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Banner Highlight for Structure-Dependent Doppler Broadening Using a Generalized Thermal Scattering Law [DOI 10.3390/jne2020013].
Traditional Doppler broadening methods assume that target nuclei velocities follow a Maxwell-Boltzmann distribution which inherently assumes that the atoms are a free gas or that their velocities are independent of each other. This approximation is reasonable at high target temperatures and high neutron energies. However, nuclei are not independent: the lattice temperature and chemical binding will define the atomic motion. The thermal scattering law (i.e., TSL or S(α,β)) is a material property which describes the chemical binding and temperature response in terms of available momentum and energy states. In the thermal energy range, this TSL will define the thermal scattering cross sections. In the resonance region, the TSL offers a first-principles description of the probability distribution function for the velocity of the target nuclei. Using the TSL in Doppler broadening captures the structure of the material consistently from the thermal range into the resonance cross sections. In this work, both traditional free-gas and precise TSL Doppler broadening methods for resonance cross section evaluation have been implemented within the Full Law Analysis Scattering System Hub (FLASSH). This framework provides a generalized formulation for evaluating low-lying resonance data and streamlines nuclear data processing methods. TSL data generated using ab initio lattice dynamics (AILD) can be used to broaden cross section libraries in ENDF format for high-fidelity input into reactor physics calculations. These capabilities are demonstrated for the lowest absorption resonances of {sup 238}U in UO{sub 2}, UC and UN. (authors)
Doppler-broadened gamma ray peaks are observed routinely in the collection and analysis of gamma-ray spectra. If not recognized and understood, the appearance of Doppler broadening can complicate the interpretation of a spectrum and the correct identification of the gamma ray-emitting material. We have conducted a study using a simulation code to demonstrate how Doppler broadening arises and provide a real-world example in which Doppler broadening is found. This report describes that study and its results.
Coincidence Doppler Broadening (CDB) Positron Annihilation Spectroscopy (PAS) is a material analysis technique that can be used to non-destructively measure characteristics of structural defects in samples. Analyzing and comparing large datasets obtained using this technique, however, can be complicated and time intensive. The Coincidence Doppler Broadening Analysis Program (CDB-AP) is a graphical user interface that facilitates rapid analysis of many data files while using transparent processes. It is already used in three laboratories at Idaho National Laboratory and can be used in laboratories worldwide.
A Fast-Doppler-Broadening method is developed in this work to broaden Continuous Energy neutron cross-sections for Monte Carlo calculations. Gauss integration algorithm and parallel computing are implemented in this method, which is unprecedented in the history of cross section processing. Compared to the traditional code (NJOY, SIGMA1, etc.), the new Fast-Doppler-Broadening method shows a remarkable speedup with keeping accuracy. The purpose of using Gauss integration is to avoid complex derivation of traditional broadening formula and heavy load of computing complementary error function that slows down the Doppler broadening process. The OpenMP environment is utilized in parallel computing which can take full advantage of modern multi-processor computers. Combination of the two can reduce processing time of main actinides (such as {sup 238}U, {sup 235}U) to an order of magnitude of 1{approx}2 seconds. This new method is fast enough to be applied to Online Doppler broadening. It can be combined or coupled with Monte Carlo transport code to solve temperature dependent problems and neutronics-thermal hydraulics coupled scheme which is a big challenge for the conventional NJOY-MCNP system. Examples are shown to determine the efficiency and relative errors compared with the NJOY results. A Godiva Benchmark is also used in order to test the ACE libraries produced by the new method. (authors)
Background: The Doppler broadening of gamma-ray peaks is due to nuclear recoil from beta-delayed nucleon emission can be used to measure the energies of the nucleons. This method has never been tested using beta-delayed proton emission or applied to a recoil heavier than A = 10. Purpose: To test and apply this Doppler broadening method using gamma-ray peaks from the P-26(beta p gamma)Al-25 decay sequence. Methods: A fast beam of P-26 was implanted into a planar Ge detector, which was used as a P-26 beta-decay trigger. The SeGA array of high-purity Ge detectors was used to detect gamma rays from the P-26(beta p gamma)Al-25 decay sequence. Results: Radiative Doppler broadening in beta-delayed proton-gamma decay was observed for the first time. Moreover, the Doppler broadening analysis method was verified using the 1613-keV gamma-ray line for which the proton energies were previously known. The 1776-keV gamma ray de-exciting the 2720 keV Al-25 level was observed in P-26(beta p gamma)Al-25 decay for the first time and used to determine that the center-of-mass energy of the proton emission feeding the 2720-keV level is 5.1 +/- 1.0 (stat.) +/- 0.6 (syst.) MeV, corresponding to a Si-26 excitation energy of 13.3 +/- 1.0 (stat.) +/- 0.6 (syst.) MeV for the proton-emitting level. Conclusions: Finally, the Doppler broadening method has been demonstrated to provide practical measurements of the energies for beta-delayed nucleon emissions populating excited states of nuclear recoils at least as heavy as A = 25.
