured with respect to that of an iodine monitor at several different temperatures and the ratio of activity at temperature T to that at 20 degree C was determined. The increase in activity is 0.9 per cent per 100 degree C for the oxide and 1.1 percent per 100 degree C for the metal. The period of U239 was found to be 23.54 +- 0.05 min.
The Effect of Fast Fission on k: The importance of fast neutron fission (i.e., fission caused by neutrons before being slowed down) was recognized by Szilard, and calculations similar to the present one have already been carried out by him, Feld, Ashkin, Wheeler, Wigner and others. The purpose of the present paper is to give a general formula for the contribution of fast fission to the multiplication constant, which will include all the cases already considered and will be applicable to more complicated geometries than those considered by the previous writers.
On the Multiplication Constant of Homogeneous Mixtures of U with Various Moderators: The following represents a summary of calculations on the multiplication constant of homogeneous mixtures of uranium and different moderators. These calculations were made possible by Fermi's determination of the age of neutrons and by the extrapolation to higher scattering cross-sections of the resonance absorption of uranium as measured by C. Creutz. According to Fermi, the former quantity is 120 sq. cm. The latter is given in the two attached graphs. The first (Fig.1) of these goes as high as a scattering cross-section of 70 x 10-24 cm.2 per uranium atom, and its highest point is taken from a measurement of Cruetz's in which a mixture of U3O8 and graphite was used.
The Contamination of Cooling Water by a P-9 Plant: The following sources of contamination in cooling water of the P-9 plant are considered: (1) Fission recoils, (2) Corrosion of metal, (3) Recoil from aluminum, (4) Induced activity in the water. It is found that for a P-9 plant of 3.5 x 10(4) KW contamination of the river at "X" should not exceed the .1 r criterion unless coating failure occurs. Tables of the amount of coating failure permissible are given as a function of holdup time.
The Resonance Absorption Spectrum of Uranium: A model for the capture spectrum of uranium is introduced in which levels occur at 7, 30, 30+D, 30+2D, ..., ev. Gamma ray and neutron widths are derived from the experimental data for values of D between 10 and 25 ev. The constants of the 7 volt level prove to be independent of D. Extrapolation, using the one level formula, gives a capture cross section at (1/40) ev of 4.9 x 10(24) cm2; this number is, however, quite sensitive to the value taken for the resonance activation. Both neutron and gamma ray widths for the higher levels are approximately proportional to D.
Some Cases of Pile Activity Flattening: Radial flattening of activity in the cores of spherical and cylindrical piles is discussed in connection with pile control and power improvement. Partial flattening as a result of k loss from temperature rise is also considered.
Temperature Effect in Homogeneous Pile: Some idealized considerations of the temperature field in the homogeneous pile are given. It is crudely estimated that the effective mean temperature rise of the pile to be used in calculating the k loss is something like 3/4 the rise in temperature of the slurry in passing through the pile.
Radioactivity Induced in Commercial Materials: Six structural materials (aluminum 2S, aluminum 72S, copper, iron, steel, lead and bismuth) were irradiated for about 100 kilowatt hours in the center of the Argonne pile. The alpha and gamma decays were then followed for 130 days on Geiger counters and are presented here graphically as number of rays per minute per gram per kilowatt hour vs. time of decay. A quantitative interpretation of the gamma-ray decay curves gave fair agreement with the chemical analysis of impurities found in the materials.
Recalculation of the Critical Size and Multiplication Constant of a Homogeneous UO2 - D2O Mixtures: The multiplication constant and optimal concentration of a slurry pile is recalculated on the basis of Mitchell's recent experiments on resonance absorption. The smallest chain reacting unit contains 45 to 55 m3 of D2O.
Eta Temperature Effect: The temperature coefficient of eta has been measured with the thermal column of the Argonne pile using uranium foils of different isotopic ratios. The temperature change was effected by filtering neutrons through silver. The measured fractional change per degree centigrade is [formula].
Calculations for Some Pile Shapes of Which the Boundaries are Partly Spherical: Some methods for calculating the k requirements of various shaped piles are indicated, with particular reference to the shape of the tank in the homogeneous plant.
