Subcritical multiplication factor and source efficiency in accelerator-driven system

The subcritical multiplication factor k_s   and the external neutron source efficiency φ^∗${\phi }^{\ast }$ are important parameters in the accelerator-driven system (ADS) performance assessment. The theoretical relation between k_s and the effective multiplication factor k_eff in a subcritical system is discussed in different cases of subcritical system. On the basis of the theoretical background, the dependence of k_s   and φ^∗${\phi }^{\ast }$ on subcriticality, source position, and energy is numerically investigated using a simple thermal subcritical model. For the sake of experimental evaluation of k_s   and φ^∗${\phi }^{\ast }$, the ADS experiments have been carried out in the subcritical systems combined with 14 MeV pulsed neutrons of the Kyoto University Critical Assembly (KUCA). The k_s   and φ^∗${\phi }^{\ast }$ parameters are successfully measured by utilizing the reaction rate distribution obtained by the optical fiber detectors in the subcritical system, within a relative difference of less than 7% and 12% for k_s   and φ^∗${\phi }^{\ast }$, respectively, between measured and calculated values for most studied cases.     

Atomic data and theoretical X-ray spectra of Ge-like through V-like W ions

The atomic structure and spectra of ten tungsten ions have been calculated using the Flexible Atomic Code. The calculations yield energy levels, radiative lifetimes, spectral line positions, transition probability rates, and oscillator strengths for the tungsten ions isoelectronic to germanium, W⁴²⁺${}^{42+}$, through vanadium, W⁵¹⁺${}^{51+}$. Collisional–radiative models for high-temperature, low-density plasmas have been implemented to produce line emissivities for X-ray transitions in the 1–4 keV (3–12 Å) spectral interval. The Ge-like through V-like W ions are important in nuclear fusion research where their spectra may provide diagnostic information on magnetically confined plasmas.     

Oscillator strengths and transition probabilities from the Breit–Pauli R-matrix method: Ne IV

The atomic parameters–oscillator strengths, line strengths, radiative decay rates (A$A$), and lifetimes–for fine structure transitions of electric dipole (E1) type for the astrophysically abundant ion Ne IV are presented. The results include 868 fine structure levels with n≤$n\le$ 10, l≤$l\le$ 9, and 1/2≤J≤$\le J\le$ 19/2 of even and odd parities, and the corresponding 83,767 E1 transitions. The calculations were carried out using the relativistic Breit–Pauli R-matrix method in the close coupling approximation. The transitions have been identified spectroscopically using an algorithm based on quantum defect analysis and other criteria. The calculated energies agree with the 103 observed and identified energies to within 3% or better for most of the levels. Some larger differences are also noted. The A$A$-values show good to fair agreement with the very limited number of available transitions in the table compiled by NIST, but show very good agreement with the latest published multi-configuration Hartree–Fock calculations. The present transitions should be useful for diagnostics as well as for precise and complete spectral modeling in the soft X-ray to infra-red regions of astrophysical and laboratory plasmas.     

Energy levels,wavelengths, and transition rates of multipole transitions (E1, E2, M1, M2) in Au and Au ions

The fully relativistic configuration interaction method of the FAC code is used to calculate atomic data for multipole transitions in Mg-like Au (Au⁶⁷⁺) and Al-like Au (Au⁶⁶⁺) ions. Generated atomic data are important in the modeling of M-shell spectra for heavy Au ions and Au plasma diagnostics. Energy levels, oscillator strengths and transition rates are calculated for electric-dipole (E1), electric quadrupole (E2), magnetic dipole (M1), and magnetic quadrupole (M2) for transitions between excited and ground states 3l−nl^′$3l-n{l}^{\prime }$, such that n=4,5,6,7$n=4,5,6,7$. The local central potential is derived using the Dirac–Fock–Slater method. Correlation effects to all orders are considered by the configuration interaction expansion. All relativistic effects are included in the calculations. Calculated energy levels are compared against published values that were calculated using the multi-reference many body perturbation theory, which includes higher order QED effects. Favorable agreement was observed, with less than 0.15% difference.     

