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At least 253 records · Page 14

Evaluation of Polyethylene and Blank Pulsed Sphere Experiments Using Deuteron Transport Feature in COG

From the late 1960s to about 1985, LLNL undertook a series of ‘pulsed sphere’ experiments for 31 materials involving 148 different experiments using 75 different spheres. The purpose was to measure the neutron leakage spectra for different materials from 14-MeV neutrons generated by 3 H(d,n) 4 He reactions induced by an incident D+ beam from the Insulated Core Transfer (ICT) accelerator at LLNL. This deuteron beam was focused to impinge upon tritium loaded onto a titanium substrate within a low mass target assembly placed within the center of a spherical shell constructed from the material of interest. COG is a three-dimensional, continuous energy, Monte Carlo code, developed by Lawrence Livermore National Laboratory (LLNL). Recent additions to COG include alpha and deuteron particle transport in order to directly calculate (α,n) and 3 H(d,n) 4 He reactions, and resulting neutron emission spectra. Results of the direct deuteron transport calculation for the 0.8 MFP (mean free path) polyethylene sphere with PILOT B detector was previously published. The purpose of this paper is to present expanded COG results showing the neutron peak from deuterium buildup ( 2 H(d,n) 3 He) due to tritium decay in the target. Cross section data libraries used are ENDF/B-VIII.0 for neutrons and ENDF/B-VII.1 for deuterons, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A Monte Carlo investigation of low-Z target image quality generated in a linear accelerator using Varian's VirtuaLinac

Purpose: The focus of this work was the demonstration and validation of VirtuaLinac with clinical photon beams and to investigate the implementation of low-Z targets in a TrueBeam linear accelerator (Linac) using Monte Carlo modeling. Methods: VirtuaLinac, a cloud based web application utilizing Geant4 Monte Carlo code, was used to model the Linac treatment head components. Particles were propagated through the lower portion of the treatment head using BEAMnrc. Dose distributions and spectral distributions were calculated using DOSXYZnrc and BEAMdp, respectively. For validation, 6 MV flattened and flattening filter free (FFF) photon beams were generated and compared to measurement for square fields, 10 and 40 cm wide and at d{sub max} for diagonal profiles. Two low-Z targets were investigated: a 2.35 MeV carbon target and the proposed 2.50 MeV commercial imaging target for the TrueBeam platform. A 2.35 MeV carbon target was also simulated in a 2100EX Clinac using BEAMnrc. Contrast simulations were made by scoring the dose in the phosphor layer of an IDU20 aSi detector after propagating through a 4 or 20 cm thick phantom composed of water and ICRP bone. Results: Measured and modeled depth dose curves for 6 MV flattened and FFF beams agree within 1% for 98.3% of points at depths greater than 0.85 cm. Ninety three percent or greater of points analyzed for the diagonal profiles had a gamma value less than one for the criteria of 1.5 mm and 1.5%. The two low-Z target photon spectra produced in TrueBeam are harder than that from the carbon target in the Clinac. Percent dose at depth 10 cm is greater by 3.6% and 8.9%; the fraction of photons in the diagnostic energy range (25–150 keV) is lower by 10% and 28%; and contrasts are lower by factors of 1.1 and 1.4 (4 cm thick phantom) and 1.03 and 1.4 (20 cm thick phantom), for the TrueBeam 2.35 MV/carbon and commercial imaging beams, respectively. Conclusions: VirtuaLinac is a promising new tool for Monte Carlo modeling of novel target designs. A significant spectral difference is observed between the low-Z target beam on the Clinac platform and the proposed imaging beam line on TrueBeam, with the former providing greater diagnostic energy content.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Dosimetric characterization and output verification for conical brachytherapy surface applicators. Part II. High dose rate {sup 192}Ir sources

