Can the Inertial Alfvén Wave Become an Electrostatic Mode in the Limit 1 ≪ λ2 e k 2?

Analytical calculations are presented to clarify that the inertial Alfvén wave cannot become an electrostatic mode in the limit ² _e k ² (where _e is the electron skin depth and k is the component of the wave vector in perpendicular direction to the external magnetic field).     

Effect of single channels and slits on reactivity

The change in reactivity due to the change in transport cross section in an inclusion in the form of a cylinder or a plain layer is expressed as a perturbation of the neutron ftux at some distance from the inclusion, where the diffusion approximation holds. By using the results of flux calculations in the layer mediunh and in the cylinder, a relation may be found between the change in reactivity and the characteristics of the inclusion (such as transport cross section, volume, shape, where it is located, etc.). The effect of shape shows up in the coefficients B and B being different from unity. These same coefficients are what determine the average diffusion coefficients D and D, An interpolation formula is constructed for B based on the various limiting expressions.Translated from Atomnaya Énergiya, Vol. 14, No. 4, pp. 364–370, April, 1963.     

Stationary transport of monoenergetic neutrons in inhomogeneous media

The passage of monoenergetic neutrons from a stationary source in an inhomogeneous medium is considered; this may be described by means of a Boltzmann equation with fluctuating coefficients. An equation is derived for the flow of neutrons (neutron flux) averaged over the fluctuations in the medium. A solution is obtained for this equation in limiting cases in which the characteristic dimension of the inhomogeneity 1_s ⁰ (free path in relation to scattering in a homogeneous medium) and 1_s ⁰. In both cases 1L₀ (diffusion length of neutrons in a homogeneous medium). By way of an example of an inhomogeneous medium, the periodic lattice of a reactor is considered.Translated from Atomnaya Énergiya, Vol. 22, No. 4, pp. 271–276, April, 1967.     

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.     

Containment of plasma in a trap with combined magnetic field

The containing properties of an adiabatic trap with a magnetic field increasing in the longitudinal and radial directions are investigated. This field is obtained from a combination of the ordinary mirror field configuration (main field H0) and the field of a system of current-carrying conductors laid parallel to the axis of the trap (stabilizing field H). The conductors are placed uniformly in azimuth around the side walls. The trap is filled with plasma of density n10⁹–10¹⁰ cm^–3 and proton energy T_i5eV (T_e20 eV). The plasma lifetime is measured as a function of H. and the neutral gas pressure. From the results obtained, it is concluded that such combined fields ensure stable containment of the plasma, unbroken by magnetohydrodynamic instabilities [at any rate for = nI/(H²/8) 10^–4]. The stabilization of the instability is confirmed by analysis of the plasma oscillations for various values of H. The disintegration of the plasma is determined by the charge exchange of fast ions in the residual gas; the maximum containment time which can be achieved is 0.06 sec for p = 7.10^–9mmHg. A qualitative picture of the plasma density over the radius of the trap is obtained.Translated from Atomnaya Énergiya, Vol. 17, No. 5, pp. 366–375, November, 1964     

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.     

Measurement of neutron emission from Ti and Pd in pressurized D2 gas and D2O electrolysis cells

Experiments using high-efficiency neutron detectors have detected neutron emission from various forms of Pd and Ti metal in pressurized D₂ gas cells and D₂O electrolysis cells. Four independent neutron detectors based on³He gas tubes were used. Both random neutrons (0.05–0.2 n/s) and time-correlated neutron bursts (10–280 n) of 100-s duration were measured using time-correlation counting techniques. The majority of the neutron burst events occurred at –30°C as the samples were warming up from the liquid nitrogen temperature.     

Deformation systems of α-zirconium

The deformation systems of -zirconium iodide have been studied in coarse-grained polycrystalline specimens deformed by upsetting. The orientation of the grains was determined from Laue patterns obtained in a special back-reflection camera using a small-diameter beam. The indices of the deformation systems were determined by the two-surface method and by the pole locus method.It was found that -zirconium is deformed by slip along the plane in the direction and along the plane. A number of twinning systems have been discovered In -zirconium: a) K₁ , 1 , K₁ , ₂ and s=0.173; b) K₁ , ₂ [1126], K₂ (0001), ₂ [1120] and s=0.629; c) K₁ (1122), ₁ [1123] and in one case, d) K₁ , ₁ .     

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.     

The Oxygen to Carbon Ratio in the Solar Interior: Information from Nuclear Reaction Cross-Sections

Mass separation in the Sun may explain a serious difficulty that has plagued nuclear astrophysics for decades: Why the oxygen to carbon ratio in the Suns photosphere is only two, O/C 2. After correcting for mass fractionation, the ratio of these helium-burning products in the Sun is much larger, O/C 9–10. The lower value, O/C 9, is probably more reliable. It is based on measurements of mass separation of stable noble gas isotopes in the solar wind over the mass range of 3–136 amu. The higher value, O/C 10, is based on a comparison of neutron-capture cross-sections and the abundances of s-products in the photosphere over the mass range of 25–207 amu. Both methods indicate that Fe, Ni, O, Si, and S are the most abundant elements in the Sun. These elements are produced in the deep interior of supernovae.     

