These evaluations are then utilized by computer codes that simulate the macroscopic measurement system under consideration, modeling the system in all necessary detail. These computer codes can be deterministic, but more often employ the Monte Carlo technique of particle transport. In addition to their vital role in the standards and measurement process, such codes find increasing use in radiation protection, medical, industrial and security applications involving dosimetry.

Some existing codes still require users to enter data in older computer languages, such as Fortran.

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Unlike present day computer operating systems, such as the widely used Windows platform, these older codes are less tolerant of errors in data entry and often generate an abundance of data, much of which is not germane to the specific circumstances being modeled. Often times data output has to be transcribed into another program in order to have graphics that clearly illustrate the output of the probability code.

The RT-Office code, for example, has been developed in Eastern Europe which functions on a Windows platform, maintains a database of properties of commonly used materials, and generates easily understood graphics directly. Royalty fees for alleged maintenance of these codes are charged on a single-user basis. Many of these codes have been developed by taxpayer funded efforts, such as those developed at NIST.

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In the computational area, this would facilitate the use of these codes in the teaching environment and broaden the end-user use of mathematical simulation. This would bring the US into line with the practice more common in the European Union where laboratories make codes available upon request. With such a diversity of sources for physical data and for simulation codes, there is a wide variety of applications that make critical use of these methods.

In recent years, modeling was useful in establishing depth-dose profiles for the US Postal Service as it adopted radiation treatment to decontaminate mail from potential biohazards, such as anthrax see Appendix H. Simulations have also been used to study of the possible treatment of high-risk passenger luggage in order to mitigate bioagents and pests. In the radiation therapy field, NIST participated in a study of the dosimetry of beta-emitting brachytherapy sources comparing code results with calibration measurements.

The core barrel is enclosed with the thermal shield between the core barrel and an inner wall of the RPV. In some instances, neutron pads are used in lieu of the thermal shield. The core shroud sets inside the core barrel. An annular downcomer surrounds the reactor core barrel. Cooling fluid, typically water, is circulated into the downcomer. Also shown is a material distribution in the PWR. The model geometry and the mesh discretization are generated using the BOT3P code, version 5.

The model extends from 0. A uniform mesh is applied throughout the model; a mesh size of 2. An Sg level symmetric quadrature set and a P 3 spherical harmonics expansion of the scattering kernel is used for the transport calculations. A system of passive neutron detectors can be installed in the reactor cavity air gap between the reflective insulation and the pressure vessel.

The dosimetry system can provide accurate information relative to the fast neutron exposure over the beltline region of the reactor vessel. Pure metal foils can be installed in the reactor cavity, encased in an aluminum shell, which minimizes distortions of the fast neutron spectrum, effectively yielding a free-field measurement.

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The neutron dosimeters installed in the reactor cavity air gap are not explicitly defined in the transport model. Thus, the resulting set of linear algebraic equations is suitable for solution on a digital computer. The energy domain is discretized using the multigroup approach into a number of discrete intervals, i. The transport equation i. Each discrete direction can be visualized as a point on the surface of a unit sphere with an associated surface area which mathematically corresponds to the weight of the quadrature scheme.

The combination of the discrete directions and the corresponding weights is referred to as quadrature set. In general, quadrature sets must satisfy a number of conditions in order to be accurate and mathematically determined; several approaches can be employed, e. The formulation developed in RAPTOR-M3G is based on the finite difference approach which includes partitioning the spatial domain into computational cells, e. In 3D Carstesian geometry, the angular flux at the cell-center location is evaluated using Eq. Petrovic and A. The angular flux defined at center-cell locations is evaluated starting from boundary conditions or from the boundary angular flux previously calculated in adjacent cells.

The cell-center angular flux is calculated using Eq. The angular flux exiting the computational cell is calculated using additional relationships referred to as the "differencing schemes".

## Computer Techniques in Radiation Transport and Dosimetry | Walter R. Nelson | Springer

This process is continued until an appropriate convergence criterion is satisfied, i. For radiation shielding calculations this cutoff value is generally set to 1. Oe '3 or 1. Oe "4. The local number of octants allocated per processor is given by Eq. The total number of fine meshes along the z-axis, i.

The number of x-y planes assigned to the P s processors is arbitrary; however, the condition in Eq. An uneven partitioning of the x-y planes on the P s processors can lead to processor load imbalance with consequent loss in performance. The hybrid decomposition includes the combination of the angular and spatial domains to include concurrent partitioning of these domains.

Hybrid domain decomposition is further described in the Example 1 below. This embodiment includes obtaining geometrical and material information on the system to be modeled. The information can be obtained from various sources such as but not limited to nuclear reactor drawings. An adequate S N order required for the calculation can then be selected. Further, the P n expansion order to the angular domain i.

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An appropriate differencing scheme i. A cross section table is generated for each material by mixing them with an appropriate data set such as BUGLE The number of processors and the corresponding decomposition strategy is selected for the problem to be solved. The calculation is then performed. Following calculation, postprocessing and analysis of the results generated may occur. In an aspect of the present invention, ex-vessel neutron dosimetry responses are calculated for a cavity in a nuclear reactor vessel. For instance, an aspect of the present invention described herein relates to the nuclear industry and in particular, nuclear reactors.

However, the present invention can also be used in a wide range of other applications such as the medical field. Accordingly, the particular arrangements disclosed are meant to be illustrative only and not limiting as to the scope of the invention which is to be given the full breadth of the appended claims and any and all equivalents thereof. The cluster was composed of 5 nodes with 2 dual-core dual processor AMD Opteron bit architecture.

The cluster total memory, i.

The test problem consisted of 50 x 50 x 50 cm box with a uniform distributed fixed source, discretized with a 1 cm uniform mesh. An S 8 quadrature set and PO isotropic scattering was used, along with a one energy group cross section set. Speed-up and parallel efficiency were defined as in Eqs. N p is the number of processors utilized to achieve the wall-clock time T p. Figure 4 shows a comparison of the speed-up obtained up to 20 processors using different decomposition strategies.

It was believed that this behavior was due to a finer computational granularity per processor; as the space domain was decomposed into smaller sub-domains, the number of operation per processor was reduced while the inter-processor communication time was increased; therefore leading to a reduced performance. The network data transfer among the nodes was generally the limiting factor on distributed memory architectures. The larger number of iterations required to converge the problem further contributed to reduce the performance of the space decomposition strategy.

However, the hybrid decomposition where the angular and spatial domains were concurrently partitioned yielded better results.

It was believed that this behavior was due to the coarser computational granularity induced by this decomposition; also for the hybrid decomposition, the number of iterations required to converge the problem did not increase as much as the space decomposition. Kodeli and A. Initially the calculated dosimetry responses were found to consistently over-predict the measured data.

The measured vs. The corrected RPV thickness using the ISI measurements improved the accuracy of the calculated responses at every dosimetry location. DTW Differencing Scheme. Ref document number : Country of ref document : CN.

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Country of ref document : EP. Kind code of ref document : A1. Country of ref document : JP. Ref country code : DE. Country of ref document : KR. Kind code of ref document : A. The invention relates generally to a method for the calculation of radiation field distributions employing a new parallel 3-D radiation transport code and, a multi-processor computer architecture. The code solves algorithms using a domain decomposition approach.