Dosimetry of Fission Neutrons and Gamma-Rays from Nuclear Reactors by Paired Fricke Solutions

It is found that the heavy-water Fricke solution showed lower sensitivity to fission neutrons (G-value of 3.7) but higher sensitivity to γ-rays (G=16.3) than the light-water Fricke solution (G=5.6 for neutrons; G=15.4 for γ-rays). Using these differential G-values of the paired solutions and the basic principles of Fricke dosimeter, the following paired equations were derived for the heavy-water and the light-water solutions that were exposed to neutron-gamma mixed radiation; D_N =1,400A–1,200A′ and D_G=460A′–270A, where D_N and D_G are the absorbed doses of neutrons and γ-rays in the light-water solution, respectively, and A and A′ are absorbance increases in the light-water and the heavy-water solution, respectively. The validity of the paired equations was tested by exposure of the paired solutions to the mixed fields of nuclear reactors at Kinki University and Musashi Institute of Technology. Obtained pairs of D_N and D_G values agreed reasonably well with those measured by paired ionization chambers.     

Utilizing RF Electric Field for Injection-Trapping High Energy Molecular Ions in Mirror Field, (I)

A method of using rf electric field in a device for high-energy injection is described, and the behavior of the molecular ions injected into a system combining rf and DC magnetic fields is investigated by calculation and observation.

In this method, some of the injected molecular ions are decelerated by the rf field, and trapped in a small region between the mirror fields, where they are dissociated by collision with the background gas or with the plasma particles, and are thus trapped in the form of atomic ion. The relation between the rf frequency ω and the Larmor frequencies ΩN⁺ ₂, ΩN⁺ ₁ is given by ω=N/2· ΩN⁺ ₂=N/4· ΩN⁺ ₁, where N is the number of rf electrodes. The number N is chosen so that N/2 is an integer and N/4 a non-integer.

Calculation shows that the ions injected in a certain favorable phase are stably decelerated despite their initially possessing a precessional motion. This is proven by observation of actual electron behavior.     

Significance of Ionization-Track Contribution to Self-Quenching Streamer (SQS) Formation Induced by Alpha-Rays

Positive-parity collective band structures of low-lying levels in even-even actinide nuclei were analyzed based on an extension of the Davydov-Chaban soft rotator model, which accounts for the rotation and β- and γ-vibrations of even-even nuclei with non-axial quadrupole deformation. The parameters to reproduce the 4-bands, i.e., the ground-state rotational band, the K≈2 band, and the n _β=1 and n _γ=l bands, were obtained, and their systematic trends were deduced. Based on this result the unassigned band having a sequence of 0⁺, 2⁺, 4⁺,…, which is observed in many actinide nuclei, was assigned likely to be the n _β=1 band. The systematic trends of the parameters found in this work could be a guide to estimate the collective band structure of nuclei for which such data are poorly known. The correct assignment of collective levels was found to be important for the calculation of neutron inelastic scattering cross sections.     

The thermal neutron induced fission cross-section of Am

The σ(n_th,f) of ²⁴³Am has been measured using the cold neutrons with a 25 K Maxwellian distribution available at the Grenoble high flux reactor. Surface barrier detectors recorded the fission fragments. A value of σ(n_th,f) = (198.3 ± 4.2)mb was obtained for ²⁴³Am relative to σ(n_th,f) = (582.2 ± 1.3)b for ²³⁵U.     

Investigation of physico-mechanical properties of ceramic oxide kernels for nuclear applications

In the present work, two different classes of oxide kernels were investigated: unirradiated thoria, urania and (Th,U)O₂ fuel kernels and low-density Al₂O₃ kernels for the incorporation of minor actinides. The physical mechanism of oxide kernel failure under uniaxial compression was investigated. A new method for determining the physico-mechanical properties of kernels has been developed and the parameters P_S and δ, characterising the level of stress required for destruction of the material structure and the brittleness of the investigated materials, respectively, were evaluated and discussed. It was shown that the value of P_S is analogous to traditional characteristics of material such as microhardness Hv. The `quantisation' effect was revealed in the kernel crushing strength and deformation distributions. The physico-mechanical properties of ceramic kernels (average particle size, microstructure, phase state, density, P_S and δ) were investigated and comparative analysis of different kernel types was performed. Additionally, the impact of annealing time on the properties of low-density Al₂O₃ kernels was examined.     

