Straight Thin Wire Antenna Research Articles

Integral Equation Formulations and Related Numerical Solution Methods in Some Biomedical Applications of Electromagnetic Fields

The paper reviews certain integral equation approaches and related numerical methods used in studies of biomedical applications of electromagnetic fields pertaining to transcranial magnetic stimulation (TMS) and nerve fiber stimulation. TMS is analyzed by solving the set of coupled surface integral equations (SIEs), while the numerical solution of governing equations is carried out via Method of Moments (MoM) scheme. A myelinated nerve fiber, stimulated by a current source, is represented by a straight thin wire antenna. The model is based on the corresponding homogeneous Pocklington integro-differential equation solved by means of the Galerkin Bubnov Indirect Boundary Element Method (GB-IBEM). Some illustrative numerical results for the TMS induced fields and intracellular current distribution along the myelinated nerve fiber (active and passive), respectively, are presented in the paper.

Frequency domain boundary element versus time domain finite element model for the transient analysis of horizontal grounding electrode

The paper deals with two different approaches to the assessment of the transient impedance of a horizontal grounding electrode: frequency domain boundary element analysis, based on the straight thin wire antenna model (AM) and generalized telegrapher’s equations combined with inverse Fast Fourier Transform (FFT); and time domain finite element analysis based on the transmission line model (TLM) and standard telegrapher’s equations. Extensive numerical experiments have been undertaken and some of illustrative numerical results are presented in this paper.

On the Oscillations Appearing in Numerical Solutions of Solvable and Nonsolvable Integral Equations for Thin-Wire Antennas

Differences between certain solvable and nonsolvable ill-posed integral equations, with the same nonsingular kernel, are discussed. The main results come from constructing a solvable equation in the context of straight thin-wire antennas. The kernel of this equation is the usual approximate (also called reduced) kernel, while its exact solution is the familiar sinusoidal current. Numerical solutions to this solvable equation are compared to corresponding numerical solutions of the usual-Halle¿n and Pocklington-equations with the approximate kernel; it is known from previous publications that these last two equations are nonsolvable and that their numerical solutions present severe oscillations when the number of basis functions is sufficiently large. It is found that the difficulties encountered in the former (solvable) equation are much less important compared to those of the nonsolvable ones. The same conclusion is brought out from other integral equations, arising in different contexts (thin-wire circular-loop antenna, Method of Auxiliary Sources, and straight wire antenna of infinite length). We discuss the consistency of our results with Picard's theorem. The results in this paper supplement previous publications regarding the difficulties of numerically solving thin-wire integral equations with the approximate kernel.

The time domain integral equation for a straight thin-wire antenna with the reduced kernel is not well-posed

We show that the Pocklington integral equation for time-domain scattering from thin-wire antennas is not mathematically well-posed. This has considerable implications for numerical solution schemes. In particular, our argument explains the observed occurrence of rapidly oscillating errors in numerical solutions as the numerical grid sizes are reduced.

Some thoughts about transient radiation by straight thin wires

The paper discusses, from a physical point of view, several basic features related to the transient radiation of electromagnetic waves by straight thin-wire antennas.

Radiation by a straight thin-wire antenna embedded in an isotropic chiral medium

Radiation characteristics of a straight thin-wire antenna embedded in an isotropic chiral medium are explored. The radiation field contains both left-circularly polarized (LCP) and right-circularly polarized (RCP) components. The radiation pattern is found to be symmetric about the plane theta = pi /2, azimuthally isotropic, and TEM (transverse electromagnetic) in nature; however, all three of these features are found as well for isotropic achiral media. Some specific features of the radiation field on certain constant spherical surfaces are also examined. If the antenna is reduced to a point dipole, it is shown that the radiation resistance is enhanced by the presence of chirality in the embedding medium, and the antenna LCP gain differs from the RCP gain.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>