Purpose: Historically, treatment of malignant surface lesions has been achieved with linear accelerator based electron beams or superficial x-ray beams. Recent developments in the field of brachytherapy now allow for the treatment of surface lesions with specialized conical applicators placed directly on the lesion. Applicators are available for use with high dose rate (HDR){sup 192}Ir sources, as well as electronic brachytherapy sources. Part I of this paper discussed the applicators used with electronic brachytherapy sources. Part II will discuss those used with HDR {sup 192}Ir sources. Although the use of these applicators has gained in popularity, the dosimetric characteristics have not been independently verified. Additionally, there is no recognized method of output verification for quality assurance procedures with applicators like these. Methods: This work aims to create a cohesive method of output verification that can be used to determine the dose at the treatment surface as part of a quality assurance/commissioning process for surface applicators used with HDR electronic brachytherapy sources (Part I) and{sup 192}Ir sources (Part II). Air-kerma rate measurements for the {sup 192}Ir sources were completed with several models of small-volume ionization chambers to obtain an air-kerma rate at the treatment surface for each applicator. Correction factors were calculated using MCNP5 and EGSnrc Monte Carlo codes in order to determine an applicator-specific absorbed dose to water at the treatment surface from the measured air-kerma rate. Additionally, relative dose measurements of the surface dose distributions and characteristic depth dose curves were completed in-phantom. Results: Theoretical dose distributions and depth dose curves were generated for each applicator and agreed well with the measured values. A method of output verification was created that allows users to determine the applicator-specific dose to water at the treatment surface based on a measured air-kerma rate. Conclusions: The novel output verification methods described in this work will reduce uncertainties in dose delivery for treatments with these kinds of surface applicators, ultimately improving patient care.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

SU-E-T-237: Monte Carlo Dosimetric Characterization of the Mobetron Mobile Linac

Purpose: The aim of this work is to characterize dosimetrically a clinical intraoperative electron beam accelerator, Mobetron (IntraOp Medical, Inc.) in clinical use in our Hospital. Once this first step is completed our purpose is to evaluate shielding requirements for such a device by preparing adequate phase space files. Methods: It is known that electron beam simulation parameters required for state-of-the-art Monte Carlo codes to obtain a good match with measured data, like the mean energy or the FWHM, may not be code-independent due to the different set of process simulated and formalisms involved. Then, to cross-check our results against any issue in the simulation we have compared experimental data (PDD and profiles for electrons in the range 4 to 12 MeV) with simulations performed independently using both Penelope2011 and Geant4 codes. To do so, the geometry and materials of the head of the accelerator have been fully characterized following information provided by the manufacturer. Results: Both simulations agree with experimental data within experimental uncertainties (±1 mm displacement), although small variations (less than 10%) in the mean energy and FWHM are required to match measured values depending on the code used. Conclusion: Independent Monte Carlo simulations were used to obtain an excellent match to measured electron dose distributions. This opens the road to use such data for evaluating shielding requirements which is the main objective of this project.

07 ISOTOPE AND RADIATION SOURCES↗

UNCERTAINTIES IN GALACTIC CHEMICAL EVOLUTION MODELS

We use a simple one-zone galactic chemical evolution model to quantify the uncertainties generated by the input parameters in numerical predictions for a galaxy with properties similar to those of the Milky Way. We compiled several studies from the literature to gather the current constraints for our simulations regarding the typical value and uncertainty of the following seven basic parameters: the lower and upper mass limits of the stellar initial mass function (IMF), the slope of the high-mass end of the stellar IMF, the slope of the delay-time distribution function of Type Ia supernovae (SNe Ia), the number of SNe Ia per M {sub ⊙} formed, the total stellar mass formed, and the final mass of gas. We derived a probability distribution function to express the range of likely values for every parameter, which were then included in a Monte Carlo code to run several hundred simulations with randomly selected input parameters. This approach enables us to analyze the predicted chemical evolution of 16 elements in a statistical manner by identifying the most probable solutions, along with their 68% and 95% confidence levels. Our results show that the overall uncertainties are shaped by several input parameters that individually contribute at different metallicities, and thus at different galactic ages. The level of uncertainty then depends on the metallicity and is different from one element to another. Among the seven input parameters considered in this work, the slope of the IMF and the number of SNe Ia are currently the two main sources of uncertainty. The thicknesses of the uncertainty bands bounded by the 68% and 95% confidence levels are generally within 0.3 and 0.6 dex, respectively. When looking at the evolution of individual elements as a function of galactic age instead of metallicity, those same thicknesses range from 0.1 to 0.6 dex for the 68% confidence levels and from 0.3 to 1.0 dex for the 95% confidence levels. The uncertainty in our chemical evolution model does not include uncertainties relating to stellar yields, star formation and merger histories, and modeling assumptions.