The Pile Safety Circuit: The present report is concerned with the electronic relay which, upon the reaching of a pre-determined value of ionization current in the associated chamber, actuates the safety rod release mechanism. The are here proposed two independent suggestions: (1) An improved trip circuit of such sensitivity and stability as to allow it to be actuated by a signal directly from the chamber without the necessity of interposing intermediate amplifier stages. The value of chamber current at which tripping occurs is stable to +- 0.4%. (2) A triple-wound relay to prevent shut-downs of the pile which would otherwise be caused by development of defects in the safety circuits.
Calculation of the Temperature Distribution in a Slug With a Solid Aluminum Cap: Calculations were made to determine the temperature at various points of a thick disc and cap, on the assumptions that the heat production rate is uniform throughout the slug and that the slug is in perfect thermal contact with the cap. Results obtained by different methods of computation are compared with each other and with results obtained by Drew on the Paschkis electrical network computer at Columbia University.
Resonance Absorption in Lumps and Mixtures: The resonance absorption of a lump is described in terms of three components. Calculations of resonance absorption are carried out using the model for the resonance spectrum of uranium recently derived; calculations are also made with variations of this model which involve local fluctuations in level strengths. For metal and oxide lumps the agreement with observation is satisfactory. For dilute mixtures, whose resonance activation was measured by Mitchell, computed values fall 20% to 30% above measured ones.
The Influence of Operation on Tuballoy: An attempt is made to estimate the influence of operation upon the mechanical properties of tubealloy. It is to be emphasized that the work is highly speculative, being base upon a set of judicious assumptions regarding the transport material within the metal and should not be used as a substitute for a set of well-planned experiments. The two principal effects considered are the hardening which results from the atomic displacement produced by the fission fragments and the changes in mechanical properties arising from the presence of the fission products. The principal conclusion to be drawn is that the disruption of the metal which accompanies operation takes place at at sufficiently high rate that it could readily cause serious changes in the mechanical properties of the slups. the reversal of the disruption resulting from thermal effects probably is sufficiently high to prevent serious embrittlement as a consequence of displacement through most of the volume of the slug if not at the surface. On the other hand, the migration of atoms also appears to be sufficiently high that the rare gas products may have time to diffuse to cracks and produce embrittlement.
Determination on Neutron Density With Bismuth Foils : Final Report - Problem Assignment 131 - X21P: It is usual to determine the density of neutrons by using foils of metals which become radioactive as a result of bombardment in the region under investigation. From the rate of disintegration of the newly formed radioactive element the number of neutrons absorbed can be calculated. By use of the capture cross section of the element of which the foil is composed the density of the neutrons can then be computed. By counting the alpha particles from a bismuth foil of known weight after exposure to neutrons the density of the neutrons which produced this activity can be calculated. The least accurately known value which enters into this evaluation is the capture cross-section of bismuth for pile neutrons. This value may be improved by future measurements. It is of importance only for absolute measurements of neutron density so that relative values can be measured with considerable accuracy on the basis of known data.
On the Boundary Condition Between Two Multiplying Media: The transition region between two parts of a pile which have different compositions is investigated. In the case where the moderator is the same in both parts of the pile, it is found that the diffusion constant times thermal neutron density plus diffusion constant times fast neutron density satisfied the use pile equations everywhere, right to the boundary. More complicated formulae apply in a more general case.
Resonance Absorption of Uranium in Mixtures: A good determination of the resonance absorption of uranium when admixed with various substances is necessary so that calculations can be made on the efficiency of homogeneous piles. The original experiments along these lines were undertaken by Creutz, Jupnik, and Snyder (C-116) and consisted of experiments on the resonance capture in pure U, UO2, U3O8, and one experiment on capture in a mixture of U3O8 and graphite. These experiments were done at the cyclotron in Princeton and consisted of determining the ratio of the twenty-three minute activity of uranium to an iodine monitor placed in some position with respect to the sample. By using spheres of different radii both the volume and the surface absorptions were measured. It was considered very desirable to extend these measurements to mixtures containing large amounts of graphite to uranium and also to investigate other substances containing hydrogen and deuterium. In addition it was decided to use both iodine and gallium monitors in the experiments. While the experiments were in progress, an absorption curve for uranium metal was made by Marshall using iodine and gallium detectors, which showed that there was a certain amount of overlapping of resonance levels of uranium and iodine.