Energy levels and radiative transition rates for Ge XXXI,As XXXII,and Se XXXIII

Fine-structure energies of the 67 levels belonging to the 1s², 1s 2l$l$, 1s3l$l$, 1s4l$l$, 1s5l$l$, and 1s6l$l$ configurations of Ge XXXI, As XXXII, and Se XXXIII have been calculated using the General-Purpose Relativistic Atomic Structure Package. In addition, radiative rates, oscillator strengths, transition wavelengths, and line strengths have been calculated for all electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transitions among these levels. Lifetimes are also presented for all excited levels of these three ions. We have compared our results with the results available in the literature and the accuracy of the data is assessed. We predict new energy levels, oscillator strengths, and transition probabilities where no other theoretical or experimental results are available, which will form the basis for future experimental work.     

Relativistic MR-MP calculations of the energy levels and transition probabilities in Ni- to Kr-like Pt ions

Ni- to Kr-like Pt ions have been studied by relativistic multi-reference Møller–Plesset many-body perturbation theory calculations. Energy levels and lifetimes of low-lying excited states within the n=4$n=4$ complex are reported for each ion. Wavelengths and transition probabilities for the strongest electric-dipole transitions are compared with available experimental data. Synthetic radiative spectra are shown for various wavelength regions.     

On the generalization of the average chord length

Recently, it has been proved that the well-known mean chord length property remains valid for some diffusive processes in bounded domains. Based on the one-velocity linear Boltzmann transport equation, this result can be extended to spaces of constant curvature. Besides, for straight lines, inequalities for the ray distribution (starting point inside the domain and exiting point on the surface of the object) are derived using simple tools from integral geometry in Rⁿ${\mathbb{R}}^n$.     

Optimal discontinuous finite element methods for the Boltzmann transport equation with arbitrary discretisation in angle

This paper describes the development of two optimal discontinuous finite element (FE) Riemann methods and their application to the one-speed Boltzmann transport equation in the steady-state. The proposed methods optimise the amount of dissipation applied in the streamline direction. This dissipation is applied within an element using a novel Riemann FE method, which is based on an analogy between control volume discretisation methods and finite element methods when integration by parts is applied to the transport terms. In one-dimension the optimal finite element solutions match the analytical solution exactly at each outlet node. Both schemes couple elements in space via a Riemann approach. The first of the two schemes is a Petrov–Galerkin (PG) method which introduces dissipation via the equation residual. The second scheme uses a streamline diffusion stabilisation term in the discretisation. These two methods provide a discontinuous Petrov–Galerkin (DPG) scheme that can stabilise an element across the full range of radiation regimes, obtaining robust solutions with suppressed oscillation. Three basis functions in angle of particle travel have been implemented in an optimal DPG Riemann solver, which include the _PN$P_N$ (spherical harmonic), _SN$S_N$ (discrete ordinate) and LW_N${\text{LW}}_N$ (linear octahedral wavelet) angular expansions. These methods are applied to a series of demanding two-dimensional radiation transport problems.     

Calculation of the importance-weighted neutron generation time using MCNIC method

In advanced nuclear power systems, such as ADS, the need for reliable kinetics parameters is of considerable importance because of the lower value for β_eff due to the large amount of transuranic elements loaded in the core of those systems. All reactor kinetic parameters are weighted quantities. In other words each neutron with a given position and energy is weighted with its importance. Neutron generation time as an important kinetic parameter, in all nuclear power systems has a significant role in the analysis of fast transients. The difference between non-weighted neutron generation time; Λ$\Lambda$; standard in most Monte Carlo codes; and the weighted one Λ^†${\Lambda }^{†}$ can be quite significant depending on the type of the system. In previous work, based on the physical concept of neutron importance, a new method; MCNIC; using the MCNP code has been introduced for the calculation of neutron importance in fissionable assemblies for all criticality states. In the present work the applicability of MCNIC method has been extended for the calculation of the importance-weighted neutron generation time. The influence of reflector thickness on importance-weighted neutron generation time has been investigated by the development of an auxiliary code, IWLA, for a hypothetic assembly. The results of these calculations were compared with the non-weighted neutron generation times calculated using the Monte Carlo code MCNP. The difference between the importance-weighted and non-weighted quantity is more significant in a reflected system and increases with reflector thickness.     