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.     

Analysis of the composition of a mixture of249Bk+249Cf on the basis of x rays

Conclusion The results of the study enable us to conclude the following: the decay of²⁴⁹Bk is accompanied by an L series of x rays from the daughter product Cf. The yield of this radiation is low: (L+L+ L) 10^–4 ( disintegration)^–1, but because of the high specific activity of²⁴⁹Bk, 1 g of this isotope emits 3.7·10⁵ x-ray quanta per minute. This enables us to detect a fairly small amount of Bk (0.01 g) on the basis of x rays in a period of 5–10 min. The rapid accumulation of the daughter product²⁴⁹Cf does not interfere with the determination of the²⁴⁹Bk on the basis of x rays. Even when the mixture contains equal numbers of Bk and Cf nuclei, the ratio of the L lines corresponding to them is 0.46. Therefore the composition of a mixture of²⁴⁹Bk+²⁴⁹Cf can be determined on the basis of x rays over broad ranges of variation of the relative concentrations of Bk+Cf, roughly from 0.03 to 80. It is important to note that for relative measurements it is not necessary to prepare special specimens, since x rays with energies of 15–20 keV are not strongly absorbed in the solution and in the walls of the chemical vessel.Translated from Atomnaya Énergiya, Vol. 48, No. 2, pp. 106–108, February, 1980.     

Immobilization of Radionuclides in Irradiated Reactor-Graphite Blocks

The immobilization of radionuclides in samples of GR-280 reactor graphite by the fixative atomik is described. A graphite block extracted from RBMK masonry after 17 years of operation is used for the investigations.The investigations showed that the strength of the fixative samples increases only with irradiation doses above 15000 Mrad. The radiation–chemical yield of gaseous products of radiolysis from samples of the fixative under irradiation in vacuum is 12·10^–10 cm³/(g·rad). , , and -emitting nuclides are leached from the samples of irradiated graphite; this process proceeds continually. When the irradiated graphite samples are permeated with the fixative atomik, no release of radionuclides is observed at 20°C for 2 yr.     

A performance comparison of lithium,helium, and flibe cooled tube/header fusion blankets

The objective of this study is to provide a comparison of thermal-hydraulic and structural performance of lithium, helium, and flibe cooled fusion blankets based on a tube/header geometry in a liquid lithium breeder. Type 316 stainless steel and TZM are considered as representative near-term and long-term, high temperature blanket structural materials, respectively, to show the potentials of each coolant. The flibe-TZM system has the best characteristics, while lithium-316SS, helium-316SS, and helium-TZM are comparable but definitely more limited in operating conditions. These results suggest that molten salt-refractory metal systems deserve more attention.Nomenclature a radial direction half-width of region cooled by single tube (m) - A A=_st/_cD - A _w first wall area (m²) - b azimuthal half-width of region cooled by single tube (m) - B magnetic field strength (T) - C _p specific heat of coolant (J/kg-°C) - C ₁ pumping power ratio - D _h ,D _t header and cooling tube diameter (m) - E _F energy deposited in the blanket region per fusion neutron, determined from neutronic calculations; 15.2 MeV used in this study - F _c allowance factor in pressure loss calculations for lithium system - h heat transfer coefficient (W/m²-°C) - Ha Hartmann number,Ha=BD _c /gm - J the ratio of percent change of first wall loading to percent change of a design parameter - K _c ,K _Li,K _s thermal conductivity of coolant, lithium, and structure (W/m-°C) - L major on-axis circumference of reactor (m) - M blanket energy multiplication factor,M=E _F /14.1 - n number of coolant tubes per header - N number of blanket modules (or headers) azimuthally - N _t total number of coolant tubes - Nu Nusselt number,Nu = hD_t/K_c - P coolant pressure (Pa) - P header and total pressure loss (Pa) - P _r Prandtl number - q _w first wall neutron energy loading (W/m²) - q average volumetric heat generation rate in the blanket (W/m³) - q(r) volumetric heat generation rate in blanket (W/m³) - r radial distance from first wall (m) - r _e radial position of the tube close to the hottest spot in the lithium pool - R gas constant - R _w first wall radius (m) - S defined by Eq. (25) - t _t ,t _h coolant tube and header tube thickness (m) - ¯T average coolant temperature (°C) - T _in inlet temperature (°C) - T _Li,max maximum lithium pool temperature (°C) - T _w,max maximum tube temperature (°C) - T _c coolant temperature rise across blanket (°C) - T _F film temperature rise (°C) - T _m temperature rise between coolant tube and maximum in pool (°C) - T _w wall temperature rise (°C) - U _h coolant velocity at header inlet for lithium system (m/s) - U _t coolant velocity in coolant tubes (m/s) - U _h ,max maximum inlet velocity for the lithium system, given by Eq. (13) - W _s surface heat flux in coolant tube (W/m²) - V _m voltage drop across the tube in flibe system (V) - V _t total blanket volume (m³) - X axial length of coolant tubes (m) - X _e entry and exit tube length in flibe system (m) - Z radial thickness of blanket (m) - _c , _s fraction of blanket volume occupied by coolant and structural material (exclusive of header region) - ratio of the minimum value ofq(r) to q, 0.4 - coolant viscosity (kg/m-s) - fiction coefficient - coolant density (kg/m³) - _t tube density (m^–3) - _c , _s electrical conductivity of coolant and structure (1/-m) - _h hoop stress (Pa) - _y structural material design yield stress limit (Pa)     