Multi-group unified nodal method with two-group coarse-mesh finite difference formulation

The one-node kernels of the unified nodal method (UNM) which were originally developed for two-group (2G) problems are extended to solve multi-group (MG) problems within the framework of the 2G coarse-mesh finite difference (CMFD) formulation. The analytic nodal method (ANM) kernel of UNM is reformulated for the MG application by adopting the Padé approximation to avoid the similarity transform required to diagonalize the G × G buckling matrix. In addition, a one-node semi-analytic nodal method (SANM) kernel which is considered adequate for multi-group calculations is also integrated into the UNM formulation by expressing it in the form consistent with the other UNM kernels. As an efficient global solution framework, the 2G CMFD formulation with dynamic group condensation and prolongation is established and the performance of the various MG kernels is examined using various static and transient benchmark problems. It turns out that the SANM kernel is the best one for MG problems not only because it retains accuracy comparable to MGANM with a shorter computing time but also because its accuracy or its convergence does not depend on the eigenvalue range of the buckling matrix of the system. The 2G CMFD formulation with MG one-node UNM kernels turns out to be very effective in that it conveniently accelerates the MG source iteration.     

Enrichment of 6Li by Ion Exchange

Elementary solutions to the energy-dependent Boltzmann equation with a one-term degenerate scattering kernel are derived in plane geometry, and the weight function W (z) is obtained which makes these solutions mutually orthogonal over the half-range interval of the continuum. The weight function greatly facilitates determination of the expansion coefficients in general solutions and is applied to the problems in infinite half space.

The diffusion length (discrete space eigenvalue) υ₀ is exactly expressed by using the halfrange characteristic function X(z). In a 1/υ-absorbing medium, as the absorption concentration q increases from zero to a critical value g^*, the diffusion length decreases from infinity to the end of the continuum 1/σ_min. For q≥q^*, v₀ vanishes and the neutron density can be represented by the transient term alone, whose exact expression is obtained.     

Estimation of Neutronic Performance in a Hybrid Reactor with Regression Analysis

This study presents regression analysis method used for prediction and investigation of neutronic performance in a hybrid reactor using UO₂ fuel and Flibe (Li₂BeF₄) coolant. The ²³⁵U fraction is increased gradually from 0 to 4% stepped by 1% and the ⁶Li fraction within the Flibe coolant is enriched gradually to 30, 60 and 90% from 7.5%. Relations between ²³⁵U fuel fraction and lithium (⁶Li) enrichment are investigated for the estimation of neutronic performance as the tritium breeding ratio (TBR), energy multiplication factor (M), total fission rate (Σ_f), ²³⁸U (n,γ) reaction and fissile fuel breeding (FFB) in the hybrid reactor. Regression analysis by results obtained by using the code (XSDRNPM/SCALE5) for TBR, M, Σ_f, ²³⁸U (n,γ) and FFB are performed. The results of the regression analysis and the values obtained by using the code (XSDRNPM/SCALE5) are compared with respect to the TBR, M, Σ_f, ²³⁸U (n,γ) and FFB of the reactor. The values calculated from the obtained formulations with regression analysis are found to be in good agreement with results obtained by using the code (XSDRNPM/SCALE5). It is observed that the derived equations from regression analysis could provide an accurate computation of the neutronic performances so that these equations could use for the prediction of TBR, M, Σ_f, ²³⁸U (n,γ) and FFB. In addition, correlation matrix is calculated to determine the degree of relationship between variables as TBR, M, Σ_f, ²³⁸U (n,γ) and FFB.     

Cross sections for the photoionization of with the formation of , and vibrational overlaps and R-centroids for the associated vibrational transitions

Cross sections for the photoionization of , initially in vibrational levels v_i = 0–14, with the production of in vibrational levels v_f = 0–18 are tabulated for the full vibrational array at 24 photon wavelengths ranging from 912 Å to 450 Å. The associated vibrational overlap integrals v_ifv_f and R-centroids, v_i|Rⁿ|v_f/v_i|v_f, N = 1 and 2 are also presented together with accurate curve fits of the bound-free (H₂-H₂⁺ + e) electronic matrix elements.     

Verification of rod safety via confidence intervals for a binomial proportion

The probabilistic safety assessed to a set of N fuel rods assembled in one core of a nuclear power reactor is commonly modelled by ∑_i≤N X_i, where X₁, …, X_N are independent Bernoulli random variables (rv) with individual probability p_i = P (X_i = 1) that the ith rod shows no failure during one cycle. This is the probability of the event that the ith rod will not exceed the failure limit during one cycle. The safety standard presently set by the German Reaktor-Sicherheitskommission (Reactor Safety Commission) requires that the expected number of unfailed rods in the core during one cycle is at least N − 1, i.e., E(∑_i≤N X_i) = ∑_i≤N p_i ≥ N − 1, whereby a confidence level of 0.95 for the verification of this condition is demanded. In this paper, we provide an approach, based on the Clopper–Pearson confidence interval for the proportion p of a binomial B(n, p) distribution, how to verify this condition with a confidence level of at least 0.95. We extend our approach to the case, where the set of N fuel rods is arranged in strata, possibly due to different design in each stratum.     