Accurate cross sections are of great importance to Monte Carlo particle transport calculation codes which use pointwise cross sections. It is well known that cross sections have much dependence on temperature on account of Doppler effect which is particularly vital for resonance absorption cross sections. In general, pre-prepared continuous-energy libraries are used in Monte Carlo codes, which is feasible in many applications. However, in multi-physics calculations where neutronics and thermal hydraulics are coupled, cross sections at a fine interval of temperatures are desired, which brings a great challenge to computer memory. Consequently, different methods about on the fly Doppler broadening for cross sections are proposed, which can generate cross sections at the specific temperature points during neutron simulations. These methods can be roughly classified into two categories: one is to calculate the required cross sections by different algorithms, such as interpolation using a high order function expansion, multipole representation, and different integration algorithms based on Doppler broadening equation. The other, for instance, target motion sampling (TMS), does not calculate the Doppler broadening cross sections but takes into account Doppler effect by rejection technique. In this paper, several on the fly Doppler broadening algorithms based on Doppler broadening equation are implemented in the Reactor Monte Carlo code RMC, and then the accuracy and efficiency are discussed and compared. In this paper, several algorithms for on the fly Doppler broadening based on Doppler broadening equation have been implemented in RMC and the focus falls on the comparison of the Gauss Legendre quadrature and Gauss Hermite quadrature. Gauss Legendre quadrature is more accurate than Gauss Hermite quadrature but also more time consuming. Base temperature has a significant impact on Gauss Hermite quadrature while increasing base temperature to room temperature (300 K) can give satisfactory results. In addition, the proportion of overhead of Doppler broadening treatment in total computational time tends to decrease with an increase number of nuclides in fuel. For depletion calculation, both algorithms are in good agreement with reference and the relative errors of K{sub inf} are within 5 times of standard deviation. As for total computational time, the ratio between Gauss Legendre quadrature or Gauss Hermite quadrature and reference decreases and reaches 9.6 or 3.4 at last, respectively. Four important isotopes are chosen to compare the atom density and all relative errors are within 0.25%. After comparisons of different algorithms and different base temperatures, it can be found that Gauss Hermite quadrature broadening from 300 K can perform on the fly cross section Doppler broadening with least total computational time and acceptable precision. (authors)
A new method to obtain Doppler broadened cross sections has been implemented into MCNP, removing the need to generate cross sections for isotopes at problem temperatures. When a neutron of energy E enters a material region that is at some temperature T, the cross sections for that material at temperature T are immediately obtained 'on-the-fly' (OTF) by interpolation using a high order functional expansion for the temperature dependence of the Doppler-broadened cross section for that isotope at the neutron energy E. The OTF cross sections agree with the NJOY-based cross sections for all neutron energies and all temperatures in the range specified by the user, e.g., 250 K - 3200 K. The OTF methodology has been successfully implemented into the MCNP Monte Carlo code and has been tested on several test problems by comparing MCNP with conventional ACE cross sections versus MCNP with OTF cross sections. The test problems include the Doppler defect reactivity benchmark suite and two full-core VHTR configurations, including one with multiphysics coupling using RELAP5-3D/ATHENA for the thermal-hydraulic analysis. The comparison has been excellent, verifying that the OTF libraries can be used in place of the conventional ACE libraries generated at problem temperatures. In addition, it has been found that the OTF methodology greatly reduces the complexity of the input for MCNP, resulting in an order of magnitude decrease in the number of input lines for full-core configurations. Finally, for full-core problems with multiphysics feedback, the memory required to store the cross section data is considerably reduced with OTF cross sections and the additional computational effort with OTF is modest, on the order of 10-15%. (authors)
Doppler broadening refers to the changing of a nuclear cross-section as a response to kinetic energy changes from interaction on a single-nucleus level. Interactions between irradiated particles causes a change in vibration of the nucleus, which is commonly correlated to the overall material's temperature, affecting how irradiate materials interact with additional incident particles. This phenomenon poses unique problems when specifically addressing transient conditions in the Transient Reactor Test Facility (TREAT) at Idaho National Laboratories (INL) because the facility is mainly concerned with in the thermal energy range (velocities beneath 2200 m/s) interacting with a plethora of alloyed metals inserted into the experimental test train slot of the facility. This work investigates the past validation of codes for on-the-fly (OTF) Doppler broadening programs and cross references them with experiments to determine the thermal range and limitations of the TREAT facility for transient conditions. (authors)