Equilibrium and stability of plasma in axially symmetric toroidal systems

Conclusions In the case when the magnetic surfaces have circular normal cross sections in the neighborhood of a magnetic axis (=1), the stability criterion reduces to a limitation on the ratio of the current density to the magnetic field on the magnetic axis j₀R/B₀<2. On the assumption of a uniform axial current, this criterion is equivalent to the Shafranov-Kruskal stability condition RB (a)/aB(a)<1/m for the first mode of oscillation m=1. If the current density falls off on going away from the magnetic axis, the stability criterion when written in the form of the Shafranov-Kruskal condition will correspond to m>1. For example, in the case of the parabolic current density distribution j=j₀ (1–₂/a ²), it turns out that m=2.To investigate the effect of the ellipticity of the magnetic surface cross sections, a study was made of the two cases when the external magnetic surface had an elliptical or semielliptical cross section. As can be seen from Figs. 2 and 4, the limiting value of j₀R/B₀ decreases rapidly when the semi-axis ratio is decreased below unity and decreases more smoothly when is increased above unity: (=l _z/l _r).In the case when toroidal aspects of the problem are very strongly expressed, when the external boundary of the plasma has a semi-elliptical cross section with a semi-axis ratio =1/2 (which corresponds to =1), the limiting ratio of the axial current in the plasma to the current in the windings of the solenoid producing the axial magnetic field amounts to J/I1/3, which corresponds to a ratio of plasma pressure to magnetic pressure 1/2.To investigate the effect of the toroidal geometry on the stability, we also investigated the case of a plasma torus in which the external magnetic surface was of rectangular cross section. As can be seen from Fig. 6, in the case when the axial magnetic field decreases on moving away from the magnetic axis (b/a>0) the limiting value of the ratio N=j₀R/B₀ is reduced somewhat with increasing toroidality, this reduction in N being associated with a corresponding increase in .In summary, as far as the conditions of hydromagnetic stability for a prescribed magnetic field are concerned, an increase in toroidality should lead to an increase in the limiting plasma current and pressure.Translated from Atomnaya Énergiya, Vol. 24, No. 5, pp. 453–459, May, 1968.     

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.     

Monitoring the radiation conditions in reactors by semiconductor spectrometry methods

Conclusions 1. Semiconductor spectrometry of the radiation facilitates the analysis of the radiation conditions in nuclear reactors for power generation and research:identification of the radiation sources (radionuclides, nuclear reactions); andquantitative determination of the intensity of the radiation from the identified radionuclides and from nuclear reactions in units of H.2. The information makes it possible to determine the origin of the radioactive contamination by man-made radionuclides on industrial sites and the degree of radionuclide migration and allows a comparison of the radiation conditions on inspected objects.3. The total H values of the monoenergetic radiation do not exceed 25% of the maximum admissible amounts in the reactor halls inspected [4].Translated from Atomnaya Energiya, Vol. 68, No. 5, pp. 385–386, May, 1990.     

Some comments on energy and particle confinement in advanced fuel EBT reactors

Results of a point model calculation for advanced fuel (cat. D and D³He) EBT reactors are used to determine some of the limitations on the ratio of ion particle to energy confinement time. The greater fraction of charged fusion products produced in the advanced fuel reactions and the greater fraction of their energy radiated cause the effect of on ash buildup to be a factor of 4 greater for the advanced fuels than that of DT fuel. Hence it is found that<5 for steady state ignited advanced fuel EBT reactors, whereas 22 is the restriction for DT fueled EBT reactors. A survey of for neoclassical bumpy torus ions reveals that in the plateau regime,<5 appears possible but is critically dependent on the nature of the electric field.     

The reversed-field-pinch (RFP) fusion neutron source: A conceptual design

The conceptual design of an ohmically heated, reversed-field pinch (RFP) operating at 5-MW/m² steady-state DT fusion neutron wall loading and 124-MW total fusion power is presented. These results are useful in projecting the development of a cost effective, low-input-power (206 MW) source of DT neutrons for large-volume (10 m³), high-fluence (3.4 MW yr/m²) fusion nuclear materials and technology testing.Work supported by U.S. DOE.