79 ASTRONOMY AND ASTROPHYSICS↗

Dosimetric characterization and output verification for conical brachytherapy surface applicators. Part I. Electronic brachytherapy source

Purpose: Historically, treatment of malignant surface lesions has been achieved with linear accelerator based electron beams or superficial x-ray beams. Recent developments in the field of brachytherapy now allow for the treatment of surface lesions with specialized conical applicators placed directly on the lesion. Applicators are available for use with high dose rate (HDR){sup 192}Ir sources, as well as electronic brachytherapy sources. Part I of this paper will discuss the applicators used with electronic brachytherapy sources; Part II will discuss those used with HDR {sup 192}Ir sources. Although the use of these applicators has gained in popularity, the dosimetric characteristics including depth dose and surface dose distributions have not been independently verified. Additionally, there is no recognized method of output verification for quality assurance procedures with applicators like these. Existing dosimetry protocols available from the AAPM bookend the cross-over characteristics of a traditional brachytherapy source (as described by Task Group 43) being implemented as a low-energy superficial x-ray beam (as described by Task Group 61) as observed with the surface applicators of interest. Methods: This work aims to create a cohesive method of output verification that can be used to determine the dose at the treatment surface as part of a quality assurance/commissioning process for surface applicators used with HDR electronic brachytherapy sources (Part I) and{sup 192}Ir sources (Part II). Air-kerma rate measurements for the electronic brachytherapy sources were completed with an Attix Free-Air Chamber, as well as several models of small-volume ionization chambers to obtain an air-kerma rate at the treatment surface for each applicator. Correction factors were calculated using MCNP5 and EGSnrc Monte Carlo codes in order to determine an applicator-specific absorbed dose to water at the treatment surface from the measured air-kerma rate. Additionally, relative dose measurements of the surface dose distributions and characteristic depth dose curves were completed in-phantom. Results: Theoretical dose distributions and depth dose curves were generated for each applicator and agreed well with the measured values. A method of output verification was created that allows users to determine the applicator-specific dose to water at the treatment surface based on a measured air-kerma rate. Conclusions: The novel output verification methods described in this work will reduce uncertainties in dose delivery for treatments with these kinds of surface applicators, ultimately improving patient care.

61 RADIATION PROTECTION AND DOSIMETRY↗

Modality comparison for small animal radiotherapy: A simulation study

Purpose: Small animal radiation therapy has advanced significantly in recent years. Whereas in the past dose was delivered using a single beam and a lead shield for sparing of healthy tissue, conformal doses can be now delivered using more complex dedicated small animal radiotherapy systems with image guidance. The goal of this paper is to investigate dose distributions for three small animal radiation treatment modalities. Methods: This paper presents a comparison of dose distributions generated by the three approaches—a single-field irradiator with a 200 kV beam and no image guidance, a small animal image-guided conformal system based on a modified microCT scanner with a 120 kV beam developed at Stanford University, and a dedicated conformal system, SARRP, using a 220 kV beam developed at Johns Hopkins University. The authors present a comparison of treatment plans for the three modalities using two cases: a mouse with a subcutaneous tumor and a mouse with a spontaneous lung tumor. A 5 Gy target dose was calculated using the EGSnrc Monte Carlo codes. Results: All treatment modalities generated similar dose distributions for the subcutaneous tumor case, with the highest mean dose to the ipsilateral lung and bones in the single-field plan (0.4 and 0.4 Gy) compared to the microCT (0.1 and 0.2 Gy) and SARRP (0.1 and 0.3 Gy) plans. The lung case demonstrated that due to the nine-beam arrangements in the conformal plans, the mean doses to the ipsilateral lung, spinal cord, and bones were significantly lower in the microCT plan (2.0, 0.4, and 1.9 Gy) and the SARRP plan (1.5, 0.5, and 1.8 Gy) than in single-field irradiator plan (4.5, 3.8, and 3.3 Gy). Similarly, the mean doses to the contralateral lung and the heart were lowest in the microCT plan (1.5 and 2.0 Gy), followed by the SARRP plan (1.7 and 2.2 Gy), and they were highest in the single-field plan (2.5 and 2.4 Gy). For both cases, dose uniformity was greatest in the single-field irradiator plan followed by the SARRP plan due to the sensitivity of the lower energy microCT beam to target heterogeneities and image noise. Conclusions: The two treatment planning examples demonstrate that modern small animal radiotherapy techniques employing image guidance, variable collimation, and multiple beam angles deliver superior dose distributions to small animal tumors as compared to conventional treatments using a single-field irradiator. For deep-seated mouse tumors, however, higher-energy conformal radiotherapy could result in higher doses to critical organs compared to lower-energy conformal radiotherapy. Treatment planning optimization for small animal radiotherapy should therefore be developed to take full advantage of the novel conformal systems.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Improving the energy response of external beam therapy (EBT) GafChromic{sup TM} dosimetry films at low energies (≤100 keV)

