Calculating current densities and fields due to shielded bi-planar radio-frequency coils

A method for the accurate computation of the current densities produced in a wide-runged bi-planar radio-frequency coil is presented. The device has applications in magnetic resonance imaging. There is a set of opposing primary rungs, symmetrically placed on parallel planes and a similar arrangement of rungs on two parallel planes surrounding the primary serves as a shield. Current densities induced in these primary and shielding rungs are calculated to a high degree of accuracy using an integral-equation approach, combined with the inverse finite Hilbert transform. Once these densities are known, accurate electrical and magnetic fields are then computed without difficulty. Some test results are shown. The method is so rapid that it can be incorporated into optimization software. Some preliminary fields produced from optimized coils are presented.

The design of planar gradient coils. Part I: A winding path correction method

In this work a new approach for designing planar gradient coils is outlined for the use in an existing MRI apparatus. A technique that allows for gradient field corrections inside the diameter-sensitive volume is deliberated. These corrections are brought about by making changes to the wire paths that constitute the coil windings, and hence, is called the path correction method. The existing well-known target held method is used to gauge the performance of a typical gradient coil. The gradient coil design methodology is demonstrated for planar openable gradient coils that can be inserted into an existing MRI apparatus. The path corrected gradient coil is compared to the coil obtained using the target field method. It is shown that using a wire path correction with optimized variables, winding patterns that can deliver high magnetic gradient field strengths and large imaging regions can be obtained.

Supersonic velocimetry in a shock tube using laser enhanced ionisation and planar laser induced fluorescence

A novel flow-tagging technique is presented which was employed to measure gas velocities in the free stream of a shock tube. This method is based on the laser spectroscopic techniques of Laser-Enhanced Ionisation (LEI) and Laser-Induced Fluorescence (LIF). The flow in the shock tube is seeded with small amounts of sodium, and LEI is used to produce a substantial depletion of neutral sodium atom concentration in a well-defined region of the flow, by using two wavelength-resonance excitation and subsequent collisional ionisation. At a specific time delay, single-laser-pulse planar LIF is utilised to produce a two-dimensional (2-D) inverse image of the depleted tagged region downstream of the flow. By measuring the displacement of the tagged region, free stream velocities in a shock tube were determined. Large variations in the concentration of sodium seeded into the flow were observed and even in the presence of these large variations accurate free-stream velocity measurements were obtained. The experimentally determined value for velocity compares very well with the predicted velocity.

Measurements of neutral atom diffusion and electron-ion recombination by laser enhanced ionisation and planar laser induced fluorescence in an air-acetylene flame

The spatial and temporal evolution of a depleted atomic distribution created by laser enhanced ionisation (LEI) was employed to determine both a diffusion coefficient for sodium (Na) and an electron (e(-)) and sodium ion recombination rate coefficient in an analytical air-C2H2 flame. A depleted distribution of neutral sodium atoms was produced in a flame by ionising approximately 80% of the irradiated sodium atoms in a well defined region using a two step LEI excitation scheme. Following depletion by ionisation, planar laser induced fluorescence (PLIF) images of the depleted region recorded the diffusion and decay of the depleted Na distribution for different depletion-probe delays. From measurements of the diffused width of the distribution, an accurate diffusion coefficient D = (1.19 +/- 0.03) x 10(-3) m(2) s(-1) for Na was determined in teh burnt gases of the flame. Measurements of the integrated fluorescence intensity in the depleted region for different depletion-probe delays were related to an increase in atomic sodium concentration caused by electron-ion recombination. At high concentrations (greater than or equal to 50 mu g ml(-1)), where the electron and ion concentrations in the depleted region were assumed equal, a recombination rate coefficient of 4.2 x 10(-9) cm(3) s(-1) was calculated. (C) 1997 Elsevier Science B.V.

Complex natural resonances of conducting planar objects buried in a dielectric half-space

A scheme is presented to incorporate a mixed potential integral equation (MPIE) using Michalski's formulation C with the method of moments (MoM) for analyzing the scattering of a plane wave from conducting planar objects buried in a dielectric half-space. The robust complex image method with a two-level approximation is used for the calculation of the Green's functions for the half-space. To further speed up the computation, an interpolation technique for filling the matrix is employed. While the induced current distributions on the object's surface are obtained in the frequency domain, the corresponding time domain responses are calculated via the inverse fast Fourier transform (FFT), The complex natural resonances of targets are then extracted from the late time response using the generalized pencil-of-function (GPOF) method. We investigate the pole trajectories as we vary the distance between strips and the depth and orientation of single, buried strips, The variation from the pole position of a single strip in a homogeneous dielectric medium was only a few percent for most of these parameter variations.

