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EvaluateFlux, VARPOW, VARPEAK, and DIF3DtoVTK Utility Programs for DIF3D (Rev. 1)

The DIF3D-VARIANT solver is part of the DIF3D code which was developed at ANL for engineering level predictive analysis of nuclear reactor cores. Over the course of the last 20 years, the DIF3D-VARIANT option of DIF3D has become increasingly more used because of improvements in computer memory capabilities and performance. This is beneficial to the users of DIF3D as DIF3D-VARIANT is able to apply both p- and h-spatial mesh refinement strategies in diffusion and transport theory. Given its greater use, utility programs were created to assist in post-processing the DIF3D output. This document discusses the basic execution process of DIF3D and the output files it creates but is primarily focused on being the manual for the utility programs EvaluateFlux, VARPOW, VARPEAK, and DIF3DtoVTK.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Gamma heating in thin heavy-element absorbers.

Gamma heating rate measured by aqueous dosimeter converted to rate in thin tungsten detector in water shield through transport theory calculations, obtaining correction factors

Crum, R. J.↗

Comparative evolution of the inverse problems (Introduction to an interdisciplinary study of the inverse problems)

The progressive realization of the consequences of nonuniqueness imply an evolution of both the methods and the centers of interest in inverse problems. This evolution is schematically described together with the various mathematical methods used. A comparative description is given of inverse methods in scientific research, with examples taken from mathematics, quantum and classical physics, seismology, transport theory, radiative transfer, electromagnetic scattering, electrocardiology, etc. It is hoped that this paper will pave the way for an interdisciplinary study of inverse problems.

Sabatier, P. C.↗

Multidimensional analysis of fast-spectrum material replacement measurements for systematic estimation of cross section uncertainties

A series of central core and core-reflector interface sample replacement experiments for 16 materials performed in the NASA heavy-metal-reflected, fast spectrum critical assembly (NCA) were analyzed in four and 13 groups using the GAM 2 cross-section set. The individual worths obtained by TDSN and DOT multidimensional transport theory calculations showed significant differences from the experimental results. These were attributed to cross-section uncertainties in the GAM 2 cross sections. Simultaneous analysis of the measured and calculated sample worths permitted separation of the worths into capture and scattering components which systematically provided fast spectrum averaged correction factors to the magnitudes of the GAM 2 absorption and scattering cross sections. Several Los Alamos clean critical assemblies containing Oy, Ta, and Mo as well as one of the NCA compositions were reanalyzed using the corrected cross sections. In all cases the eigenvalues were significantly improved and were recomputed to within 1 percent of the experimental eigenvalue. A comparable procedure may be used for ENDF cross sections when these are available.

Klann, P. G.↗

Study, selection, and preparation of solid cationic conductors

Crystal chemical principles and transport theory were used to predict structures and specific compounds which might find application as solid electrolytes in rechargeable high energy and high power density batteries operating at temperatures less than 200 C. More than twenty compounds were synthesized or obtained and screened by nuclear magnetic resonance and conductivity. Many were densified by sintering or hot pressing. Encouraging results were obtained for nine of these materials but none have yet been good ionic conductors at low temperature.

Roth, W. L.↗

A rigorous cosmic-ray transport equation with no restrictions on particle energy.

A new transport equation for the cosmic-ray omnidirectional intensity is obtained. This equation follows exactly from the coupled pair of differential moment equations we presented earlier. It can be characterized as a nonlocal convection-diffusion equation in which the usual transport coefficients are replaced by time integral operators. The nonlocal equation is shown to reduce to the standard convection-diffusion form if the adiabatic approximation can be applied. In general, the adiabatic approximation does not apply; however, by going to the limits of infinite and zero gyroradius and, in addition, applying the adiabatic approximation, the large- and small-gyroradius transport theories due originally to Jokipii are regained. The validity of these theories as asymptotic limits and as approximate theories in the interplanetary magnetic field is discussed.

Klimas, A. J.↗

Study, selection, and preparation of solid cationic conductors

Crystal chemical principles and transport theory have been used to predict structures and specific compounds which might find application as solid electrolytes in rechargeable high energy and high power density batteries operating at temperatures less than 200 C. Structures with 1-, 2-, and 3-dimensional channels were synthesized and screened by nuclear magnetic resonance, dielectric loss, and conductivity. There is significant conductivity at room temperature in some of the materials but none attain a level that is comparable to beta-alumina. Microwave and fast pulse methods were developed to measure conductivity in powders and in small crystals.

Roth, W. L.↗

Coherent propagation of charged-particle bunches in random magnetic fields

When the distribution function for energetic particles moving in interplanetary space is expressed in terms of eigenfunctions of an operator which describes pitch-angle scattering by random magnetic fields, the familiar phenomenon of diffusion is the dominant solution of the transport equations provided that the spectrum of magnetic fluctuations is not too steep. However, if the power-versus-wavenumber spectrum of the random fields has a spectral index greater than 2, the dominant solution of the same equations is a qualitatively different mode of transport in which density inhomogeneities propagate coherently along the guiding field with a characteristic velocity equal to half the particle speed. The present work, which extends classical transport theory to give a detailed treatment of the new mode, presents explicit formulae which describe the spatial and temporal structure of the coherent disturbance. It is shown that this disturbance evolves asymptotically into a moving Gaussian pulse whose width increases with time.

