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.

中文翻译：

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冷磁化等离子体中电流驱动天线电磁场的半解析模型

在这项半解析研究中，我们开发了一个数学模型，用于确定由于电流驱动天线浸入冷磁化等离子体中产生的电磁场，该模型适用于低于电子等离子体频率的频率。在等离子体中的每个点，表明天线的真空电场耦合到等离子体电导张量并充当驱动等离子体电流的无穷小源项 - 然后从这些点源的总和中找到总场，表示为整个真空场的积分。为方位对称柱坐标以及完全广义笛卡尔解都提供了通用解。作为如何应用这种通用解决方案的示例，我们求解由长度为的电偶极子天线引起的场 $\ell$ ，沿背景场对齐，频率低于离子回旋加速器频率。发现近场随着增加而呈指数衰减 $k_{\bot }z$ ，而远场表现出波状行为。辐射区展示了从偶极子两端发出的传播锥，传播角度与过去对惯性阿尔文波的分析研究一致。此处介绍的数学模型可能优于其他数值方法，因为它允许用户分析解决部分问题，从而显着减少计算时间，并提供对系统的物理洞察力，而其他方法可能不明显数值求解器。