Multiple Scattering of Electrons

Goudsmit, S.; Saunderson, J. L.

doi:10.1103/physrev.57.552.2

Cited by 54 publications

(40 citation statements)

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“…To summarize them here, we again begin with Eq. (1), which we rewrite as (8) with the same boundary conditions (2). Once again expanding the single scattering phase function f in Legendre polynomials, and rearranging, (8) may be rewritten (9) where is the scattering mean free path in the medium.…”

Section: Improved Models: Transport Condensed History (Tch) Methodsmentioning

confidence: 99%

“…To accommodate this artificial selection of intercollision distances, the scattering angle is sampled from a probability density function (pdf) derived from the original single scattering pdf, f (sometimes called the differential scattering cross-section) that represents multiple scattering events. In the CCH model, the multiple scattering pdf is called the Goudsmit-Saunderson [2] (GS) probability density function, designated here by f GS ; it is the exact 1 conditional pdf for the multiple scattering angle, conditioned upon traveling a fixed, but arbitrary distance s > 0 between successive (multiple) collisions. While the CCH model has made it possible to apply Monte Carlo methods to electron transport in problems that would otherwise be prohibitively costly to simulate, it has several shortcomings.…”

Section: Overviewmentioning

confidence: 99%

“…The approach that is adopted here can be traced to work of Lewis [6], Goudsmit and Saunderson [2], and Larsen and Tolar [7,8]. We refer to this general philosophy as the Lewis-Larsen theory.…”

Section: Overviewmentioning

confidence: 99%

“…For ease of exposition, we specialize the RTE (1) to planar geometry and assume that initially each particle starts at r = (0, 0, 0) and moves along the positive z-axis, which also serves as the north pole for a spherical coordinate system that will be used to characterize the unit direction vectors ω, ω′. That is (2) where μ = cos(θ) and θ is the angle between the direction of travel and the positive z-axis. Under these conditions, (1) and (2) simplify to (3) with the initial condition (4) The derivation of (3) can be found, for example, in [14,23]; for completeness here we include it in Appendix A.…”

Section: The Cch and Related Modelsmentioning

confidence: 99%

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Condensed history Monte Carlo methods for photon transport problems

Bhan

Spanier

2007

Journal of Computational Physics

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We study methods for accelerating Monte Carlo simulations that retain most of the accuracy of conventional Monte Carlo algorithms. These methods -called Condensed History (CH) methodshave been very successfully used to model the transport of ionizing radiation in turbid systems. Our primary objective is to determine whether or not such methods might apply equally well to the transport of photons in biological tissue. In an attempt to unify the derivations, we invoke results obtained first by Lewis, Goudsmit and Saunderson and later improved by Larsen and Tolar. We outline how two of the most promising of the CH models -one based on satisfying certain similarity relations and the second making use of a scattering phase function that permits only discrete directional changes -can be developed using these approaches. The main idea is to exploit the connection between the space-angle moments of the radiance and the angular moments of the scattering phase function. We compare the results obtained when the two CH models studied are used to simulate an idealized tissue transport problem. The numerical results support our findings based on the theoretical derivations and suggest that CH models should play a useful role in modeling light-tissue interactions.

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Section: Improved Models: Transport Condensed History (Tch) Methodsmentioning

confidence: 99%

Section: Overviewmentioning

confidence: 99%

Section: Overviewmentioning

confidence: 99%

Section: The Cch and Related Modelsmentioning

confidence: 99%

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Condensed history Monte Carlo methods for photon transport problems

Bhan

Spanier

2007

Journal of Computational Physics

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“…The energy loss per unit length along the trajectory of an electron is described as a distribution function [63] whose mean is the nominal stopping power of the material [64]. Likewise, the angular deflection of the electron (i.e., θ 12 ), and the production of bremsstrahlung are also treated as probability distribution functions [65].…”