Metallurgical Laboratory, Nuclear Physics Division, Report for the Month Ending May 25, 1944: Technical report with short reports from the (1) Experimental Nuclear Physics Group; (2) Theoretical Physics Group ; (3) Lattice Design Group; (4) Pile Design Group; (5) Exponential Experimental Group; (6) Radiation Group; and (7) Shielding Group.
Thermal Stresses Arising from Defective Strip in Bond: Stresses set up by an insulating strip in the bond are estimated and found to be small compared to those normally present without the defect.
The Diffusion Length of Thermal Neutrons in Uranium: Measurements made in a uranium cylinder result in a mean value of 1.55 cm. for the diffusion length L for distances of 1 to 4 cm. from the base of the cylinder. Calculations give a value which agrees with the experimental result and show further that L increases from 1.40 to 1.63 cm. as the neutrons diffuse a distance of 5 cm. into the uranium.
Experiments on the Evaporation of Boron in Vacuo : Progress Report No. 1 on a Phase of Problem No. 132 - ML - 56-3; File Serial 13: It was desired to determine a method of evaporating boron to form a rather pure uniform tenacious coat of specified thickness. These coats are needed as monitoring films for neutron intensities, particularly in steel ionization cylinders. The most satisfactory method of evaporating boron employed a graphite filament. A mixture of amorphous boron and Carbenoid A was painted onto the filament which was then heated by electrical resistance method to 2300 degree C at which temperature the boron evaporated. Opaque films with purities up to 98% boron or better could be deposited by this method. Much heat was liberated by the filament, and it was found necessary to cool the steel cylinders during evaporation to prevent alloying of boron with the steel. Cathodic deposition also proved satisfactory for producing high purity films; this method has the advantage that little or no heat is produced during the process, but requires much time. Other less efficacious methods of depositing lighter films of born were developed; these are included in the following discussion.
A Case of Rod Warping: Warping of a rod by a variation in heat transfer coefficient around the periphery is considered. Estimates for some simple cases are given, and a more precise numerical calculation is carried out in ne instance.
Representation of Slowing Down Functions in Water by Synthetic Kernels: Fermi, Anderson, and Nagle's experimental distribution of Indium resonance neutrons around a point source of fission neutrons in water has been fitted by analytic expressions which are source functions in the two-group, three-group, Fermi and Christy-Wheeler pile theory. The Christy-Wheeler function (exponential followed by a Gaussian) is the best fit; the two-group function (exponential) is slightly better than the Fermi Gaussian.
Jacket Temperature Near End of Slug: Some situations which give rise to a hot ring around the slug near the end are considered; namely rounded slug ends in the long cartridge design, and the Wilkins effect in the current unbonded short slug design.
The Effect of the Maxwell Distribution of Velocities on the Neutron Density and Diffusion Length in a Metal Sphere: The change in the simple [formula] distribution of neutrons in a spherical lump of uranium caused by the distribution in velocities of thermal neutrons is calculated. If the calculated curve is fitted as well as possible by a simple [formula] curve, it is shown that the value of [formula] obtained in this way is a function of [formula], the radius of the sphere. For small radii the [formula] obtained in this manner will be as much as 25% greater than the [formula] corresponding to average velocity neutrons. The change in the thermal utilization caused by the distribution in velocities is discussed. The flux of neutrons into a sphere is calculated taking into account the velocity distribution and this is compared with the usual theory.