Purpose: Purpose of this work is to investigate the effects of varying the active layer composition of external beam therapy (EBT) GafChromic{sup TM} films on the energy dependence of the film, as well as try to develop a new prototype with more uniform energy response at low photon energies (⩽100 keV). Methods: First, the overall energy response (S{sub AD,} {sub W}(Q)) of different commercial EBT type film models that represent the three different generations produced to date, i.e., EBT, EBT2, and EBT3, was investigated. Pieces of each film model were irradiated to a fixed dose of 2 Gy to water for a wide range of beam qualities and the corresponding S{sub AD,} {sub W}(Q) was measured using a flatbed document scanner. Furthermore, the DOSRZnrc Monte Carlo code was used to determine the absorbed dose to water energy dependence of the film, f(Q). Moreover, the intrinsic energy dependence, k{sub bq}(Q), for each film model was evaluated using the corresponding S{sub AD,} {sub W}(Q) and f(Q). In the second part of this study, the authors investigated the effects of changing the chemical composition of the active layer on S{sub AD,} {sub W}(Q). Finally, based on these results, the film manufacturer fabricated several film prototypes and the authors evaluated their S{sub AD,} {sub W}(Q). Results: The commercial EBT film model shows an under response at all energies below 100 keV reaching 39% ± 4% at about 20 keV. The commercial EBT2 and EBT3 film models show an under response of about 27% ± 4% at 20 keV and an over response of about 16% ± 4% at 40 keV.S{sub AD,} {sub W}(Q) of the three commercial film models at low energies show strong correlation with the corresponding f{sup −1}(Q) curves. The commercial EBT3 model with 4% Cl in the active layer shows under response of 22% ± 4% at 20 keV and 6% ± 4% at about 40 keV. However, increasing the mass percent of chlorine makes the film more hygroscopic which may affect the stability of the film's readout. The EBT3 film prototype with 7.5% Si shows a significant improvement in the energy response at very low energies compared to the commercial EBT3 films with 4% Cl. It shows under response of 15% ± 5% at about 20 keV to 2% ± 5% at about 40 keV. However, according to the manufacturer, the addition of 7.5% Si as SiO{sub 2} adversely affected the viscosity of the active fluid and therefore affected the potential use in commercial machine coating. The latest commercial EBT3 film model with 7% Al as Al{sub 2}O{sub 3} shows an overall improvement in S{sub AD,} {sub W}(Q) compared to previous commercial EBT3 films. It shows under response at all energies <100 keV, varying from 20% ± 4% at 20 keV to 6% ± 4% at 40 keV. Conclusions: The energy response of films in the energy range <100 keV can be improved by adjusting the active layer chemical composition. Removing bromine eliminated the over response at about 40 keV. The under response at energies ≤30 keV is improved by adding 7% Al to the active layer in the latest commercial EBT3 film models.

61 RADIATION PROTECTION AND DOSIMETRY↗

Comparison of Temperature-Dependent Cross Section Treatments Within the Shift Monte Carlo Radiation Transport Code

Multiple calculation methods have been developed to account for Doppler broadening of cross sections in Monte Carlo radiation transport simulations. This work compares the accuracy and performance of four different broadening methods, including an on-the-fly multipole treatment, applied to three different geometries of increasing complexity, including a nuclear reactor assembly with a realistic temperature profile. The comparisons reveal how the combination of physics implementations in the Shift Monte Carlo code result in slightly different temperature-dependent behavior, and different levels of performance, for a variety of materials and situations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Development and application of a reverse Monte Carlo radiative transfer code for rocket plume base heating

A reverse Monte Carlo radiative transfer code to predict rocket plume base heating is presented. In this technique rays representing the radiation propagation are traced backwards in time from the receiving surface to the point of emission in the plume. This increases the computational efficiency relative to the forward Monte Carlo technique when calculating the radiation reaching a specific point, as only the rays that strike the receiving point are considered.