Section: F5 Electron Stopping Treatment In Mcnpmentioning

confidence: 99%

Nuclear Resonance Fluorescence to Measure Plutonium Mass in Spent Nuclear Fuel

Ludewigt¹

2011

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Executive SummaryThe Next Generation Safeguard Initiative (NGSI) of the U.S. Department of Energy is supporting a multi-lab/university collaboration to quantify the plutonium (Pu) mass in spent nuclear fuel (SNF) assemblies and to detect the diversion of pins with non-destructive assay (NDA) methods. Nuclear Resonance Fluorescence (NRF) has been investigated as one of 14 NDA techniques included in the NGSI study. In contrast to many of the other, older techniques, NRF had not previously been considered for nuclear safeguards or similar applications and basic aspects including nuclear data, modeling and simulation tools, measurement methods, and instrumentation needed to be researched.Nuclear resonance fluorescence is the process by which a nucleus is excited to a specific state by the absorption of a photon, then subsequently de-excites to the ground state by the emission of one or more γ rays. The energies of the γ rays are characteristic of the specific state that underwent NRF and therefore are characteristic of the isotope. The emitted NRF γ rays are detected at backwards angles where the backgrounds from elastically and inelastically scattered photons are lowest. Two distinct assay methods, the backscatter and the transmission methodsare analyzed in this report. In both cases a beam of energetic photons excites nuclear resonances of the isotopes of interest (IOI) within the SNF. In the backscatter assay geometry, the emitted NRF γ rays detected at backwards angles are a measure of the amount of a specific isotope in the SNF. In transmission assay, a detection system down-stream of the SNF measures the excess attenuation of resonant-energy photons due to NRF in the SNF assembly. The detection system consists of a thin sheet composed of the isotope of interest, called the transmission detector (TD), and a detector array that measures the NRF γ rays emanating from the TD. Given the low concentrations of the Pu isotopes in SNF and the relatively small integrated nuclear resonance cross sections, the main challenge for achieving precise and accurate measurements lies in accruing sufficient counting statistics in an acceptable measurement time.The goals of this study were to design and model suitable NRF measurement methods, to quantify capabilities and corresponding instrumentation requirements, to investigate possible implementations, and to evaluate the prospects and potential of the technique for the assay of SNF assemblies, i.e., for the measurement of their Pu isotopic content.Analytical models were developed that enabled calculation of NRF signals for a variety of backscatter and transmission geometries. Extensive simulations were performed using the computer code, Monte Carlo N-particle eXtended (MCNPX) to calculate photon scattering effects, i.e., to determine scattered, non-resonant background and the notch refilling in transmission measurements. We found that MCNPX underestimated the non-resonant elastic scattering at backwards angles by multiple orders of magnitude mainly due to a flawed treatment of ...

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Generation and analysis of clinically relevant breast imaging x-ray spectra

et al. 2017

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Purpose The purpose of this work was to develop and make available x-ray spectra for some of the most widely used digital mammography (DM), breast tomosynthesis (BT), and breast CT (bCT) systems in North America. Methods The Monte Carlo code MCNP6 was used to simulate minimally-filtered (only beryllium) x-ray spectra at 8 tube potentials from 20 to 49 kV for DM/BT, and 9 tube potentials from 35 to 70 kV for bCT. Vendor-specific anode compositions, effective anode angles, focal spot sizes, source-to-detector distances, and beryllium filtration were simulated. For each 0.5 keV energy bin in all simulated spectra, the fluence was interpolated using cubic splines across the range of simulated tube potentials to produce spectra in 1 kV increments from 20 to 49 kV for DM/BT and from 35 to 70 kV for bCT. The HVL of simulated spectra with conventional filtration (at 35 kV for DM/BT and 49 kV for bCT) was used to assess spectral differences resulting from variations in: (1) focal spot size (0.1 and 0.3 mm IEC), (2) solid angle at the detector (i.e. small and large FOV size), and (3) geometrical specifications for vendors that employ the same anode composition. Results Averaged across all DM/BT vendors, variations in focal spot and FOV size resulted in HVL differences of 2.2% and 0.9%, respectively. Comparing anode compositions separately, the HVL differences for Mo (GE, Siemens) and W (Hologic, Philips, and Siemens) spectra were 0.3% and 0.6%, respectively. Both the commercial Koning and prototype “Doheny” (UC Davis) bCT systems utilize W anodes with a 0.3 mm focal spot. Averaged across both bCT systems, variations in FOV size resulted in a 2.2% difference in HVL. In addition, the Koning spectrum was slightly harder than Doheny with a 4.2% difference in HVL. Therefore to reduce redundancy, a generic DM/BT system and a generic bCT system were used to generate the new spectra reported herein. The spectral models for application to DM/BT were dubbed the Molybdenum, Rhodium, and Tungsten Anode Spectral Models using Interpolating Cubic Splines (MASMICSM-T, RASMICSM-T, and TASMICSM-T ; subscript “M-T” indicating mammography and tomosynthesis). When compared against reference models (MASMIPM, RASMIPM, and TASMIPM; subscript “M” indicating mammography), the new spectral models were in close agreement with mean differences of 1.3%, −1.3%, and −3.3%, respectively, across tube potential comparisons of 20, 30, and 40 kV with conventional filtration. TASMICSbCT-generated bCT spectra were also in close agreement with the reference TASMIP model with a mean difference of −0.8%, across tube potential comparisons of 35, 49, and 70 kV with 1.5 mm Al filtration. Conclusions The Mo, Rh, and W anode spectra for application in DM and BT (MASMICSM-T, RASMICSM-T, and TASMICSM-T) and the W anode spectra for bCT (TASMICSbCT) as described in this study should be useful for individuals interested in modeling the performance of modern breast x-ray imaging systems including dual energy mammography which extends to 49 kV. These new spectra are t...

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Multiple Scattering of Electrons

Cited by 54 publications

References 1 publication

Condensed history Monte Carlo methods for photon transport problems

Condensed history Monte Carlo methods for photon transport problems

Nuclear Resonance Fluorescence to Measure Plutonium Mass in Spent Nuclear Fuel

Generation and analysis of clinically relevant breast imaging x-ray spectra

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