On the fast approximation of Green's functions in MPIE formulations for planar layered media

The numerical implementation of the complex image approach for the Green's function of a mixed-potential integralequation formulation is examined and is found to be limited to low values of k(0) rho (in this context k(0) rho = 2 pirho/ lambda(0), where rho is the distance between the source and the field points of the Green's function and lambda(0) is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large k(0) rho is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Green's functions. In this paper, the method developed for the computation of the Green's function is used for planar structures containing both lossless and lossy media.

Lexicographic decomposition of chains and the concept of a planar chain

In an earlier paper [Journal of Mathematical Economics, 37 (2002) 17-38], we proved that if a preference relation on a commodity space is non-representable by a real-valued function then that chain is necessarily a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. In this paper, we study the class of planar chains, the simplest example of which is the Debreu chain (R-2, <(l)). (C) 2002 Elsevier Science B.V. All rights reserved.

Stability of planar flames as gasdynamic discontinuities

The stability of a steadily propagating planar premixed flame has been the subject of numerous studies since Darrieus and Landau showed that in their model flames are unstable to perturbations of any wavelength. Moreover, the instability was shown to persist even for very small wavelengths, i.e. there was no high-wavenumber cutoff of the instability. In addition to the Darrieus-Landau instability, which results from thermal expansion, analysis of the diffusional thermal model indicates that premixed flames may exhibit cellular and pulsating instabilities as a consequence of preferential diffusion. However, no previous theory captured all the instabilities including a high-wavenumber cutoff for each. In Class, Matkowsky & Klimenko (2003) a unified theory is proposed which, in appropriate limits and under appropriate assumptions, recovers all the relevant previous theories. It also includes additional new terms, not present in previous theories. In the present paper we consider the stability of a uniformly propagating planar flame as a solution of the unified model. The results are then compared to those based on the models of Darrieus-Landau, Sivashinsky and Matalon-Matkowsky. In particular, it is shown that the unified model is the only model to capture the Darrieus-Landau, cellular and pulsating instabilities including a high-wavenumber cutoff for each.

An electromagnetic-field method modeling of a radial line planar antenna with coupling probes

This communications describes an electromagnetic model of a radial line planar antenna consisting of a radial guide with one central probe and many peripheral probes arranged in concentric circles feeding an array of antenna elements such as patches or wire curls. The model takes into account interactions between the coupling probes while assuming isolation of radiating elements. Based on this model, computer programs are developed to determine equivalent circuit parameters of the feed network and the radiation pattern of the radial line planar antenna. Comparisons are made between the present model and the two-probe model developed earlier by other researchers.

Numerical evaluation of three dimensional effects in planar flow birefringence

The influence of three dimensional effects on isochromatic birefringence is evaluated for planar flows by means of numerical simulation. Two fluid models are investigated in channel and abrupt contraction geometries. In practice, the flows are confined by viewing windows, which alter the stresses along the optical path. The observed optical properties differ therefore from their counterpart in an ideal two-dimensional flow. To investigate the influence of these effects, the stress optical rule and the differential propagation Mueller matrix are used. The material parameters are selected so that a retardation of multiple orders is achieved, as is typical for highly birefringent melts. Errors due to three dimensional effects are mainly found on the symmetry plane, and increase significantly with the flow rate. Increasing the geometric aspect ratio improve the accuracy provided that the error on the retardation is less than one order. (C) 2004 Elsevier B.V. All rights reserved.

The design of planar gradient coils. Part ll: A weighted superposition method

In this work a superposition technique for designing gradient coils for the purpose of magnetic resonance imaging is outlined, which uses an optimized weight function superimposed upon an initial winding similar to that obtained from the target field method to generate the final wire winding. This work builds on the preliminary work performed in Part I on designing planar insertable gradient coils for high resolution imaging. The proposed superposition method for designing gradient coils results in coil patterns with relatively low inductances and the gradient coils can be used as inserts into existing magnetic resonance imaging hardware. The new scheme has the capacity to obtain images faster with more detail due to the deliver of greater magnetic held gradients. The proposed method for designing gradient coils is compared with a variant of the state-of-the-art target field method for planar gradient coils designs, and it is shown that the weighted superposition approach outperforms the well-known the classical method.

Investigations into a wideband spatial beamformer employing a rectangular array of planar monopoles

This paper presents a rectangular array antenna with a suitable signal-processing algorithm that is able to steer the beam in azimuth over a wide frequency band. In the previous approach, which was reported in the literature, an inverse discrete Fourier transform technique was proposed for obtaining the signal weighting coefficients. This approach was demonstrated for large arrays in which the physical parameters of the antenna elements were not considered. In this paper, a modified signal-weighting algorithm that works for arbitrary-size arrays is described. Its validity is demonstrated in examples of moderate-size arrays with real antenna elements. It is shown that in some cases, the original beam-forming algorithm fails, while the new algorithm is able to form the desired radiation pattern over a wide frequency band. The performance of the new algorithm is assessed for two cases when the mutual coupling between array elements is both neglected and taken into account.