• Journal of Radiation Protection and Research
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• v.32 no.4
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• pp.168-177
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• 2007

A neural network model to evaluate the neutron exposure on the reactor pressure vessel inner diameter was developed. By using the three dimensional synthesis method described in Regulatory Guide 1.190, a simple linear equation to calculate the neutron spectrum on the reactor pressure vessel was constructed. This model can be used in a quick estimation of fast neutron flux which is the most important parameter in the assessment of embrittlement of reactor pressure vessel. This model also used in the selection of an optimum core loading pattern without the neutron transport calculation. The maximum relative error of this model was less than 3.4% compared to the transport calculation for the calculations from cycle 1 to cycle 23 of Kori unit 1.

• Nuclear Engineering and Technology
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• v.4 no.2
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• pp.102-108
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• 1972

Time-dependent neutron transport equation with delayed neutrons is analytic-ally solved in the case of isotropic scattering with constant cross sections. The equations in the two divided time regions are obtained from the original equation by the asymptotic method. It is shown that the approximate solutions in each time region are uniformly valid in time to the order of the inverse magnitude of the velocity.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.16 no.2
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• pp.203-209
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• 2018

To correctly predict the neutron behavior based on diffusion calculations, it is necessary to adopt well-specified boundary conditions using suitable diffusion approximations to transport boundary conditions. Boundary conditions such as the zero net-current, the Marshak, the Mark, the zero scalar flux, and the Albedo condition have been used extensively in diffusion theory to approximate the reflective and vacuum conditions in transport theory. In this paper, we derive and analyze these conditions to prove their mathematical validity and to understand their physical implications, as well as their relationships with one another. To show the validity of these diffusion boundary conditions, we solve a sample problem. The results show that solutions of the diffusion equation with these well-formulated boundary conditions are very close to the solution of the transport equation with transport boundary conditions.

• Nuclear Engineering and Technology
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• v.52 no.3
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• pp.485-498
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• 2020

A diffusion synthetic acceleration (DSA) technique for the S_N transport equation discretized with the linear discontinuous expansion method with subcell balance (LDEM-SCB) on unstructured tetrahedral meshes is presented. The LDEM-SCB scheme solves the transport equation with the discrete ordinates method by using the subcell balances and linear discontinuous expansion of the flux. Discretized DSA equations are derived by consistently discretizing the continuous diffusion equation with the LDEM-SCB method, however, the discretized diffusion equations are not fully consistent with the discretized transport equations. In addition, a fine mesh rebalance (FMR) method is devised to accelerate the discretized diffusion equation coupled with the preconditioned conjugate gradient (CG) method. The DSA method is applied to various test problems to show its effectiveness in speeding up the iterative convergence of the transport equation. The results show that the DSA method gives small spectral radii for the tetrahedral meshes having various minimum aspect ratios even in highly scattering dominant mediums for the homogeneous test problems. The numerical tests for the homogeneous and heterogeneous problems show that DSA with FMR (with preconditioned CG) gives significantly higher speedups and robustness than the one with the Gauss-Seidel-like iteration.

• Nuclear Engineering and Technology
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• v.55 no.7
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• pp.2572-2577
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• 2023

A field determination method for small D-T neutron source yield based on the oxygen prompt gamma rays was established. A neutron-gamma transport equation of the determination device was developed. Two yield field determination devices with a thickness of 20 mm and 50 mm were made. The count rates of the oxygen prompt gamma rays were calculated using three energy spectra processing approaches, which were the characteristic peak of 6.13 MeV, the overlapping peak of 6.92 MeV and 7.12 MeV, and the total energy area. The R-square of the calibration curve is better than 94% and the maximum error of the yield test is 5.21%, demonstrating that it is feasible to measure the yield of D-T neutron source by oxygen prompt gamma rays. Additionally, the results meet the requirements for field determination of the conventional D-T neutron source yield.

• Nuclear Engineering and Technology
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• v.22 no.2
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• pp.151-158
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• 1990

The new discrete elements method (DEM) is applied to the one-group neutron transport equation in one-dimensional slab geometry. The fixed source and the criticality problems are treated and three spatial differencing schemes (the DD, the SC, -and the LC schemes) are tested to determine the most computationally efficient in the DEM. In all cases, the accuracy of the results obtained from the DEM shows an improvement over that obtained from the standard discrete ordinates calculations. And the LC scheme gives the most accurate results in the DEM.

• Nuclear Engineering and Technology
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• v.2 no.4
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• pp.263-268
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• 1970

The spectrum of continuous transfer operator arising in a time-energy dependent neutron transport equation is analyzed. Four theorems concerning on the spectrum are proved. A convolution theorem of the generalized Mellin energy transform is given. Also the completeness theorem necessary for a final solution is proved. A unique time decay constant 1 - c is found, which is dominant asymptotically.

• Proceedings of the Korean Nuclear Society Conference
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• 2002.10a
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• pp.51.2-51
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• 2002

• Nuclear Engineering and Technology
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• v.53 no.12
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• pp.3861-3878
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• 2021

The steady-state simplified spherical harmonics equations (SP_N equations) are a higher order approximation to the neutron transport equations than the neutron diffusion equation that also have reasonable computational demands. This work extends these results for the analysis of transients by comparing of two formulations of time-dependent SP_N equations considering different treatments for the time derivatives of the field moments. The first is the full system of equations and the second is a diffusive approximation of these equations that neglects the time derivatives of the odd moments. The spatial discretization of these methodologies is made by using a high order finite element method. For the time discretization, a semi-implicit Euler method is used. Numerical results show that the diffusive formulation for the time-dependent simplified spherical harmonics equations does not present a relevant loss of accuracy while being more computationally efficient than the full system.

• Proceedings of the Korean Nuclear Society Conference
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• 2004.10a
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• pp.151-152
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• 2004

An acceleration technique combined with the discrete ordinates method which has been widely used in the solution of neutron transport phenomena is applied to the solution of radiative transfer equation. The self-adjoint form of the second order radiation intensity equation is used to enhance the stability of the solution, and a new linearization method is developed to avoid the nonlinearity of the material temperature equation. This new acceleration method is applied to the well known Marshak wave problem, and the numerical result is compared with that of a non-accelerated calculation