Calculating the transient temperature field in a reactor tube and the thermoelastic stresses in the fuel element cladding

Approximate analytic methods are given for calculating the transient temperature field in the fuel elements and the coolant temperatures at any point along the reactor tube, as well as the transient thermoelastic stresses in the cladding of a cylindrical fuel element. The coolant temperature at the input to the tube is constant, and the coolant undergoes no changes in state of aggregation. The approximate methods are illustrated by examples.Results are given, for comparison, of accurate calculations of the same examples made with a rapid calculating machine.List of symbols time - r; z coordinates (radius, distance along tube) - r₁; r₂ internal and external radii of fuel element cladding respectively - H total active length of fuel element - a₁; ₁;c _{1 1} coefficients of temperature conductivity, heat conductivity, specific heat capacity and specific gravity of fissionable material respectively - a₂; ₂; C_p2; ₂ cladding parameters - a; ; c_p; coolant parameters - mean cladding radius - f:f₂ cross-sectional area of tube for coolant and cladding respectively - w coolant velocity - coefficient of heat release to coolant - t (r, ); (); () fuel temperature, mean temperature over cross section of cladding, and coolant temperature at pointz. along tube respectively - qv() specific volume of coolant at pointz - values averaged overz - quantities at the initial instant of time - ₃ delay time - _n time required for coolant to go from z=0 to the point in question     

Methods for preparing ions of short-lived isotopes

Conclusions A source with thermal ionization in a cavity is extremely convenient for obtaining ion beams with an ultralow quantity of the starting material. Its efficiency with ionization potentials of the starting atoms V_i<6 eV is equal to 100% and drops to 1% for V_i=8 eV [7]. This makes it possible to use it in the study or more than two-thirds of the periodic system of elements, including the actinides. Thus for 10¹² uranium and plutonium atoms ^*9% and 50%, respectively; for 10⁶ curium atoms ^*70%; and, for 10⁵ californium atoms ^*37% [13]. It was shown in [14] that this source can be successfully used in mass spectroscopy to analyze trace quantities of different elements in the solid phase. With its help yttrium isotopes with _1/2=0.4 sec were detected in [16].This source is now widely used in our country, where with its help tens of new isotopes have been discovered [15, 17], and abroad (for example, [16]). The source is effective for short-lived isotopes with _i/_1/2<10 and V_i<7 eV. To study isotopes with _i/_1/2<10 and V_i>7 eV but with _i/_1/2>10 it is desirable to develop sources with thermal and photoionization in the cavity. For elements whose atoms have a long residence time on the surface, these sources, just as the gas-discharge sources, are inefficient. Means must be developed for raising the rate of desorption of the indicated atoms from the surface within the framework of the techniques examined here.Translated from Atomnaya Énergiya, Vol. 60, No. 2, pp. 114–119, February, 1986.     

Lawson concepts and criticality in DT fusion reactors

The original Lawson concepts (amplification factorR and parametern as well as their applications in DT reactors are discussed in two cases: the ignition regime and the subignition regime in a self-sufficient plant. The modified Lawson factor or internal amplification factorR (a function of alpha power) is proposed as a means to measure the ignition level reached by the plasma, in a more precise way than that given by the collective parameter (nkT). The self-sufficiency factor () is proposed as a means to measure the plant self-sufficiency, being more significant than the traditionalQ factor. It is stated that the ignition regime (R =1) is equivalent to a critical state (energy equilibrium); then, the corresponding critical mass concept is proposed. The analysis of theR relationship with temperature (kT), (n), and recirculating factor () gives the conditions for the reactor to reach ignition or for the plant to reach self-sufficiency; it also shows that an approach to ignition is not improved by heating from 50 to 100 KeV.     

Slowing down of fission neutrons by water

In this articie we describe the method and results of measurement offor U²³⁵ fission neutrons slowed down by water to energies of 1.46 ev. The value obtained for _{1.46 ev} = 294 ± 1.5 cm² In conclusion, the authors express their sincere gratitude to I. I. Gurevich and D. V. Timoshuk for reviewing the results, to A. P. Venediktov for help in the work, and to G. R. Golbek for lending the -apparatus with low background.     

