This paper surveys the wide range of radiation physics topics that involve the transport of energetic electrons and x-rays. Applications in the high-energy range (100 keV to 30 MeV) include: radiation therapy physics (including treatment planning), industrial radiation processing of materials, shielding, experimental and theoretical dosimetry, dose profiles near material interfaces, beta-ray dosimetry, characterization of the photon spectrum from radioisotope sources, bremsstrahlung (x-ray) generation, and radiation charging of insulators. Lower energy applications (from below100eV to 100 keV) include: positron transport, electron probe microanalysis (EPMA), prediction of x-ray tube spectra, x-ray fluorescence analysis (XRF), electron-beam-induced-current (EBIC), auroral phenomena, x-ray lithography, electron beam lithography, Auger electron spectroscopy (AES), x-ray photoelectron spectroscopy (XPS), secondary electron emission, and electron energy loss spectroscopy (EELS). As examples, we briefly discuss (1) radiation therapy physics,(2) dose enhancement at material interfaces, and (3) x-ray target spectrum prediction. Mathematical methods and models for electron/photon transport are briefly described. These include (1) the Monte Carlo simulation method, (2) numerical solution of the transport equation, (3) analytic or semi-empirical models, (4) several miscellaneous methods, and (5) multidimensional methods. These models must be verified be comparison with benchmark experimental data, such as for electron backscatter and transmission, energy and charge deposition, and x-ray target spectra. Finally we list some topics where further transport model research would be desirable. We also describe a book in progress, which will provide a broad introduction to the theory of electron/photon transport and its many applications in radiation physics.

Year after year the Dosimetry and Facilities Session has been a fixture in the Nuclear Space and Radiation Conference (NSREC). As well as being home to subjects absolutely fundamental to dosimetry such as radiation transport, energy deposition, and X-ray photoemission, this session often included newly introduced topics such as hardness assurance and experimental techniques. This review paper describes the 40-year history of this session, whose title changed constantly over the years to reflect new developments. We have attempted to follow the logical chronological development and simultaneously give the reader a pedagogical tour through the main technical areas. Because of the wide variety of subjects in this session, this review covers first the context and background, and then four major subcategories as follows: the development of dosimetry devices and techniques; the basic physics of dosimetry and electron-photon/material interactions; neutron dosimetry and reactor facilities; and bremsstrahlung sources and other radiation facilities.

The transmitted photon energy fluence was calculated as a function of layer thickness for 1.25 MeV photons in Al, Ag, and Pb using the CEPXS/ONELD coupled electron-photon code. The energy fluence vs. layer thickness was also calculated as a function of beam radius using the CYLTRAN Monte Carlo code. We compare these results with predictions using the photon "energy absorption coefficient attenuation law" equation recommended in ASTM Standard E666-91 and suggest replacing this equation with more realistic expression.

CEPXS/ONELD code predictions of dose enhancement in a 1-D geometry were examined. Relative dose calculations at Co-60 energies were compared with ionization chamber data of Wall and Burke for 54 different cases. Excellent agreement was found.

This paper presents a new method of solution to the Fokker-Planck (F-P) equation for electron transport. By using the maximum entropy method, we have obtained an analytic representation for the scalar flux function f(x,s), where x is the distance along the x direction and s (which increases with decreasing electron energy) is the path length of an electron along its track. By this method, we have obtained a nearly exact analytic solution for f(x,s) due to a beam source in an infinite medium.