A general method of solutions for treating effects of Doppler-broadened Rayleigh backscattering in H2O Differential Absorption Lidar (DIAL) measurements are described and discussed. Errors in vertical DIAL measuremtns caused by this laser line broadening effect can be very large and, therfore, this effect has to be accounted for accurately. To analyze and correct effects of Doppler-broadened Rayleigh backscattering in DIAL experiments, a generalized DIAL approximation was derived starting from a lidar equation, which includes Doppler broadening. To evaluate the accuracy of H2O DIAL measurements, computer simulations were performed. It was concluded that correction of Doppler broadened Rayleigh backscattering is possible with good accuracy in most cases of tropospheric H2O DIAL measurements, but great care has to be taken when layers with steep gradients of Mie backscattering like clouds or inversion layers are present.
With the rapid development of computational power and parallel algorithms, Monte Carlo method has been widely investigated and used in neutron transport simulations due to its advantages in geometry modelling and usage of continuous energy point-wise cross sections. Nowadays the road has been paved to couple Monte Carlo codes with thermal-hydraulics codes to make multi-physics calculations. One of the most important aspects of thermal-hydraulics feedback is the detailed temperature distribution, which demands temperature dependent cross sections in neutron transport simulations. The conventional pre-generated cross section libraries at each temperature point are no longer feasible for detailed temperature distributions because of tremendous memory footprint. Hence, different on-the-fly Doppler broadening methods have been proposed for resolved resonance energy region and thermal energy region, such as the interpolation, regress model fitting, multipole representation (MPR), target motion sampling (TMS) and different integration algorithms based on Doppler broadening equation. Compared to resolved resonance energy region and thermal energy region, the representation of cross sections in unresolved resonance region is slightly different. As a result of the limitation of experiment measurements, the overlapped resonances cannot be distinguished from each other and the statistic average resonance parameters are given in the evaluated nuclear data file. In early applications, infinite-dilute pointwise cross sections were obtained from average parameters and were directly used in neutron simulations. However, it was proven that these infinite-dilute pointwise cross sections cannot capture the energy self-shielding effect, thus leading to an overestimate of reaction rates and usually an underestimate of k{sub eff} owing to the increased absorption rates and increased scattering probability to energy below unresolved resonance region where the capture-to-fission ratio is typically higher. This phenomenon is of great importance especially for problems where there is a considerable flux in unresolved resonance region. Then the probability table method was put forward by Levitt to take energy self-shielding effect into account, which provides probability distribution function of cross sections in unresolved resonance region instead of specific cross section values. The probability distribution function is presented in the form of tables and the mean values are equal to the infinite dilution cross sections. To obtain the temperature dependent cross sections in unresolved energy region, there are two different methods. One is to calculate cross sections directly from average resonance parameters and their statistical distributions , which is effective and precise but time-consuming. The other is to interpolate between pre-generated probability table files, which is much more efficient. In this paper, on-the-fly Doppler broadening of cross sections in unresolved resonance regions based on probability tables interpolation was implemented in RMC codes as a supplement to on-the-fly Doppler broadening for resolved resonance energy region and thermal region, which is based on the integration of Doppler broadening equation. The results of criticality calculation and depletion calculation show that on-the-fly Doppler broadening for the whole energy region is accurate and efficient. (authors)
This paper establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (T j ). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T 0 to a higher temperature T — namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (T j ). The choice of the L 2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (T j ) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [T min ,T max ]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238 U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238 U total cross section over the temperature range [300 K,3000 K] with only 9 reference temperatures.
