Mutual Coupling and Impedance of a VLF Curtain Array in an Anisotropic Magnetoplasma

Abstract

In this letter, we investigate and propose an analytical method for calculating the mutual impedance of a very low frequency (VLF: 3–30 kHz) curtain array immersed in an anisotropic magnetoplasma. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> simultaneous integral equations satisfied by the array are first built with full consideration of the coupling effect between different elements. Under the assumption that the currents of adjacent elements differ from a fixed phase, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -coupled integral equations are reduced to an independent one, which is solved to determine the complete distribution of current on each element. The self- and mutual impedances of the array are then evaluated through the induced electromotive force method. Computations show that the current is more concentrated at the middle part of the antenna as its electrical length increases, and the error that appeared on both the amplitude and phase of the required voltages verifies the existence of the mutual coupling effect. It is also found that both the self- and mutual impedances will experience certain fluctuations when the electrical length of the elements changes, with maxima and minima occurring at several particular lengths. The approach may provide theoretical support to the prediction of mutual impedance in practical VLF array applications.