Dose characteristics of a mixture of uranium fission fragments

Results are presented for calculations for the different dose characteristics of fragment elements: the percentage composition of the mixture for a uranium exposure time t₀=100 days and a cooling off period =15–540 days, the time variation of the activity of the mixture for t₀, equal to 60, 100 and 150 days. The calculated data are in satisfactory agreement with the results of radiochemical analyses.The gamma constant of the mixture is essentially independent of t₀ (within the limits 60–150 days) and also remains approximately constant for values of ranging from 15–180 days.     

Effect of elastic fields of dislocations of the equilibrium configurations of self-interstitial atoms in cubic crystals. Part I. BCC iron crystal

Conclusion On the basis of the results from our discussion of the elastic interaction of a selfinterstitial atom with screw and edge dislocations in a bcc iron crystal, we can make the following conclusions.The interaction of a dislocation with a self-interstitial atom can lead not only to a change in the migration energy of the SIA but also to the stabilization of the SIA configurations that are metastable in the absence of elastic fields.The region of stabilization of the crowdion configuration and the 111 dumbbell configuration forms the nearest-neighborhood (r_sb) of the screw dislocation, and the axis of the crowdion or the 111 dumbbell is oriented toward the dislocation line.The region of stabilization of the crowdion configuration and the 111 dumbbell configuration in the field of elastic stresses of the edge dislocation is of considerable size (r_e5b). The axes of the crowdion configuration and the 111 dumbbell configuration are oriented in the direction of the Burgers vector b=/2 [111] of the dislocation.The elastic field of the edge dislocation stabilizes the crowdion configuration and the 111 dumbbell configuration in an orientation such as to cause the self-interstitial atom to hover at some distance from the dislocation without forming a jog. Subsequent absorption of the self-interstitial atom by the dislocation requires an activation energy greater than the energy of migration of the SIA in the absence of a dislocation.The coupling energy between the screw dislocation and the crowdion configuration of the self-interstitial atom considerably exceeds the energy of formation of a double kink on the screw dislocation, which ensures activationless slip of screw dislocations because of the interaction with SIAs and, consequently, the radiation softening of bcc iron crystals in the range of sufficiently low temperatures.Translated from Atomnaya Énergiya, Vol. 61, No. 6, pp. 422–428, December, 1986.     

Pulse method of measuring neutron age in graphite

Using a pulse source located within a prism, the age of thermal neutrons from the reactions D-D and D-T in graphite was measured. From the time dependence of the thermal neutron density the author calculated the effective age of D-D neutrons _eff = 355 ± 9 cm², recalculated for a graphite density equal to 1.6 g/cm³.The slowing down of D-T neutrons in graphite can be approximately expressed with the aid of two neutron groups: neutrons suffering but one inelastic collision when slowed down (_eff =600 cm²), and neutrons suffering several inelastic collisions (_eff = 240 cm²). In determining the age the relative contributions of both groups were assumed equal to 0.65 and 0.25, respectively. A third group is composed of neutrons slowed down only by means of elastic collisions. These neutrons may be neglected in the first approximation, since their contribution is small (about 0.1), while the increase is large.This work was carried out at the P. N. Lebedev Physics Institute of the Academy of Sciences of the USSR.In conclusion, the author expresses his gratitude to Corresponding Member of the Acad. of Sei. of the USSR I. M. Frank for suggesting the research topic, for his steadfast interest in the work, and for valuable remarks during the course of discussion.     

Measurement of slowing down of neutrons by water in the energy interval from 1.46 to 0.025 ev

With the aid of an indium detector the spatial distribution of resonance (E_r = 1.46 ev) and thermal neutrons that arise as a result of the slowing down in water of the photoneutrons emitted by an Sb + Be source is measured. The age of the neutrons _{1.46 ev}, the thermal neutron diffusion length in water, and the square of the slowing-down length from neutron energies of 1.46 ev to thermal energies (0.025 ev) are determined.In conclusion the authors express their sincere appreciation to Professor I. I. Gurevich for valuable discussions of the results of the work to A. P. Venediktov and B. V. Sokolov, who took part in the preparation of the apparatus and in the measurements, and to A. V. Teinov, who helped in preparing the apparatus.     

