Abstract
In this semi-analytic study we develop a mathematical model for determining the electromagnetic field due to a current-driven antenna immersed in a cold, magnetized plasma, valid for frequencies below the electron plasma frequency. At each point in the plasma, it is shown that the vacuum electric field of the antenna couples to the plasma conductivity tensor and acts as an infinitesimal source term to drive plasma currents – the total field is then found from the aggregate sum of these point sources, expressed as an integral across the vacuum field. A general solution is provided for both azimuthally symmetric cylindrical coordinates as well as a fully generalized Cartesian solution. As an example of how this general solution may be applied, we solve for the field due to an electric dipole antenna of length $\ell$ , aligned along the background field, at frequencies below the ion cyclotron frequency. It is found that the near field decays exponentially with increasing $k_{\bot }z$ , whereas the far field exhibits wave-like behaviour. The radiation zone exhibits propagation cones emanating from either end of the dipole, with a propagation angle that is consistent with past analytic studies of inertial Alfvén waves. The mathematical model presented here may be advantageous over other numerical methods, as it allows the user to solve parts of the problems analytically, thereby cutting down significantly on computation time, as well as offering physical insight into the system that may not be evident with other numerical solvers.
Highlights
Understanding the behaviour and propagation of plasma waves is of fundamental importance in both laboratory and space plasmas
In this paper we successfully developed a semi-analytic model for determining the electromagnetic field due to a current-driven antenna in a cold, magnetized plasma
The general solution is a superposition of the fast and slow waves, which are the two fundamental modes of the cold plasma. It is typical in many laboratory plasmas for the fast wave to be evanescent, with only the slow wave being measurable far away from the antenna
Summary
Understanding the behaviour and propagation of plasma waves is of fundamental importance in both laboratory and space plasmas. Similar experiments were later done in the kinetic regime using the same antenna (Gekelman et al 1997), and the corresponding theoretical paper again agreed with the results (Morales & Maggs 1997) Both theoretical models take the general solution to the azimuthally symmetric cold plasma wave equation, and use the boundary conditions imposed by the antenna (which can either be an equipotential or constant current surface) to uniquely determine the resulting spatial structure of the excited wave. A similar semi-analytical model for analysing inductively coupled waves was previously devised by Jaeger et al (1995) and used to model the behaviour of radio frequency (RF) power deposition in high-density plasma tools Both of these theoretical models for inductively coupled antennae are similar in that they treat the external antenna currents as a ‘source’ term to the cold plasma wave equation, which is contrary to the strategy of boundary condition matching that was employed for the electrostatic disk exciter.
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