Why a session on one-group transport theory and its applications? The motivation for this session stems from the belief my co-chairman and I have had for some time that there is a need for a time and place where the wide range of solution methods for the transport equation and its areas of application can be reviewed and compared - for the benefit of transport theory experts and nonexperts alike. When suggestions for invited sessions were requested last November, this topic came to mind almost immediately. I believe there are many {open_quotes}interested bystanders{close_quotes} who would like to apply available mathematical methods for solving the transport equation to their own applications but are not sure what method to use. They do not want to spend a lot of time collecting and digesting the literature, but they want to know {open_quotes}how to get started.{close_quotes} Likewise, I feel there is a need for the {open_quotes}methods developers,{close_quotes} those who are deeply involved in transport theory for, say, nuclear reactor or shielding applications to exchange information with their counterparts in radiative transfer and other areas. This forum provides an opportunity for them both to review their own specialty within the context of the general transportmore » problem and hear a comparison of most of the major mathematical approaches.« less

This paper is another in a series concerning the generation of analytical benchmarks in one-group transport theory. Comparisons are made betwen analytical Green`s function scalar flux solution and Monte carlo calculations. The Green`s fnuction was determined with a Fourier transform rather than a Laplace transform.

In the last several years we have been developing a simplified electron transport model to calculate energy deposition profiles in multilayered structures irradiated by X rays and gamma rays. This model was implemented in a rapidly running algorithm MULTILAYER, for an IBM-compatible personal computer suitable for radiation-hardened electronics and dosimetry applications. In particular, we have been seeking to model the dose enhancement phenomenon near material interfaces for which experimental results were reported by Wall and Burke. In Refs. 1, 2, and 3, a simple one-group S{sub 2} transport model is described. This rod model arose as an extension of a semi-empirical model developed by Burke and Garth which was, in turn, based on exponential fits to Monte Carlo calculations of dose profiles at gold/silicon interfaces at photon energies from 10 to 2000 keV.

A method for calculating dose, charge deposition, current, and electric field profiles across a dielectric slab irradiated by 1-3 MeV electron beams has been developed. The model consists of following the electric field build-up with time. A sequence of Monte Carlo calculations for relativistic electrons moving in an electric field determines the motion of the high-energy electrons. This is coupled with electric field solutions using a 1-D electrostatic field code. As time proceeds, the profile of high-energy electron current changes as well as the dose deposition which affects the magnitude of the conduction currents. Several mechanisms for conduction in the dielectric are taken into account. The model predictions are compared with Kerr-effect electric field data on irradiated polymethylmethacrylate (PMMA) obtained by M. Hikita et al. (1988). >

The Sn method for solving the Spencer-Lewis equation for electron transport has been extended to treat three-dimensional multiregion problems. The flux continuity condition, which holds when the flux is expressed as a function of path length for single material region problems, is generalized for multiregion problems by reexpressing the flux as a function of energy. Expressing the fluxes in terms of fixed energy increments, independent of material, rather than fixed path length increments, results in a set of Sn/diamond-difference equations that are nearly identical in form to conventional Sn/diamond-difference equations. The Sn method is then applied to calculate electron energy deposition due to 200-keV electron beams incident on problem geometries typical of silicon and gallium-arsenide semiconductor microelectronic devices. The energy deposition results were found to compare well with results of ACCEPT Monte Carlo calculations. Computer run times required for the Sn calculations were found to be lower than that required for Monte Carlo by factors ranging from 30 to 50.

Using a semi-empirical electron transport model and the solution of the one-group S>2 transport equation for a multilayered system, we have developed a fast algorithm for calculating X-ray dose enhancement in device structures. The program MULTILAYER, written in BASIC for an IBM-PC compatible microcomputer, calculates (1) the dose profile across a multilayered structure including electron transport, (2) the absorbed dose neglecting electron transport and (3) the ratio of these two quantities: the “dose enhancement” profile. The dose as a function of position can be found for a structure with 1–10 layers. MULTILAYER uses monoenergetic photons and is valid over the 100–1250 keV photon energy range. The output compares well with much longer electron Monte Carlo and discrete-ordinales transport calculations.

The Spencer-Lewis equation for kilovolt electron transport in two dimensions was solved using a discrete ordinates, diamond difference method. Calculations of dose profiles in 2-D were made for 200 keV electrons normally and isotropically incident on aluminum and are compared with ACCEPT Monte Carlo calculations. Isodose contour plots are also presented for 200 keV electrons making angles of 0 and 45 degrees with the normal. Running times compare very favorably with Monte Carlo.