Sealing of Holes in Aluminum Sheet by Oxidation: Aluminum oxide occupies a larger volume than the aluminum it contains would fill as metal, consequently, the assumption has been made that holes in metallic aluminum would close by a sufficient amount of oxidation. Therefore, we were asked to investigate the rate of plug formation under conditions to be expected in the pile. For the latter we were requested to approach the pile conditions as nearly as we could by employing the Chicago cyclotron. It seems to us that the problem divides itself into two separate questions: (1) under what conditions may holes be expected to close? (2) if holes do close how much corrosion of uranium may be expected before the closure becomes impervious to water vapor? In this report only the first question is considered. The experiments and theory coupled with the data collected by other workers on the project definitely define the limits within which pores in the aluminum cans may be expected to close by an oxidation process. Under the most favorable conditions only small holes may be sealed in this manner. In the large majority of the cases the holes not only fail to close but become larger.
Extrusion of Compound Tubes of Aluminum and B4C: Various experimenters have shown (H.H. Gersman U.S. Patent 2,335,590, Nov. 30, 1943; Aluminum Co. of America, various technical papers; also CT-482) that when a billet is extruded by proper technique into a rod (or tube by a floating mandril) that flow of material is streamline and and the extruded article is essentially a space replica of the billet, with linearly distorted coordinates. Advantage is taken of this fact in the manufacture of alclad tubing in which a billet containing an inner core of one alloy with the outer part of another alloy cast around it is extruded together into an integral tube, e.g., to combine high corrosion resistance with high strength. The following experiments were carried out because of the desirability of obtaining a control rod which can be water cooled (or immersed in P9) and which contains boron. For some pile structures it may be desirable to have the major portion of the energy released by the neutron absorption of the control rod be spend in the rod itself by the nuclear reactions [formula] rather than in the surrounding media as is the case when absorption of neutrons is by cadmium according to the reaction [formula]. In the later case most of the energy appears as gamma rays so the heating effect cannot be localized to an easily cooled region. One possible objection to the use of boron (as in boron-steel and other alloys) is the possibility of building up high pressures when an appreciable fraction of it is converted to helium n a confined space. the present method provides channels for the diffusion of this gas away from the region where it is produced so that there is no danger of its cracking the material in which it is formed.
The Distribution of Thermal Neutrons in a Slug with Thick End Caps: The distribution of thermal neutrons in a W slug having a one centimeter aluminum end cap has been calculated on the basis of simple diffusion theory. It is found that the average neutron density, and therefore the power output, at the end of the slug is about 34% higher than the density far from the end cap. This result agrees well with the recent Argonne pile experiments (CP-1729).
Temperature and Heat Flow in a Graphite Electrode: In making various experimental heat studies a power producing metal slug is simulated by a slug with a graphite rod electrode of 3/8" diameter inserted lengthwise through it. There is a helium filled annular space between the graphite and the inner surface of the slug cylinder. Radiant heat passes from the electrode to the metal; with proper adjustment of the electrode current the slug in the steady state will therefor "produce" the same amount of energy from its exterior surface as it would under operating conditions. The question arises, however, as to how uniform the electrode temperature is along its length. And also, in some cases one end of the electrode is embedded in the slug metal; it is then desirable to know how much heat flows by conduction from the electrode into the slug.
Progress Report : Low Geometry Alpha Particle Ionization Chambers: ABSTRACT. When solutions of high specific alpha activity are to be assayed for product, it is often difficult to obtain reproducible results by diluting the solution sufficiently to remove a small volume from which a sample can be prepared and counted at 52% geometry. In order to assay such a solution, most reproducible results have been obtained with minimum effort in sample preparation by making use of low geometry chambers. Two types of low geometry chambers are described: 1) The air-screen type which reduces the geometry simply by placing screens of various transparencies above the sample; and 2) The vacuum low geometry chamber which accomplishes geometry reduction by increasing the distance between sample and collecting electrode thus decreasing the solid angle subtended by the sample and aperture through which the particles pass into the ionization chamber. This type chamber was developed concurrently by this group and the instrument group of Chemistry Section C-I at the Metallurgical Laboratory. Because the geometry of the air-screen type chamber is quite critical to sample spreading and be- cause 12 mm sample plates are required, it has found very little use. On the other hand, the vacuum chamber, because it is noncritical to sample spreading and especially noncritical to sample thickness, has found widespread use in product chemistry studies and high alpha activity experiments. Photographs and drawings are included.
