Mathematics Interdisciplinary Research

Mathematics Interdisciplinary Research

A Useful Mathematical Lemma‎: ‎Shifted Coordinate Transformations for Analytical Modeling of Plasma Multi-Ring Antennas

Document Type : Original Scientific Paper

Authors
‎Department of Photonics-Plasma‎, ‎Faculty of Physics, ‎University of Kashan, ‎Kashan‎, ‎I‎. ‎R‎. ‎Iran
10.22052/mir.2026.258025.1557
Abstract
‎Transformations of scalar and vector quantities from one Cartesian coordinate system to a shifted Cartesian frame constitute a powerful tool in linear algebra with wide applicability in solving physical problems‎. ‎In this work‎, ‎we employ such coordinate transformations to construct a unified analytical formulation for multi-ring plasma antennas‎. ‎By expressing the vector and scalar potentials in systematically shifted Cartesian coordinates‎, ‎the electromagnetic fields and radiation impedance of single-ring and multi-ring structures are derived in closed form‎. ‎The method clarifies how radiation resistance and field distributions depend on ring number‎, ‎radii‎, ‎and vertical displacements‎, ‎while showing that symmetric arrangements lead to notable mathematical simplifications‎. ‎Because the framework is built upon generalizable coordinate transformations‎, ‎it naturally extends to a broad class of antenna geometries composed of repetitive or modular elements‎. ‎This highlights the strength of the mathematical approach‎: ‎many complex antenna configurations become analytically tractable once reformulated through shifted Cartesian transformation techniques‎.
Keywords
Subjects

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Articles in Press, Accepted Manuscript
Available Online from 30 October 2026