Earl, J. A.↗

Proton tissue dose for the blood forming organ in human geometry: Isotropic radiation

A computer program is described which calculates doses averaged within five major segments of the blood forming organ in the human body taking into account selfshielding of the detailed body geometry and nuclear star effects for proton radiation of arbitrary energy spectrum (energy less than 1 GeV) and isotropic angular distribution. The dose calculation includes the first term of an asymptotic series expansion of transport theory which is known to converge rapidly for most points in the human body. The result is always a conservative estimate of dose and is given as physical dose (rad) and dose equivalent (rem).

Khandelwal, G. S.↗

Proton tissue dose

Program calculates dosage averaged over five major segments of blood-forming organ, treating human body geometry in detail but assuming isotropicity of incident primary particles. Approximate form of transport theory is used, incorporating nuclear star effects. Two numerical integrations are used to evaluate intermediate equation and then dosage equation.

Wilson, J. W.↗

Chandrasekhar-type algorithms for fast recursive estimation in linear systems with constant parameters

In this recursive method proposed, the gain matrix for the Kalman filter and the convariance of the state vector are computed not via the Riccati equation, but from certain other equations. These differential equations are of Chandrasekhar-type. The 'invariant imbedding' idea resulted in the reduction of the basic boundary value problem of transport theory to an equivalent initial value system, a significant computational advance. Initial value experience showed that there is some computational savings in the method and the loss of positive definiteness of the covariance matrix is less vulnerable.

Choudhury, A. K.↗

Effects of particle drift on cosmic-ray transport. I - General properties, application to solar modulation

Although gradient and curvature drifts are explicitly contained in the general equations of cosmic-ray transport, they have been almost universally neglected in applications of these equations. The drifts are evaluated explicitly for the Parker (1965) spiral magnetic field, and it is shown that for particles with rigidities greater than about 0.3 GV in the solar wind, they are larger than the solar-wind velocity over much of the heliosphere. Hence most current models of solar modulation and solar-flare particle events neglect terms which in many cases are as important as those retained. Calculations are presented which demonstrate the importance of the effects for simple modulation models. It is concluded that comparisons of presently available model calculations with observations do not provide a fair test of transport theory since they neglect drifts, which may substantially reduce the net modulation.

Jokipii, J. R.↗

Software development: Stratosphere modeling

A more comprehensive model for stratospheric chemistry and transport theory was developed for the purpose of aiding predictions of changes in the stratospheric ozone content as a consequence of natural and anthropogenic processes. This new and more advanced stratospheric model is time dependent and the dependent variables are zonal means of the relevant meteorological quantities which are functions of latitude and height. The model was constructed by the best mathematical approach on a large IBM S360 in American National Standard FORTRAN. It will be both a scientific tool and an assessment device used to evaluate other models. The interactions of dynamics, photochemistry and radiation in the stratosphere can be governed by a set of fundamental dynamical equations.

Chen, H. C.↗

The role of atmospheric shear, turbulence and a ground plane on the dissipation of aircraft vortex wakes

Enhanced dispersion of two-dimensional trailed vortex pairs within simplified neutral atmospheric backgrounds is studied numerically for three conditions: when the pair is imbedded in a constant turbulent bath (constant dissipation); when the pair is subjected to a mean cross-wind shear; and when the pair is near the ground. Turbulent transport is modeled using second-order closure turbulent transport theory. The turbulent background fields are constructed using a superequilibrium approximation. The computed results allow several general conclusions to be drawn with regard to the reduction in circulation of the vortex pair and the rolling moment induced on a following aircraft: (1) the rate of decay of a vortex pair increases with increasing background dissipation rate; (2) cross-wind shear disperses the vortex whose vorticity is opposite to the background; and (3) the proximity of a ground plane reduces the hazard of the pair by scrubbing. The phenomenon of vortex bounce is explained in terms of secondary vorticity produced at the ground plane. Qualitative comparisons are made with available experimental data, and inferences of these results upon the persistence of aircraft trailing vortices are discussed.

Bilanin, A. J.↗

A summary of research on the NASA-Global Atmospheric Sampling Program performed by the Atmospheric Sciences Research Center

The annual variations of ozone near the tropopause are derived from aircraft exhibit year-to-year differences which are not explicitly accounted for by the simple, classical ozone transport theory. Phenomena such as tropopause lifting, interannual variations in the rates of stratospheric-tropospheric exchange and meridional mixing, contribute differently to the distribution of ozone in this altitude region. Ozone encounter climatologies have been represented by global maps which show the probabilities of exceeding ambient ozone levels of 200, 300, and 400 ppbV along flight routes during the year. Continuous ozone records obtained from the GASP system revealed the presence of gravity waves whose wavelength is of the order 20 km. The GASP data cannot, however, be utilized for the evaluation of horizontal fluxes of such quantities as ozone, sensible heat, and zonal momentum; the data are too sparsely and irregularly distributed for the computation of stable correlations. Multiple species data from the unique circumglobal flight of a Pan American airliner on 28-30 October 1977 are discussed with particular regard to the apparent interhemispheric differences in tropospheric species concentrations, variation between the Arctic and Antarctic stratospheres, to possible covariations between species, and to potential source regions for various constituents.

Falconer, P. D.↗