Impedance of a finite insulated cylindrical antenna in a cold plasma with a longitudinal magnetic field

Abstract

A variational formulation is developed for the impedance of a finite cylindrical antenna embedded in a dielectric cylinder, which is surrounded by a magnetoionic medium (cold electron plasma) with the static magnetic field impressed in a direction parallel to the antenna axis. Closed form expressions are obtained in the limit of low frequencies, and for short antennas in a uniaxial medium. The impedance of a short antenna is nearly the same as for an assumed triangular current distribution, except that further resonances are observed in the vicinity of the gyro frequency, where the antenna becomes electrically long. These resonances may be shifted to frequencies exceeding the gyro frequency in the presence of an insulating layer around the antenna. For very thin insulating layers the wave number of the variationally approximated current distribution is to the first order equal to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sqrt{\epsilon_{1}} k_{0}</tex> ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\epsilon_{1}</tex> is the leading diagonal element of the permittivity matrix), where the gyro frequency may be both smaller or larger than the plasma frequency. However, this approximation does not apply to current distributions along the insulated antenna. The present calculations are also compared with earlier work on antenna impedances.