Everson, John↗

Establishing a neutronics design and equilibrium cycle analysis for the I 2 S-LWR reactor with UO 2 and U 3 Si 2 Fuel

The Integral Inherently Safe (I 2 S-LWR) reactor was developed not only to enhance passive reactor safety performance, but also to improve reactor economics. This paper describes the steady-state and depletion analysis of the I 2 S-LWR core using both UO 2 and U 3 Si 2 fuel designs. The development and validation of the core models are described, to include the generation of HELIOS cross sections and comparison with the WEC lattice code PARAGON and the Monte Carlo code SERPENT. The few group homogenized cross sections were then prepared for the U.S. NRC PARCS core simulator using the GenPMAXS code. The multicycle capability in PARCS was used to determine the equilibrium core condition for three batch cores loaded with the UO 2 and then with the U 3 Si 2 fuel designs. Comparing the results from the WEC code ANC at beginning, middle, and end of cycle showed good agreement. Core conditions at beginning and end of cycle were then used to determine the converged steady-state conditions of a coupled RELAP5/PARCS model, which provided the initial condition for various transient accident simulations which are reported in a companion paper.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Electron transport in gaseous detectors with a Python-based Monte Carlo simulation code

Understanding electron drift and diffusion in gases and gas mixtures is a topic of central importance for the development of modern particle detection instrumentation. The industry-standard MagBoltz code has become an invaluable tool during its 20 years of development, providing capability to solve for electron transport (‘swarm’) properties based on a growing encyclopedia of built-in collision cross sections. We have made a refactorization of this code from FORTRAN into Cython, and studied a range of gas mixtures of interest in high energy and nuclear physics. The results from the new open source PyBoltz package match the outputs from the original MagBoltz code, with comparable simulation speed. An extension to the capabilities of the original code is demonstrated, in implementation of a new Modified Effective Range Theory interface. We hope that the versatility afforded by the new Python code-base will encourage continued use and development of the MagBoltz tools by the particle physics community.

97 MATHEMATICS AND COMPUTING↗

ITER ECH Transmission Line System Design and Status

The electron cyclotron (EC) heating & current drive (H&CD) system on ITER provides plasma heating by generating, transmitting, and launching high-intensity, high-frequency (170 GHz) electromagnetic wave energy steerable across the plasma cross-section. The transmission line (TL) subsystem connects the Matching Optics Unit (MOU) on each of the 24 gyrotrons to the 32 feed points in the four upper launchers and the 24 feed points in the equatorial launcher. Each TL must be able to operate at up to 1.2 MW of input power for up to 1 hour pulse lengths. The TL system contains 50 mm water-cooled corrugated waveguide, 90o miter bends, 140o miter bends, polarizer miter bend pairs, switches, expansion units, pumpouts, DC breaks, MOU-TL adapters, Radio Frequency (RF) loads, and isolation shutter valves. A detailed finite element analysis has been used to verify the thermo-mechanical performance of each component. The microwave performance has been analyzed using a 2-D electromagnetic code combined with a Monte Carlo code. This approach allows the impact of manufacturing and installation tolerances to be assessed and optimized to provide a high probability of achieving the system performance requirements. Prototypes of the waveguide and TL components have been fabricated and tested at high-power. Production contracts are now being issued for fabrication and delivery of the waveguide and components to ITER.