An electron transport solver has been developed based on a streaming ray (SR) solution to the Spencer-Lewis equation. Several special numerical techniques were used to make the algorithm fast and accurate. These include 1. an efficient routine for simulating energy loss straggling2. use of extended-transport-corrected and Fokker-Planck equivalent cross sections, which speed convergence and reduce both angular and spatial differencing errors3. a discrete transport correction, which further speeds convergence and further reduces spatial differencing errors4. the method of numerical shoves and countershoves, which attempts to estimate and correct the remaining spatial differencing errors.The extended transport correction and the Fokker-Planck equivalent cross sections were originally developed for SN computations. The remaining techniques are new. The use of all these techniques together with the SR method has led to a complicated but highly efficient electron transport algorithm. Its efficiency is especially evident in energy spectrum calculations for which other fast algorithms such as the SN method often yield poor results. Several sample calculations involving electron transport in aluminum slabs are presented.

Electron beam dose profiles have been calculated using a multigrouip, discrete ordinates solution of the Spencer-Lewis electron transport equation. This was accomplished by introducing electron transport crosssections into the ONETRAN code in a simple manner. Our purpose is to benchmark this electron transport model and to demonstrate its accuracy and capabilities over the energy range from 30 keV to 20 MeV. Many of our results are compared with the extensive measurements and TIGER Monte Carlo data published by Lockwood et al. In general the ONETRAN results are smoother, agree with TIGER within the statistical error of the Monte Carlo histograms and require about one tenth the running time of Monte Carlo.

The use of analytic first collision sources can greatly improve the accuracy of neutral particle S/sub N/ calculations. For electrons, because of the strong anisotropy of the electron scattering kernel, many collisions are required before the flux from a beam source is smooth enough to lend itself to practical numerical treatment. Thus the use of a conventional analytic first collision source is of little value. With smart scattering theory, the true electron scattering law is replaced by an equivalent one that involves many times fewer collisions but larger angular deflections per collision. With such a scattering law, the electron transport emulates that of neutral particles. Hence, application of an analytic first collision source should be effective. However, smart scattering cross sections are defined in terms of a scattering matrix and thus only apply for scatter from one quadrature direction to another. Here, the authors extend the theory to include scatter from (but not to) an arbitrary beam direction. This entails the generation of one additional column S/sup b/ of the smart scattering matrix. The m'th element S/sup b/ of the vector S/sup b/ is a smart cross section for transfer from the beam to direction Omega/sup m/.

The ONETRAN code was used to compute dose profiles near gold/aluminum interfaces for photon energies from 100 to 1250 keV. Weighted by a four component photon spectrum obtained from a least-squares fit to measured dose distribution data, the calculated profiles agree closely with Cobalt-60 ionization chamber data.

In this study, we have calculated the energy spectrum of electron flux near the interface between two semi-infinite media for a uniform isotropic source of electrons in one of the media. The following cases of medium 1/medium 2 (with denoting the side containing the electron source) were studied: Al/Al, Au/Al, Al/Au, and Au/Au for several source energies between 50 and 500 keV. The purpose of the study was to find an improved algorithm for rapid calculations of dose enhancement in electronics devices irradiated by x rays. Our approach was to compare a simple analytic model for the electron flux energy spectrum and for the dose profile as a function of distance from the interface with calculations using the ONETRAN code.

Two discrete ordinates methods, the Sn and streaming ray methods, are applied to electron transport problems. Calculational results in the form of energy deposition profiles are compared with those obtained by the method of moments for the case of a 200-keV plane perpendicular source embedded in infinite aluminum. In a second set of calculations, Sn and streaming ray flux data are compared with results of a recently developed analytical benchmark technique applied to the solution of the energy-independent form of the Spencer-Lewis equation for electron transport. Satisfactory agreement with moments and analytical benchmark calculations is found. Areas of divergence among the various calculational methods are examined.