The Uranium-Carbon-Nitrogen System

In the previous work⁽¹⁾ dealing with the equilibrium phase relations in the ternary system U-C-N, a qualitative phase diagram was constructed from thermodynamical calculations and experiments. In the thermodynamical calculations, it was assumed that the free energy of formation of the solid solution between UC and UN, i.e., UC_1-x N _x , is the sum of (1-x)ΔG ⁰(UC), xΔG ⁰ and a term for the entropy of mixing RT{x logx+(1-x)log(1-x)}, neglecting the heat of mixing.

The purpose of the present work is to consider the same U-C-N system statistico-thermodynamically, and to evaluate the heat of mixing from the results of several experiments. A value of about ?1.3 kcal/mole was obtained as the heat of mixing corresponding to {2φ(C-N)-φ(C-C)-φ(N-N)}N, where φ(C-N), φ(C-C) and φ(N-N) are the bond energies of C-N, C-C and N-N respectively.     

A measurement of the Li(n,α) cross-section

The relative shape of the ⁶Li(n,α)/²³⁵U(n,f) cross-section ratio has been determined in the range of incident neutron energy from 2 to 800 keV. The measurements were made by the time-of-flight method using the Harwell 45 MeV linac to provide the pulsed source of neutrons. A thin ⁶Li-glass scintillator was used to register the (n,α) events, and the (n,f) events (in a metallic sample of ²³⁵U) were registered with fission neutron detectors. The shape of the ⁶Li(n,α) cross-section was obtained by combining the measured ⁶Li(n,α)/²³⁵U(tn,f) cross-section ratio with an evaluation of the ²³⁵U(n,f) cross-section. The cross-section so derived was placed on an absolute scale by normalization in the neutron energy interval 2–10 keV, where the ⁶Li(n,α) cross-section is accurately known. The cross-section at the peak of the prominent p-wave resonance near 240 keV is found to be 3.29 ± 0.12 b. The results are compared with other measurements and also with a recent theoretical calculation of the cross-section.     

Simplified method to evaluate upper limit stress intensity factor range of an inner-surface circumferential crack under steady state thermal striping

Simplified method to evaluate the upper limit stress intensity factor (SIF) range of an inner-surface circumferential crack in a thin- to thick-walled cylinder under steady state thermal striping was considered in this paper. The edges of the cylinder were rotation-restrained and the outer surface was adiabatically insulated. The inner surface of the cylinder was heated by a fluid with constant heat transfer coefficient whose temperature fluctuated sinusoidally at constant amplitude ΔT. By combining our analytical temperature solution for the problem and our semi-analytical-numerical SIF evaluation method for the crack, we showed that the desired maximum steady state SIF range can be evaluated with an engineering accuracy after ΔT, the mean radius to wall thickness ratio r_m/W of the cylinder, the thermal expansion coefficient and Poisson's ratio are specified. By applying our method, no transient SIF analysis nor sensitivity analysis of the striping frequency on the SIF range is necessary. Numerical results showed that our method is valid for cylinders in a range of r_m/W = 10–1.     

A simple method for estimating the structure temperatures and the cesium revaporization inside the reactor pressure vessel – II: Feasibility study for the Fukushima Daiichi Nuclear Power Plant

The present article is the second part of a two-part article, examining the feasibility of the method proposed in the preceding part. In this method, the ratio of the core uncovered from water x _u, the ratio of the core flooded by water x _f, the ratio of the core slumped into the pedestal area of the drywell x _s, and the ratio of the injected water leaking before reaching the core x _wl are the four important uncertain parameters. The base case study shows that water injection via the core spray line is more effective to cool the uncovered core and to reduce the amount of cesium hydroxide (CsOH) released from the drywell. The sensitivity study is conducted by introducing the dimensionless decay heat N _qd, which combines the effects of x _f, x _s, and x _wl on the steam generation rate associated with the forced convection cooling in the reactor pressure vessel (RPV). The results show that the temperatures of the uncovered core and the other structures increase with N _qd. Consequently, the release rate of CsOH also increases with N _qd. The relationships of the measurable RPV wall temperature with the temperatures of the uncovered core and the structures as well as the release characteristics of CsOH are also examined.     

Change of Composition of UC1-xNx in Nitrogen Gas

The UC-UN solid solution, UC_1-xN_x, exists stably in monophase within a certain range of nitrogen pressure at constant temperature. At the upper limit of this range, UC_1-xN_x, coexists with UC₂, or with carbon, and it precipitates metallic uranium at the lower limit which corresponds to the decomposition pressure of UC_1-xN_x.

In order to measure the decomposition temperature of UC_1-xN_x with given x under constant nitrogen pressure, it is necessary to heat UC_1-xN_x without changing its composition, at a constant pressure.