Hanson, Gregory↗

Organ S values and effective doses for family members exposed to adult patients following I-131 treatment: A Monte Carlo simulation study

Purpose: To calculate organ S values (mGy/Bq-s) and effective doses per time-integrated activity (mSv/Bq-s) for pediatric and adult family members exposed to an adult male or female patient treated with I-131 using a series of hybrid computational phantoms coupled with a Monte Carlo radiation transport technique.Methods: A series of pediatric and adult hybrid computational phantoms were employed in the study. Three different exposure scenarios were considered: (1) standing face-to-face exposures between an adult patient and pediatric or adult family phantoms at five different separation distances; (2) an adult female patient holding her newborn child, and (3) a 1-yr-old child standing on the lap of an adult female patient. For the adult patient model, two different thyroid-related diseases were considered: hyperthyroidism and differentiated thyroid cancer (DTC) with corresponding internal distributions of {sup 131}I. A general purpose Monte Carlo code, MCNPX v2.7, was used to perform the Monte Carlo radiation transport.Results: The S values show a strong dependency on age and organ location within the family phantoms at short distances. The S values and effective dose per time-integrated activity from the adult female patient phantom are relatively high at shorter distances and to younger family phantoms. At a distance of 1 m, effective doses per time-integrated activity are lower than those values based on the NRC (Nuclear Regulatory Commission) by a factor of 2 for both adult male and female patient phantoms. The S values to target organs from the hyperthyroid-patient source distribution strongly depend on the height of the exposed family phantom, so that their values rapidly decrease with decreasing height of the family phantom. Active marrow of the 10-yr-old phantom shows the highest S values among family phantoms for the DTC-patient source distribution. In the exposure scenario of mother and baby, S values and effective doses per time-integrated activity to the newborn and 1-yr-old phantoms for a hyperthyroid-patient source are higher than values for a DTC-patient source.Conclusions: The authors performed realistic assessments of {sup 131}I organ S values and effective dose per time-integrated activity from adult patients treated for hyperthyroidism and DTC to family members. In addition, the authors’ studies consider Monte Carlo simulated “mother and baby/child” exposure scenarios for the first time. Based on these results, the authors reconfirm the strong conservatism underlying the point source method recommended by the US NRC. The authors recommend that various factors such as the type of the patient's disease, the age of family members, and the distance/posture between the patient and family members must be carefully considered to provide realistic dose estimates for patient-to-family exposures.

61 RADIATION PROTECTION AND DOSIMETRY↗

Reactor physics benchmark of Westinghouse PWR core design suite for high burnup/high enrichment fuel - Part 1: Pin and lattice

Westinghouse has performed a comprehensive set of code-to-code benchmark comparisons to corroborate application of its state-of-the-art NEXUS-based code suite to high burnup and high enrichment (HB/HE) fueled PWR core design and reload analysis. This paper focuses on analysis of the predictions for pin and lattice designs representative of HB/HE core reloads from the Westinghouse advanced lattice code PARAGON2, the Monte-Carlo code SERPENT2 and MPACT, the deterministic neutronic component of VERA. A companion paper presented at this conference analyzes results obtained with the Westinghouse ANC9 core simulator, using lattice data provided by PARAGON2 with the NEXUS cross-section methodology, and MPACT for 2D and 3D core configurations incorporating HB/HE fuel reloads to achieve cycle length extension to 24-month in high-power density PWRs. The results of the pin and lattice benchmark presented in this paper show that the neutronic predictions from PARAGON2 for HB/HE fueled PWRs are in remarkable agreement with predictions from both SERPENT2 and MPACT including for depletion to high fuel burnup values, and employing a set of challenging lattices which feature combined use of burnable absorbers to obtain the required reactivity hold-down to support PWR transition to HB/HE fuel and 24-month operational cycles. As corroborated by this analysis and the analysis contained in the companion paper, the Westinghouse NEXUS-based PWR core analysis package can be confidently applied by industry for design analysis of PWR core reloads adopting HB/HE fuel and properly support the industry commercialization plans for in-reactor deployment. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

(U) LNK3DNT Capability in SENSMG

The SENSMG multigroup neutron sensitivity code has been extended to read materials and geometry from redoin and lnk3dnt files written by the PARTISN multigroup discrete ordinates code or the MCNP6 Monte Carlo code. This report describes the user interface for this capability and the code verification that was done. Not all of the capability of SENSMG is available for redoin/lnk3dnt inputs. The only responses allowed are k eff or α eigenvalues. Fixed-source problems are not allowed, and there is no mechanism to input reaction rates or reaction-rate ratios. The next section of this report describes the user interface. Section III describes the verification of the capability. Section IV is a summary and conclusions. The input files used for verification are listed in the appendix.

97 MATHEMATICS AND COMPUTING↗