Ionization of Air by Beta Rays from Point Sources

Clark, R. K.; Brar, S.S.; Marinelli, L. D.

doi:10.1148/64.1.94

Cited by 24 publications

(5 citation statements)

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“…Other results of [1] proved to be in good agreement with experiments using P^^beta ray sources in air (Clark, Brar, and Marinelli, point isotropic source geometry) [10], and in polystyrene (Loevinger, [11] plane isotropic source geometry).…”

Section: Calculation Of the Energy Dissipation From Its Momentssupporting

confidence: 80%

“…The methods which were used were essentially those outlined in [1].^Results are given for Eq varying in approximately logarithmic intervals from 0.025 to 10 Mev, for the following materials: C, Al, Cu, Sn, Pb, air, and polystyrene. In the case of Sn and Pb, some of the lower and some of the higher values of Eo have been omitted, the lower values because the range and cross-section data are unreliable near the atomic binding energies, the higher values because radiation straggling, which has not been taken into account, tends to dominate at high energies.…”

Section: Contentsmentioning

confidence: 99%

“…In terms of these quantities, and by means of the summation device [1, eq 27], we can rewrite (8) in the form of coupled equations to be evaluated successively ia the order stated below: i';:,=c^i+j^i^i-\ (10) Equations (9) and (10) particularly for large a, the /J^a nd C^, were set equal to zero. More frequently, a crude estimate of these quantities was used, which was based on approximate evaluation of the sums in (8) for large M, namely r«.…”

Section: Contentsmentioning

confidence: 99%

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Energy dissipation by fast electrons

Spencer¹

1959

108

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but the errors are probably important only for very large distances from the source, where only a minor fraction of the energy is dissipated. Since a major effort is required to improve the results further, and since experimental studies show generally good agreement where comparisons have been made, it is felt that the data are of sufficient accuracy and usefulness to justify their publication. ' Figures in brackets indicate the literature references at the end of this Monograph. 1The remainder of this Monograph is divided into two parts, the first outHning the methods and data which were used to make the calculations and the second presenting and describing the tabular data. Section 3 describing the tabular data, has been made almost completely self-contained so that persons who need data but do not wish to follow the derivations may turn immediately to this latter section and find all the information they require.Since the basic theoretical methods used to calculate electron energy dissipation distributions have already been given in considerable detail in [1]. We only sketch the arguments and procedures here.The assumption that electrons lose their energy continuously established a relation between the residual range r of the electrons, measured along their path, and the average rate of energy loss, i.e., the stopping power {dEjdr):where 0<^E'CEo is the kinetic energy of an electron which has slowed down but not lost its energy completely.This equation is the basis for the tabulations of electron ranges [2].It is convenient to measure both distances and residual ranges in units of ro=r{Eo) . For an electron source located on the plane 2=0 which emits electrons of kinetic energy Eq in the direction perpendicular to this plane and towards increasing z, the distance of a point from the source plane will be conveniently identified by a dimensionless parameter x=z/ro-Similarly, we replace the residual range r by a dimensionless ratio t=rjro.We define the flux of electrons, I(t,d,x)2ir d{cos d)dt, as the number of electrons per second that cross a small spherical probe of unit cross sectional area at a distance x from the source, having residual ranges between t and t-\-dt and obliquities between 6 and 6-\-dd relative to the direction from the source to the probe.The electron flux must satisfy a transport equation, which has the following form in steady state conditions for the plane perpendicular source:where 6 is the angle between the electron directions {6' ,4>') and {6,) before or after a collision. This is basically a continuity equation. The terms on the left describe a rate of change in Iit,9,x) due to slowing down (first term) and due to spatial displacement (second term). The terms on the right describe a rate of change in the flux due to elastic collisions (first term) and due to generation of electrons by the source.The last term, describing a unit-electron source current, is the product of three Dirac delta functions which guarantee that the electrons are generated only at a;=0, t= 1 , and cos 6=1...

