A method to determine the planar dose distributions in patient undergone radiotherapy

A 2D-array equipped with 729 vented plane parallel ion-chambers has been calibrated as a portal dose detector for radiotherapy in vivo measurements. The array has been positioned by a radiographic film stand at 120 cm from the source orthogonal to the radiotherapy beam delivered with the gantry angle at 180°. The collision between the 2D-array and the patient’s couch have been avoided. In this work, using the measurements of the portal detector, we present a method to reconstruct the dose variations in the patient treated with step and shoot intensity-modulated beams (IMRT) for head-neck tumours. For this treatment morphological changes often occur during the fractionated therapy.In a first step an in-house software supplied the comparison between the measured portal dose and the one computed by a commercial treatment planning system within the field of view of the computed tomography (CT) scanner. For each patient, the percentage P_γ of chambers, where the comparison is in agreement within a selected acceptance criteria, was determined 8 times. At the first radiotherapy fraction the γ-index analysis supplied P_γ values of about 95%, within acceptance criteria in terms of dose-difference, ΔD, and distance-agreement, Δd, that was equal to 5% and 4 mm, respectively. These acceptance criteria were taken into account for small errors in the patient’s set-up reproducibility and for the accuracy of the portal dose calculated by the treatment planning system (TPS) in particular when the beam was attenuated by inhomogeneous tissues and the shape of the head-neck body contours were irregular. During the treatment, some patients showed a reduction of the P_γ below 90% because due to radiotherapy treatment there was a change of the patient’s morphology.In a second step a method, based on dosimetric measurements that used standard phantoms, supplied the percentage dose variations in a coronal plane of the patient using the percentage dose variations measured by the 2D-array portal detector. The results showed that the dose variations due to the change of the patient’s morphology reached 15% and such discrepancies were displayed on the digitally reconstructed radiography of the patient. The dose discrepancies were confirmed by the hybrid plan obtained by the treatment planning system. The good results here reported show that once it is possible to have the portal dose distributions even for other gantry angles, these tests could be introduced in the clinical protocol to have major support to decide when to repeat the patient’s CT scan and to re-plan the new IMRT dose calculation.     

Optimization method to determine mass transfer variables in a PWR crud deposition risk assessment tool

Optimization numerical method was implemented to determine several mass transfer coefficients in a crud-induced power shift risk assessment code. The approach was to utilize a multilevel strategy that targets different model parameters that first changes the major order variables, mass transfer inputs, then calibrates the minor order variables, crud source terms, according to available plant data. In this manner, the mass transfer inputs are effectively simplified as “dependent” on the crud source terms. Two optimization studies were performed using DAKOTA, a design and analysis toolkit, with the difference between the runs, being the number of model runs using BOA, allowed for adjusting the crud source terms, therefore, reducing the uncertainty with calibration. The result of the first case showed that the current best estimated values for the mass transfer coefficients, which were derived from first principle analysis, can be considered an optimized set. When the run limit of BOA was increased for the second case, an improvement in the prediction was obtained with the results deviating slightly from the best estimated values.     

主动法缓发中子探测金属铀的~(235)U丰度

主动法缓发中子监测U材料被认为是核查技术的有效手段之一.本文建立了特定的模型,以数值模拟D-T中子诱发相同质量、不同~(235)U丰度的金属铀裂变产生的出壳缓发中子及BF_3探测器所能产生的响应,验证了特定情形下主动法D-T中子源诱发金属铀裂变,测量其缓发中子反演~(235)U丰度的可行性.     

Finite integral transform method to solve asymmetric heat conduction in a multilayer annulus with time-dependent boundary conditions

The separation of variables (SOV) method has recently been applied to solve time-dependent heat conduction problem in a multilayer annulus. It is observed that the transverse (radial) eigenvalues for the solution in polar (r-θ) coordinate system are always real numbers (unlike in the case of similar multidimensional Cartesian problems where they may be imaginary) allowing one to obtain the solution analytically. However, the SOV method cannot be applied when the boundary conditions and/or the source terms are time-dependent, for example, in a nuclear fuel rod subjected to time-dependent boundaries or heat sources. In this paper, we present an alternative approach using the finite integral transform method to solve the asymmetric heat conduction problem in a multilayer annulus with time-dependent boundary conditions and/or heat sources. An eigenfunction expansion approach satisfying periodic boundary condition in the angular direction is used. After integral transformation and subsequent weighted summation over the radial layers, partial derivative with respect to r-variable is eliminated and, first order ordinary differential equations (ODEs) are formed for the transformed temperatures. Solutions of ODEs are then inverted to obtain the temperature distribution in each layer. Since the proposed solution requires the same eigenfunctions as those in the similar problem with time-independent sources and/or boundary conditions—a problem solved using the SOV method—it is also “free” from imaginary eigenvalues.     

A method to determine the gamma-ray linear attenuation coefficient

In this work, gamma-ray linear attenuation coefficients of the materials such as Pb, Fe, Cu and Al were determined by means of traditional energy method and the developed timing detection technique. 1.33 MeV-energy radiation emitted from ⁶⁰Co radioisotope was used in the experiments. The gamma-ray linear attenuation coefficient values of the materials were calculated by using Xcom code, and the experimental results were compared with the theoretical ones.     