The University of Michigan, ANL, and LANL have been collaborating on a US-DOE-NE University Programs project 'Implementation of On-the-Fly Doppler Broadening in MCNP5 for Multiphysics Simulation of Nuclear Reactors.' This talk describes the project and provides results from the initial implementation of On-The-Fly Doppler broadening (OTF) in MCNP and testing. The OTF methodology involves high precision fitting of Doppler broadened cross-sections over a wide temperature range (the target for reactor calculations is 250-3200K). The temperature dependent fits are then used within MCNP during the neutron transport, for OTF broadening based on cell temperatures. It is straightforward to extend this capability to cover any temperature range of interest, allowing the Monte Carlo simulation to account for a continuous distribution of temperature ranges throughout the problem geometry.
The multigroup energy Doppler-broadening approximation agrees with continuous energy Dopplerbroadening generally to within ten percent for the total cross sections of 1 H, 56 Fe, and 235 U at 250 lanl. Although this is probably not good enough for broadening from room temperature through the entire temperature range in production use, it is better than any interpolation scheme between temperatures proposed to date, and may be good enough for extrapolation from high temperatures. The method deserves further study since additional improvements are possible.
In conventional transient analysis, thermal hydraulics calculations are generally coupled to deterministic neutronics solvers. Due to the limited accuracy of deterministic methods and the rapid development of computer power, Monte Carlo neutronics calculations have received increasing attention nowadays. One of challenges for Monte Carlo methods coupled to thermal hydraulics calculations is the temperature dependent cross sections. Taking the detailed temperature distribution feedback into account, each nuclide may be in a large range of temperatures, pre-generated libraries at every temperature point are no longer applicable owing to unaffordable memory footprint. Different solutions have been proposed to deal with this problem. TMS, accounting for Doppler broadening effect by the explicit treatment of thermal motion, was used to model fast transients in Serpent 2. Stochastic mixing, using two sets of libraries for each nuclide and mixing them to get the correct temperature, was used in transient analysis by Sjenitzer and Hoogenboom. Besides, there are other on the fly Doppler broadening methods being developed, including series expansion of cross sections, multipole representation, different integration algorithms based on Doppler broadening equation. In this paper, on the fly Doppler broadening treatment based on integration algorithms was applied to transient calculation in Reactor Monte Carlo code RMC . In the following section, the integration algorithms implemented and dynamic simulation method in RMC is briefly introduced. Finally, a pure physical transient fuel assembly model was chosen for numerical validation. (authors)
Legendre moments of a double-differential Doppler-broadened elastic neutron scattering cross section on {sup 238}U are computed near the 6.67 eV resonance at temperature T = 10{sup 3} K up to angular order 14. A covariance matrix of these Legendre moments is computed as a functional of the covariance matrix of the elastic scattering cross section. A variance of double-differential Doppler-broadened elastic scattering cross section is computed from the covariance of Legendre moments.
Multigroup cross sections at a one target temperature can be Doppler-broadened to multigroup cross sections at a higher target temperature by matrix multiplication if the group structure suf- ficiently resolves the original temperature continuous energy cross section. Matrix elements are the higher temperature group weighted averages of the integral over the lower temperature group boundaries of the free-atom Doppler-broadening kernel. The results match theory for constant and 1/v multigroup cross sections at 618 lanl group structure resolution.
In this paper I attempt to document what I have learned and still remember about temperature effects, particularly Doppler broadening, on nuclear data, as it applies to ENDF formatted data. My focus is on the SIGMA1 method of Doppler broadening that I developed over 50 years ago. However, I do realize that there are currently many different methods used in computer codes, and I have tried to keep my discussion general as it applies to ALL of these methods. In particular, ALL of the MYTHS I describe below apply to all Doppler broadening methods: they all solve the parabolic diffusion equation in spherical geometry in (speed, reaction rate) versus temperature. These methods differ only in how the cross section is represented. So, at 85 years old here is what I still remember.