An analytical solution for the solid angle subtended by a circular detector for a symmetrically positioned linear source

Galiano, Eduardo; Pagnutti, Christopher

doi:10.1016/j.apradiso.2005.12.006

Cited by 7 publications

(4 citation statements)

References 14 publications

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“…The solid angle of the registration system has been estimated based on the model presented in ref. 12 and is equal to 0.022 sr. The intensity of the Rayleigh scattering signal depends on the number density of scattering particles (N R ), the differential cross section ðd=dÞ and the total laser power P L and can be expressed as 11)…”

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confidence: 99%

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Absolute Concentration of OH Radicals in Atmospheric Pressure Glow Discharges with a Liquid Electrode Measured by Laser-Induced Fluorescence Spectroscopy

Nikiforov

Xiong

Britun

et al. 2011

Appl. Phys. Express

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The OH radical density and gas temperature in atmospheric pressure glow discharges with a liquid cathode or anode is measured with a laserinduced fluorescence (LIF) technique exciting the P 2 (3), Q 1 (4), and Q 1 (9) branches of the X 2 Å, 00 ¼ 0-A 2 AE, 0 ¼ 3 transition. Glow discharge in contact with liquid is generated by positive and negative voltages at currents of 10-28.5 mA. The density of OH radicals linearly increases from 1:32 Â 10 21 (water anode) and 1:3 Â 10 21 m À3 (water cathode) to 8:95 Â 10 21 and 1:78 Â 10 22 m À3 , respectively, with the increase of the discharge current from 10 to 28.5 mA. #

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mentioning

confidence: 99%

“…The solid angle of the registration system has been estimated based on the model presented in ref. 12 and is equal to 0.022 sr.…”

mentioning

confidence: 99%

Absolute Concentration of OH Radicals in Atmospheric Pressure Glow Discharges with a Liquid Electrode Measured by Laser-Induced Fluorescence Spectroscopy

Nikiforov

Xiong

Britun

et al. 2011

Appl. Phys. Express

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“…Following the work of Paxton [17] and Galiano et al [19], we calculated the solid angle formula for the circular-type coil for three dimensions. The basic equation of solid angle formulation can be expressed as [17]…”

Section: B Solid Angle Calculation For Z-gradient Coil Patternmentioning

confidence: 99%

“…There is no direct traditional formula to compute inductive couplings between a planar gradient coil and different subdomains. As the formulation of a solid angle expression for three dimensions (3D) subtended by a twodimensional (2D) current-carrying coil of arbitrary shape can be easily performed by simple mathematical manipulations in the Cartesian coordinates [17][18][19][20][21], we have implemented the solid angle form of Ampere's law [22] to compute the inductive coupling between planar gradient coil and any subdomain. We have calculated the 3D solid angle formula for both Zgradient (Gz coil) and X-gradient (Gx coil) coil patterns with the aim of computing coupling relations to subdomains in any position.…”

Section: Introductionmentioning

confidence: 99%

Coupled circuit numerical analysis of eddy currents in an open MRI system

Akram

Terada

Ishi

et al. 2014

Journal of Magnetic Resonance

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We performed a new coupled circuit numerical simulation of eddy currents in an open compact magnetic resonance imaging (MRI) system. Following the coupled circuit approach, the conducting structures were divided into subdomains along the length (or width) and the thickness, and by implementing coupled circuit concepts we have simulated transient responses of eddy currents for subdomains in different locations. We implemented the Eigen matrix technique to solve the network of coupled differential equations to speed up our simulation program. On the other hand, to compute the coupling relations between the biplanar gradient coil and any other conducting structure, we implemented the solid angle form of Ampere's law. We have also calculated the solid angle for three dimensions to compute inductive couplings in any subdomain of the conducting structures. Details of the temporal and spatial distribution of the eddy currents were then implemented in the secondary magnetic field calculation by the Biot-Savart law. In a desktop computer (Programming platform: Wolfram Mathematica 8.0®, Processor: Intel(R) Core(TM)2 Duo E7500 @ 2.93GHz; OS: Windows 7 Professional; Memory (RAM): 4.00GB), it took less than 3min to simulate the entire calculation of eddy currents and fields, and approximately 6min for X-gradient coil. The results are given in the time-space domain for both the direct and the cross-terms of the eddy current magnetic fields generated by the Z-gradient coil. We have also conducted free induction decay (FID) experiments of eddy fields using a nuclear magnetic resonance (NMR) probe to verify our simulation results. The simulation results were found to be in good agreement with the experimental results. In this study we have also conducted simulations for transient and spatial responses of secondary magnetic field induced by X-gradient coil. Our approach is fast and has much less computational complexity than the conventional electromagnetic numerical simulation methods.

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The solid angle subtended by a circular detector for a linear source

Pommé

2007

Applied Radiation and Isotopes

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An analytical solution for the solid angle subtended by a circular detector for a symmetrically positioned linear source

Cited by 7 publications

References 14 publications

Absolute Concentration of OH Radicals in Atmospheric Pressure Glow Discharges with a Liquid Electrode Measured by Laser-Induced Fluorescence Spectroscopy

Absolute Concentration of OH Radicals in Atmospheric Pressure Glow Discharges with a Liquid Electrode Measured by Laser-Induced Fluorescence Spectroscopy

Coupled circuit numerical analysis of eddy currents in an open MRI system

The solid angle subtended by a circular detector for a linear source

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