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Section: Calculation Of the Energy Dissipation From Its Momentssupporting

confidence: 80%

Section: Contentsmentioning

confidence: 99%

Section: Contentsmentioning

confidence: 99%

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Energy dissipation by fast electrons

Spencer¹

1959

108

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“…Measurements of electron dose deposition from point sources or broad-parallel beams raise difficult problems due to the sharp dose gradient and the very short ranges of these particles in condensed tissue-like media (Vynckier and Wambersie 1982, Simpkin and Mackie 1990. Nevertheless, DPKs measured in air and other solids have been reported in a number of studies (Loevinger 1950, 1954, Clark et al 1955, Cross 1967a, 1968, 1969. With respect to DDPs, measurements are mostly available for the case of electron beams from medical linear accelerator units (e.g.…”

Section: Introductionmentioning

confidence: 99%

A Monte Carlo study of absorbed dose distributions in both the vapor and liquid phases of water by intermediate energy electrons based on different condensed-history transport schemes

Bousis¹,

Emfietzoglou²,

Hadjidoukas³

et al. 2008

Phys. Med. Biol.

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Monte Carlo transport calculations of dose point kernels (DPKs) and depth dose profiles (DDPs) in both the vapor and liquid phases of water are presented for electrons with initial energy between 10 keV and 1 MeV. The results are obtained by the MC4 code using three different implementations of the condensed-history technique for inelastic collisions, namely the continuous slowing down approximation, the mixed-simulation with delta-ray transport and the addition of straggling distributions for soft collisions derived from accurate relativistic Born cross sections. In all schemes, elastic collisions are simulated individually based on single-scattering cross sections. Electron transport below 10 keV is performed in an event-by-event mode. Differences on inelastic interactions between the vapor and liquid phase are treated explicitly using our recently developed dielectric response function which is supplemented by relativistic corrections and the transverse contribution. On the whole, the interaction coefficients used agree to better than approximately 5% with NIST/ICRU values. It is shown that condensed phase effects in both DPKs and DDPs practically vanish above 100 keV. The effect of delta-rays, although decreases with energy, is sizeable leading to more diffused distributions, especially for DPKs. The addition of straggling for soft collisions is practically inconsequential above a few hundred keV. An extensive benchmarking with other condensed-history codes is provided.

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“…14 Because of the short ranges of electrons, direct measurement of the dose deposition of these sources is very difficult. Several investigations have been made by Loevinger, 15 Clark et al, 16 Cross, 17 Cole, 18 and others to determine measured dose point kernels. Spencers numerical solution to the transport equation of primary electrons in a uniform unbounded medium in the continuous-slowing-down approximation showed a very good agreement with previous measurements.…”

Section: Introductionmentioning

confidence: 99%

Discrete beta dose kernel matrices for nuclides applied in targeted radionuclide therapy (TRT) calculated with MCNP5

2009

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The good accordance with the only discrete dose kernels published up to date justifies the method chosen. Together with the additional six nuclides, this report provides a considerable database for three-dimensional kernel matrices with regard to beta radionuclides applied in TRT. In contrast to analytical dose point kernels, the discrete kernels elude the problem of overestimation near the source and take energy depositions into account, which occur beyond the range of the continuous-slowing-down approximation (csda range). Recalculation of the 1 x 1 x 1 mm3 kernels to other dose kernels with varying voxel dimensions, cubic or noncubic, is shown to be easily manageable and thereby provides a resolution-independent system of dose calculation.

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Ionization of Air by Beta Rays from Point Sources

Cited by 24 publications

References 0 publications

Energy dissipation by fast electrons

Energy dissipation by fast electrons

A Monte Carlo study of absorbed dose distributions in both the vapor and liquid phases of water by intermediate energy electrons based on different condensed-history transport schemes

Discrete beta dose kernel matrices for nuclides applied in targeted radionuclide therapy (TRT) calculated with MCNP5

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