In the present work, preliminary considerations have been given to change in composition. Experiments were also performed in which the solid solution was heated at a rate of 200°C/min under different nitrogen pressures.

From the results, it is concluded that there exists a temperature range within which the value of x in UC_1-xN_x, is maintained constant when the nitrogen pressure is fixed.     

2D crack growth simulation with an energetic approach

It is well known that the tearing resistance curve J–Δa is not a material property. A recent approach, based on an energetic critical parameter to model ductile tearing propagation, is used to model 3D effects. The approach considered in this work aims to estimate the dissipated energy in the fracture process during ductile tearing represented by an intrinsic parameter G_fr. A fracture criterion, which accounts for the crack extension length, is defined and lies on a critical energy release rate, noted G_c, which is compared to G_fr. Previously, this parameter was obtained from a numerical local energy release rate, which handicaps the application field of the approach: a fine mesh for the whole propagation area was needed and the criterion allowed only to model 1D propagation. A new manner to estimate G_c is then proposed in this article, based on the J plastic part variation, which allows to model 2D propagation by defining a local criterion. This new calculation method is validated on a CT specimen made in Tu52b ferritic steel, by comparing the results obtained from the two methods of G_c calculation. Then, the 2D crack growth case is studied, by modelling the propagation in a ring, loaded in compression. It is shown that a 3D effect, such as tunnel effect, could be successfully represented with this approach.     

Solvent Extraction of Pentavalent Neptunium with n-Octyl(phenyl)-N,N-Diisobutyl- carbamoylmethylphosphine Oxide

Solvent extraction of Np(V) from HNO₃ solution was experimentally studied with n-octyl(phenyl)-N, N-diisobutylcarbamoylmethylphosphine oxide (CMPO) as an extractant mixed with TBP and n-dodecane. In the low HNO₃ concentration, the Np(V) is weakly extractable, but effectively extracted in the high HNO₃ concentration (>4M) due to the disproportionation of Np(V) to Np(IV)and Np(VI). The distribution ratio of Np was increased by use of H₂O₂as a reductant of Np(V). More than 95% of Np was extracted with 0.8 M H₂O² in 2.2 M HNO₃ solution. It was shown that most of the Np extracted is in tetravalent state as expected from redox mechanism. The Np(IV) extracted in the organic phase was effectively stripped to the aqueous phase with H₂C₂O₄.     

Secondary ion emission from stainless steel and inconel due to hydrogen ion bombardment

Secondary ion emission from stainless steel 304 and inconel 625 resulting from the impact of H⁺, H₂⁺, and H₃⁺ at 5 keV is studied and secondary ion energy distributions for Fe⁺, Cr⁺, Ni⁺, CrOH⁺ and FeOH⁺ are reported. For the metallic bulk ions, the energy distribution, N⁺(E), is described by the random collision cascade model modified by the probability of charge transfer in the surface region: N⁺(E) = CEⁿ⁺¹ (E + E_b)⁻³, where E_b is the sublimation energy, and n describes the charge transfer in the surface region. This model does not describe N⁺(E) for the hydroxyl ions or for the metallic bulk ions at non-normal emission from a heavily contaminated surface. The results are also discussed with reference to magnetic fusion energy devices.     

Natural convection heat transfer from horizontal rod bundles in liquid sodium. Part 2: Correlations for horizontal rod bundles based on theoretical results

Natural convection heat transfer from horizontal rod bundles in N_xm × N_ym arrays (N_xm, N_ym = 5–9) in liquid sodium was numerically analyzed for three types of the bundle geometry (in-line rows, staggered rows I and II). The unsteady laminar two-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady state. The PHOENICS code was used for the calculation considering the temperature dependence of thermophysical properties concerned. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, R_f, ranging from 0.0637 to 63.1 (q = 1×10⁴ to 7×10⁶ W/m²). S_x/D and S_y/D for the rod bundle, which are the ratios of the distance between center axes on the abscissa and the ordinate to the rod diameter, respectively, were ranged from 1.6 to 2.5 on each bundle geometry. The spatial distribution of Nusselt numbers, Nu, on horizontal rods of a bundle was clarified. The average value of Nusselt number, Nu_av, for three types of bundle geometry with various values of S_x/D and S_y/D were calculated to examine the effect of the array size, S/D and R_f on heat transfer. The bundle geometry for the higher Nu_av value under the condition of S_x/D×S_y/D = 4 was examined by changing the ratio of S_x/S_y. A correlation for Nu_av for the three types of bundle geometry above mentioned including the effects of S_x/D and S_y/D was developed. The correlation can describe the theoretical values of Nu_av for the three types of bundle geometry in N_xm × N_ym arrays (N_xm, N_ym = 5–9) for S_x/D and S_y/D ranging from 1.6 to 2.5 within 10% difference.