Thermodynamics of the extraction equilibria for uranyl nitrate

The fundamental thermodynamic principles of the extraction equilibria for uranyl nitrate are examined. The equilibrium characteristics are associated with considerable nonideality of the aqueous phase — a strong electrolyte, and the organic phase -a practically undissociated nonelectrolyte.It is shown that, at ionic strengths of up to 10, ion association in the aqueous phase does not significantly influence the distribution of uranyl nitrate. It is noted that in most instances the solutions of uranyl nitrate in the organic phase are close to regular solutions, and therefore there is no need to postulate solvation in the organic phase for interpretation of the equilibria. The effect of a salting out agent on the activity coefficient at constant concentrationx of the latter is examined. It is shown that the relationship between _{(x, m)} and the concentration of the salting out agentm is determined by the ratio of the Harned coefficient for the salting out agent to a quantity _e, characteristic for uranyl nitrate: log _{(x, m)}/_{(x, o)} = 2(_U— _s)J_s, where _(x,o) is the activity coefficient of uranyl nutrate in the absence of a salting out agent, and J_s is the ionic strength of the salting out agent. If _s < _U, then addition of salting out agent raises , and conversely; when _s = = _U (ammonium nitrate), is practically independent of the concentration of salting out agent. The value of _s decreases and the salting out agent becomes more effective with increasing number of molecules hydrating the cation. Equivalents of the salting out agents differ from chemical equivalents by activity coefficient corrections, and they can be only approximately constant.The variation of the distribution coefficient with the degree of dilution or saturation of tributyl phosphate in extraction by mixed solvents, and the conditions of mutual displacement of the substances being extracted from the organic phase are examined. The role of nonideality of tributyl phosphate — dilutent solutions in the extraction of uranyl nitrate is demonstrated.The parameters which determine the distribution of uranyl nitrate when different solvents and salting out agents are used are the distribution constantk, the nonideality constant of the solvent , and _s. The most important parameter is the distribution constantk, which varies several 1000-fold for different solvents. It is shown that the distribution curves have three characteristic regions, the extents of which depend on the value ofk and the nonideality constant of the solvent .     

Study of the zirconium apex op the Zr-Ta-Nb phase diagram

Metallographical examination thermal analysis and electrical resistance measurements have been applied to a study of the zirconium apex, up to 82% zirconium and a temperature of 1200C, of the ternary system Zr-Ta-Nb, with limited solubility of tantalum and niobium in -zirconium ( phase), limited solubility and complete solubility of niobium in -zirconium, with eutectoid decomposition of the \ solid solution and three-phase eutectoid equilibrium + between - and-zirconium. In the investigated portion of the Zr-Ta-Nb phase diagram, the following phase regions were found: a) two one-phase regions and ; b) three two-phase regions + , + and + : c) one three-phase region + + ; the region contracts as the temperature falls below 1200 C.The solubility of tantalum and niobium in -zirconium in the system Zr—Ta—Nb is about 0.5%. On passing from Zr—Ta to Zr—Nb, the + and + regions are displaced toward lower temperature and high niobium concentrations; the boundaries of the + and + + regions are lowered from 790 for Zr—Ta to 612 C for Zr-Nb. Passing between the + and + regions is a binary eutectoid line which, from Zr-Ta to Zr-Nb is displaced toward lower temperatures and higher niobium concentrations. The solubility of niobium in ot zirconium in the Zr-Nb system is about 0.5%by weight. Eutectoid decomposition in the Zr-Ta system shifts the maximum of the martensitic-like transformation to the left and results in an increase in the stability of the phase at room temperature in quenched alloys.     

Corrections for multiple scattering in spherical and circular geometries

In this paper a method is considered of introducing corrections for multiple scattering into the results of measurements of angular distributions of elastically scattered neutrons. It is assumed that the mean path of the neutron in the sample in which scattering takes place is comparable with the neutron free path.In the first part, using direct calculation of the integrals, we find the probability for double scattering and estimate the probabilities for triple and higher-order scattering for a sphere and for a ring of circular and rectangular cross section in the case of isotropic neutron scattering. In the case of anisotropic neutron scattering, at neutron energies of the order of several million electron volts the cross section may be given as a sum () = ₁ () + ₂ (), where ₁() is the forward peak and ₂() is more or less isotropic. Using this representation all elastic scattering events may be provisionally divided into two groups while all double scattering events can be divided into four groups. The probabilities of double scattering for all four are calculated on the basis of results obtained for isotropic scattering. Triple and higher-order scattering are evaluated in similar fashion.     