Warping Instability in Long Rods: Abstract. If a pile rod gets bowed within its cooling tube it becomes warmer on the side which approaches the tube wall, and thermal expansion tends to warp it in the same direction as the original displacement. This was discussed roughly in N-601, and it was there concluded that the mechanism was not important for an isolated short slug. In connection with current development of continuous jacket (cartridge) assemblies, it seems desirable to look at this question again. In this case it is possible that the effect may be of some concern.
Further End Cap Temperature Calculations: Abstract. Recently (CP-1989) it has been shown that the neutron density, and thus the heat production, at the end of a slug with an A1 cap may be appreciably higher than that at the middle of the slag. A re-examination of earlier temperature calculations is made in light of this effect.
Engineering Group Instrument Specification Report : Tests on Aquadag Treated Polyethylene Cable: Effect of aquadag coating on noise reduction in polyethylene coaxial cable was tested. A satisfactory combination of coaxial cables and connectors interconnecting sources of small ion currents or ionizing impulses with the measuring device is described.
A Final Report on the Experiment : the Penetration of Graphite of Different Purities by Lead Bismuth Eutectic: Bi-Pb eutectic and pure Bi penetration of graphites of various densities under 300 degrees C and pressures up to 20 psi was found be of the order of magnitude of 1.0 g/cm(2) and was uniform throughout the graphite. Bi was absorbed less than the eutectic but the oxidation rate of Bi would be prohibitive. There was heavy nitriding in N atmospheres with the Bi and the eutectic.
Flexibility of a Tube in Which Slugs Slide: An approximate calculation is made of the variations of the flexibility of a long cartridge with the length of the slug used, assuming that the jacket slides without friction.
A Sensitive Particle Ionization Chamber for Neutron Detection: Abstract. A particle ionization chamber of sensitivity sufficient to detect a source of one neutron per second has been used to measure the neutron yield from a thick target of sulfur upon bombardment with polonium alpha particles. The high-geometry boron trifluoride chamber used had an efficiency of 1.9 percent for fission neutrons. The neutron yield from a thick target of sulfur was measured by this instrument and found to be .0035 +- .0013 neutrons per million incident polonium alpha particles.
A Method for Neutron Energy Measurement: This technical report discusses a method proposed to measure neutron energies by accurately determining the momenta of recoil protons in a magnetic spectrometer specially designed for this purpose. The main consideration in the design of the spectrometer is the shielding of the detector from the high radiation background associated with intense neutron beams.
Passage of a Rod Around a Corner: Maximum curvatures and forces set up in taking a rod in a tube are considered.
The Slow Neutron Transmission of Be Metal as Measured by a Neutron Beam Spectrometer in the Energy Region 0.004 eV to 50 eV: Abstract. Slow neutron transmission measurements as a function of the time of flight of the incident neutron have been made for three different thicknesses of Beryllium. The energy region from 0.004 eV to 50 eV was investigated using the Columbia neutron beam spectrometer system. Particular emphasis was placed on the very low energy region (from 0.004 eV tp 0/2 eV or from 0.6 to 5 [length]) where pronounced crystal interference effects were observed. The effective slow neutron cross section (in the unity of X 10(-24)ce(2)atom) for several different energy values were: 6.1 at 0.2 [length], 3.5 at 1.5 [length], 2.3 at 2.5 [length] and 0.6 at 4.6 [length]. The positions of the discontinuities in the cross section agree fairly well with the values obtained from the X-ray measurements.
Maximum Force of a Warped Rod Against a Rigid Constraint: Abstract. Given the maximum intrinsic curvature of a rod, the maximum force required to confine it between parallel rigid walls is computed.
The Temperature Coefficient of the Diffusion Length for Thermal Neutrons in Water: Abstract. The diffusion length of thermal neutrons in water as a function of the water temperature has been measured. The results are expressed as a linear relation: L = 2.644 + 0.0061T where L is the diffusion length in centimeters and T is the temperature in degrees centigrade.

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