Multiple Scattering with Energy Loss

Eyges, Leonard

doi:10.1103/physrev.74.1534

Cited by 297 publications

(181 citation statements)

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“…In a few of these the influence of surface irregularities and tissue inhomogeneities on the distribution of absorbed dose are taken into 'account. Most reports are based on semi-empirical modifications of the Fermi-Eyges solution to the Boltzmann equation with the Fokker-Planck collision term (FERMI 1940, EYGES 1948, BRAHME 1971, KAWACHI 1975) using a variety of analytic functions that are fitted to experimentally determined absorbed dose distributions.…”

mentioning

confidence: 99%

Electron Beam Dose Planning Using Discrete Gaussian Beams: Mathematical background

Brahme

Lax

Andreo

1981

Acta Radiologica: Oncology

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mentioning

confidence: 99%

Electron Beam Dose Planning Using Discrete Gaussian Beams: Mathematical background

Brahme

Lax

Andreo

1981

Acta Radiologica: Oncology

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“…The straight line labelled 22 mrad deflection, shows the axial intensity distribution of this component of muons, on the assumption that the lens has bent all the muons through this angle, so that the axis of the muon distribution now makes a 22 mrad angle with the former beam axis. The on-axis intensity at 1200 m is 10- 7 with the lens off; with the lens on, it is less than 10- As earlier discussed, GROUNDSHINE (II) cannot be explicitly calculated using the Alsmiller program. For muon energies in the decay tunnel in excess of 350 GeV, however, we estimate that 10-11 muons per interacting proton emerge from around the disc.…”

Section: Summary Of Proceduresmentioning

confidence: 98%

“…6 We have used the Alsmiller progranl in our work. This muon transport program calculates the intensities of muons in a semi-infinite homogeneous medium, using the theory of Eyges 7 to include the effects of both multiple Coulomb scattering and collision energy loss.…”

Section: Deflection Shielding-general Considerationsmentioning

confidence: 99%

Design of a Magnetized Iron Muon Shield for a High Energy Neutrino Laboratory

Kang¹,

Lee²,

Roberts³

1972

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Several new ideas are adduced to the problem of designing muon shielding for a neutrino experimental facility operated at high energy, a problem of interest for the National Accelerator Laboratory (NAL) and CERN-II. We outline a practical calculational procedure which permits the evaluation of the effect of magnetized-iron-Iens geometries on the intensity distribution of muons at the detector location. Such relevant effects as range straggling and multiple scattering within and around the lens are included in the evaluation. A specific design is outlined which would increase the maximum energy of bubble chamber beams in the NAL neutrino area from 350 to about 500 GeV. however, to provide a basis for non-experts and for our own discussion.The basic elements of a neutrino facility are shown in Fig. 1. A primary proton beam is impinged on a target T to produce secondary particles, primarily nand K mesons. The mesons are allowed to decay in the two-body mode:The drift (decay) space is usually terminated by a beam stop followed by a massive radiation shield and the detector in series. The neutrinos, of course, being neutral and participating only in weak interactions easily penetrate the beam stop and shield and reach the detector attenuated only by geometry.If we refer to Fig. 1 we see that the drift space (decay tunnel) has length L and is followed by a beam stop of negligible length, a 'disc' of radius R (for purposes of later discussion), a massive muon shield and a detector area at a distance x downstream of the beam stop. The total space available for the facility is L+x. For a given available space we wish to maximize L (up to the point of 1'-12 mean lives for the parent mesons) and minimize x in order to maximize the neutrino flux at the detector always subject to the constraint that the charged particle flux at the detector be low enough for personnel safety and bubble chamber operation.

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“…A pencil beam is made up of particles which pass through a differential cross sectional a,rea, 6x6~. The off-axis dependence of the dose distribution for each pencil beam is described by the Fermi-Eyges theory of thick-target multiple Coulomb scattering [23]. The on-a,xis dose information is obtained from measured depth-dose data.…”

Section: Deterministic Methodsmentioning

confidence: 99%

The macro response Monte Carlo method for electron transport

Svatos

1999

Med. Phys.

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The main goal of this thesis was to prove the feasibility of basing electron depth dose calculations in a phantom on first-principles single scatter physics, in an amount of time that is equal to or better than current electron Monte Carlo mcthods.The Macro Response Monte Carlo (MRMC) method achieves run times that are on the order of conventional electron transport methods such as condensed history, with the potential to be much fa,ster. This is possible because MRMC is a Local-toGlobal method, meaning the problem is broken down into two separate transport calculations. The first stage is a local, in this case, single scatter calculation, which generates probability distribution functions (PDFs) to describe the electron's energy, position and trajectory after leaving the local geometry, a small sphere or "kugel" A number of local kugel calculations were run for calcium and carbon, creating a library of kugel data sets over a range of incident energies and sizes (0.025 cm to 0.1 cm in radius).The second transport stage is a global calculation, where steps that conform to the size of the kugels in the library are taken through the global geometry. For each step, the appropriate PDFs from the MRMC library are sampled to determine the electron's new energy, position and trajectory. The electron is immediately advanced to the end of the step and then chooses another kugel to sample, which continues until transport is completed.The MRMC global stepping code was benchmarked as a series of subroutines inside of the Peregrine Monte Carlo code. It was compared to Peregrine's class II condensed history electron transport package, EGS4, and MCNP for depth dose in i ii simple phantoms having density inhomogeneities. Since the kugels completed in the library were of relatively small size, the zoning of the phantoms was scaled down from a clinical size, so that the energy deposition algorithms for spreading dose across 5-10 zones per kugel could be tested. Most resulting depth dose calculations were within 2-3s of well-benchmarked codes, with one excursion to 4%.This thesis shows that the concept of using single scatter-based physics in clinical calculations would not only be possible, but would likely be more efficient than current methods, provided large kugels were generated.

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Multiple Scattering with Energy Loss

Cited by 297 publications

References 1 publication

Electron Beam Dose Planning Using Discrete Gaussian Beams: Mathematical background

Electron Beam Dose Planning Using Discrete Gaussian Beams: Mathematical background

Design of a Magnetized Iron Muon Shield for a High Energy Neutrino Laboratory

The macro response Monte Carlo method for electron transport

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