Neutron kinetics in subcritical cores with application to the source modulation method

The subject of this paper is an investigation of the performance of the so-called source modulation technique for the measurement of reactivity in subcritical, source-driven cores. Methods of measuring reactivity by a single detector, including the source modulation method, are based on the assumption of point kinetic behaviour of the core. Deviations from point kinetic behaviour will lead to an inaccurate estimation of the reactivity. Hence, first, the conditions of point kinetic behaviour in subcritical source-driven cores are revisited. In addition to the known conditions for such behaviour, which have an analogy to those in critical cores, some additional cases are found which only exist in subcritical cores. Then the performance of the source modulation technique is investigated. It is found that the error of the method, originally thought to be due exclusively to the deviation of the local detector signal from the amplitude factor of point kinetics, remains finite and non-zero even in the limit of exact point kinetic behaviour (e.g., with low frequencies or deep subcriticalities). This is demonstrated and explained by analytical formulae. Some remedies for this shortcoming of the method are also suggested and discussed.     

Theoretical Approach to Pseudo-Mode Neutron Waves in a Moderator

An analysis is presented on neutron wave propagation in moderators in the frequency region above the limiting frequency for discrete eigenvalues, and the distribution of the modulated neutrons in the medium is described by integrals over the continua.

When a discrete eigenvalue reaches the edge of a continuum, a singularity appears in the angular distribution of the waves and causes the discrete mode waves to disappear. Further pursuit of the root of the dispersion law making use of the analytic continuation in the angular integral locates the root on a branch of the complex eigenvalue planes that adjoins the principal branch. This root on the adjacent branch can in certain cases bring about a sharp resonance. i.e. a “pseudo-discrete wave eigenvalue” in the continuum. The conditions for the effective excitation of this kind of pseudo-mode wave were examined, which revealed that for this it is essential that the neutrons causing the limiting frequency have a weak coupling and that their injection be light. It was also demonstrated that the distance from source affects the pseudo-discrete eigenvalue.

An application of this analysis to the case of graphite is also presented.     

Finite element program for moisture and heat transfer in heated concrete

A new axisymmetric finite element program for the analysis of pore pressure, moisture content and temperature in heated concrete is described. The program is based on the diffusion equations for coupled heat and moisture transfer and uses a step-by-step time integration. The finite element scheme is based on Galerkin method. For time integration a step-by-step solution with iterations is used. The numerical analysis is complicated by the fact that the sorption isotherms exhibit a steep jump at saturation-nonsaturation transitions, and that the permeability dependence on temperature exhibits a jump of two orders of magnitude at 100°C. The mathematical model takes into account the release of chemically bound water due to dehydration and the associated changes in the pore space. The program may also be used at normal temperatures. Predictions of the program are compared with tests by HEDL as well as two other existing programs.     

反应堆物理实验中的源倍增法研究

给出了反应堆物理实验中临界测量和次临界度测量通常所采用的源倍增方法研究。首先从有源的扩散理论出发,导出了与以前不同的源倍增方法的公式。源倍增方法测量的参数实际是次临界系统在外源作用下的有源次临界中子倍增因子ks,而不是在这之前的中子有效倍增因子keff,然后研究了实验装置的临界质量,研究了ks与外源位置和能谱的关系,证明了导出的源倍增方法的理论是正确的。该方法可像过去那样用于反应堆物理实验中的临界外推测量,但不能用于次临界度测量。解决了长期困扰人们有关源倍增方法测量的参数问题。最后讨论了ks和keff的差别和关系以及对临界外推测量和核临界安全的影响。     

The survival probability of neutrons in supercritical convex bodies using a time-dependent collision probability method

We consider the probability of the survival of the neutron population when one neutron is injected into a supercritical fissile convex body. The formalism developed by Pal and Bell is used and the equations arising for the survival probability are solved by using a time-dependent collision probability technique. In principle, this method can be used for arbitrarily shaped convex bodies. A simple one-region case is seen to lead to reasonably accurate results when compared with the work of Gregson and Prinja [Gregson, M.W., Prinja, A.K., 2008. Time-dependent non-extinction probability for fast burst reactors. Transactions of the American Nuclear Society 98, 533 (Anaheim, CA)]. The calculations are extended to the case where a steady background neutron source is present. The time-dependent, self-collision probabilities are evaluated for slab, sphere and infinite cylindrical geometries. A method due to Lefvert [Lefvert, T., 1979. New applications of the collision probability method in neutron transport theory. Progress in Nuclear Energy 4, 97] for solving time-dependent collision probability equations is shown to give accurate results. The usefulness of diffusion theory to solve this problem is also investigated.     

Measurement of Neutron Life in a D2O-System by Neutron Fluctuation

The neutron life has been determined in a D₂O system by combining observation of the inherent fluctuations which occur in the neutron population and reactivity measurements by period method.

The ratio of variance to mean number of counts was measured as a function of counting intervals. Short counting-time intervals were chosen in the experiment to eliminate contribution of delayed neutrons. Also, the variance was measured in the subcritical state, to eliminate the counting loss due to the dead time of the detector.

The decay constant for the critical state has been determined by extrapolation of the observed relation between the decay constant and reactivity.