Monte Carlo simulation of core physics parameters of the Syrian MNSR reactor

A 3-D neutronic model for the Syrian Miniature Neutron Source Reactor (MNSR) was developed earlier to conduct the reactor neutronic analysis using the MCNP-4C code. The continuous energy neutron cross sections were evaluated from the ENDF/B-VI library. This model is used in this paper to calculate the following reactor core physics parameters: the clean cold core excess reactivity, calibration of the control rod and calculation its shut down margin, calibration of the top beryllium shim plate reflector, the axial neutron flux distributions in the inner and outer irradiation positions and calculations of the prompt neutron life time (_lp$l_p$) and the effective delayed neutron fraction (_βeff${\beta }_{\mathit{eff}}$). Good agreements are noticed between the calculated and the measured results. These agreements indicate that the established model is an accurate representation of Syrian MNSR core and will be used for other calculations in the future.     

A high-order discontinuous Galerkin method for the SN transport equations on 2D unstructured triangular meshes

This paper presents high-order numerical solutions to the _SN$S_N$ transport equation on unstructured triangular meshes using a Discontinuous Galerkin Finite Element Method (DGFEM). Hierarchical basis functions, up to order 4, are used for the spatial representation of the solution. Numerical results are provided for source-driven and eigenvalue problems. Convergence rates (as a function of the mesh size and CPU time) are discussed.     

Riemann boundary conditions for the Boltzmann transport equation using arbitrary angular approximations

In this paper a method for resolving the various boundary conditions (BCs) for the first order Boltzmann transport equation (BTE) is described. The approach has been formulated to resolve general BCs using an arbitrary angular approximation method within any weighted residual finite element formulation. The method is based on a Riemann decomposition which is used to decompose the particles’ angular dependence into in-coming and out-going information through a surface. This operation recasts the flux into a Riemann space which is used directly to remove any incoming information, and thus satisfy void boundary conditions. The method is then extended by its coupling with a set of mapping operators that redirect the outgoing flux to form incoming images resembling other specified boundary conditions. These operators are based on Galerkin projections and are defined to enable reflective and diffusive (white) BCs to be resolved. A small number of numerical examples are then presented to demonstrate the method’s ability in resolving void, reflective and white BCs. These examples have been chosen in order to show the method working for arbitrary angled surfaces. Furthermore, as the method has been designed for an arbitrary angular approximation, both _SN$S_N$ and _PN$P_N$ calculations are presented.     

Sensitivity analysis for delayed neutron data

In this paper a framework is derived based on first order perturbation theory to calculate the sensitivity of a transient in a nuclear reactor to delayed neutron parameters. The approach is based on the Adjoint Sensitivity Analysis Procedure as outlined in Cacuci [Cacuci, D., 2003. Sensitivity and Uncertainty Analysis. Theory, vol. I. CRC Press]. In this paper, the required adjoint system is defined and discussed, and an analytical solution is provided for a simplified case. Application of the ASAP requires that the time-dependent adjoint for neutrons and precursors is solved, and the implementation of such a solver is discussed. Proof-of-concept calculations have been performed for a 0D and a 3D case. It is found that sensitivities for the delayed neutron data are generally low. For increasing transients, the sensitivities increase with reactivity, with the highest sensitivities occuring for the delay groups with largest delayed neutron fraction _βk${\beta }_k$, and for the largest ratio _λk/_βk${\lambda }_k/{\beta }_k$. For decreasing transients, the trends are less clearly defined, with some sensitivities increasing, and others decreasing, for increasingly negative reactivity. The proof-of-concept calculations have shown that the ASAP method yields good accuracy, but especially for 2D or 3D problems the method requires the use of advanced ordinary differential equation (ODE) solvers with built-in sensitivity capabilities, to keep the memory requirements and computational overhead in manageable bounds.