Investigation of the Effect of Radiation and High-Temperature Treatment on the x-Ray Luminescence of Quartz Glasses

The x-ray luminescence of KI, KV, and KU-1 quartz glasses, irradiated with and n– radiation in the dose range 10²–10⁷ Gy and neutron fluence range 10¹⁵–10¹⁷ cm^–2 and subjected to high-temperature annealing in air at 450 and 900°C is investigated. It is shown that the spectra of the nonirradiated and the and n– irradiated glasses of the first two types are a superposition of bands with _max = 410 and 460 nm, which are due to an impurity center initially present in the glasses (_max = 410 nm) and the initial and radiation-generated with dose 10⁶ Gy and fluence 10¹⁶ cm^–2 E' centers (_max = 460 nm). X-Ray luminescence is not observed in nonirradiated KU-1 glasses; a band with _max = 460–470 nm, due to radiation-generated E' centers, appears in the spectra of and n– irradiated glasses. As the radiation dose and the neutron fluence increase, the number of impurity centers decreases and the number of E' centers increases. It is established that the 410 nm band is due to the component of the n– radiation. High-temperature annealing in air at 900°C induces in the spectra new bands with _max = 470 and 520–540 nm, which are believed to be due to interstitial defects of the type O^– and O₂ ^–, formed when oxygen from air diffuses into the glass and localizes in interstices. 6 figures, 7 references.     

Requirements for ohmic ignition

An analysis of ohmic ignition criteria is presented, giving the requirements onT, n, andn/j in a form easily applicable to various confinement assumptions. For circular cross-section NeoAlcator tokamaks with Spitzer resistivity, a value ofB ₂ a approximately equal to 250 T²m is required. The outstanding uncertainties in schemes to lower this value are how much increase in current density is achievable by plasma shaping and what the exact NeoAlcator coefficient is.     

Resonance scattering of γ-rays in Mg24

Resonance scattering of -rays With energies E₁=1.38 Mev, corresponding to the transition to the ground state in Mg²⁴. have been observed in metallic magnesium. The energy given off by the -ray (E₁=1.38 Mev) in emission and collision with the nucleus, is compensated for by the energy obtained due to recoil associated with the emission of the preceding -ray with an energy E₂ = 2.76 Mev. Using a fast coincidence method and amplitude discrimination, coincidences were recorded between the -rays with energies E₁=1.38 Mev and E₂=2.76 Mev. Scattercrs of magnesium and aluminum were alternately placed in the path of the 1.38 Mev -rays. The source was radioactive Na²⁴ in a water solution of NaOH. At an angle of 120 ° between the -rays a strong attenuatlon of the 1.38 Mev -rays was observed; this is attributed to resonance scattering. When the angle between the -rays was varied by 5 °. the strong attenuation of the flux disappeared. The width of the level at 1.38 Mev in Mg²⁴ has been estimated at > 1.6· in^–4 Mev.     

Effecting the condition of quasistationary thermonuclear burning in tokamaks with a high plasma density

Conclusion The zero-dimensional analysis and the numerical calculations have shown that stable conditions of the thermonuclear burning in a tokamak with a high plasma density are achieved only when _E depends strongly upon the plasma temperature (_E – ^m, where m<–2). Since in the experiments the retention laws have a significantly weaker temperature dependence, special measures are required for obtaining stable burning. Such conditions are reached by introducing feedbacks over, say, the plasma temperature and the rate of plasma-temperature change. It was shown in the present work that the corresponding regulation parameters are on the 0.3–0.5 level. Feedback can be obtained by, say, relaying operation of the source of additional heating.Translated from Atomnaya Énergiya, Vol. 63, No. 2, pp. 147–148, August, 1987.     

Measuring the mean lifetime of thermal neutrons from a small specimen

The author describes a method of measuring the mean lifetime of thermal neutrons for specimens whose dimensions a r e commensurate with the thermal transport length. The method makes use of a pulsed neutron generator and is intended for determining for rocks by means of measurements on core samples. It can also be used to estimate the concentrations in rocks of elements with large thermal-neutron absorption cross sections.Translated from Atomnaya Énergiya, Vol. 22, No. 1, pp. 33–38, January, 1967.     

Anisotropy of crack resistance of the channel tubes produced using Zr-2.5% Nb alloy

Conclusions Using experimentally determined values of the critical opening of the differently oriented cracks (_c), we evaluated the anisotropy of crack resistance of the material of nine channel tubes (Zr-2.5% Nb alloy) under different structural conditions. Determination of the strucutral (_o) and texture (R) parameters of crack resistance according to the bend tests carried out using specimens having a cross section of 4×4 mm makes it possible to evaluate the individual contribution of the texture and the structure to the crack resistance of the material of the channel tubes. The parameter _c is a constant that depends on the type of the alloy and its structural state: the higher the crack resistance of a material, the higher is the magnitude of ₀. The parameter R depends on the crack orientation in the tube. It affects the coefficient of rigidity of the stress state (K_ij) at the crack tip and, thereby, characterizes the embrittling effect of the given crack.The experimental results obtained when determining _c of the material of the channel tubes having cracks of different orientations can be expressed by the following equation _c=0.741₀(2.35-K _ij), where K_ij is calculated using the parameters of anisotropy of plastic deformation of the material of the tubes.Translated from Atomnaya Énergiya, Vol. 69, No. 4, pp. 230–233, October, 1990.     

Analysis of the observed resonance-width distributions of U233 and Pu239

As a result of the strong fluctuations of fission and reduced neutron widths, a significant number of resonances occur with such a small reduced height 2gF_n ⁰/ that they will not be noticed experimentally. If the fraction of transmitted resonances is considerable, then this should lead to the following effects which might be observable in an experiment: 1) change of the distribution function of the reduced neutron and fission widths, which is particularly sharply manifested for _n ⁰/<_n ⁰> 1 and _f/<_f> 1; 2)appearance of correlation between the form of the neutron distribution b of fission channels; 3) appearance in the total cross section and fission cross section of a background which is approximately proportional to . All the effects mentioned are manifested for the U²³³ nucleus. For Pu²³⁹ this effect is smal! and the observed values are welI described by X² distributions.Translated from Atomnaya Énergiya, Vol. 17, No. 1, pp. 22–27, July, 1964     

Paramagnetic effect under the influence of high-frequency pressure and electron paramagnetic resonance in plasma

The interaction of uhf fields ( = 2· 10¹⁰ sec^–1) in a space resonator containing dense plasma (n 10¹³ – 10¹⁴ cm^–3) in a steady magnetic field was studied experimentally. Under the influence ofhf pressure a paramagnetic current arises in the plasma; the associated effect of an increase in the static magnetic field inside the plasma agrees closely with the calculated relation.For _H/ = 0.5 paramagnetic resonance of the electrons takes place; this leads to a sharp rise in plasma pressure p₀, up to =8p₀/H₀ ²0.2.Translated from Atomnaya Énergiya, Vol. 20, No. 5, pp. 401–407, May, 1966.     

3D Wave Propagation and an Ultra–Low-Frequency Instability in Magnetopause

A model set of equations for the low-frequency electromagnetic perturbations in a magnetized nonuniform plasma is presented. A more convenient and systematic procedure is suggested to treat the fluid equations in order to deduce electrostatic and electromagnetic limits. A general dispersion relation is derived for the waves propagating in 3D under local approximation in nonuniform plasmas, which includes almost all the known modes of cold ion magnetized plasmas in the limit < _i (where _i is the ion cyclotron frequency). Both the limits 1 and O(1) have been discussed briefly. The shear Alfvén waves and electromagnetic ion acoustic waves near ultra low frequency (ULF) range are found unstable in the high plasma of magnetopause. The results are in complete agreement with the satellite observations.