关于求各向异性介质中电磁场的格林张量函数的一个方法

本文提出一个方法,来推求在(3)式中所定义的、在全空间中的格林张量函数。它有时亦称为对应微分方程的基本解。这个方法是以富氏变换为基础。由于问题的复杂性,我们不得不作某些近似。首先,把各向异性介质分为两类,一类是磁迴旋介质,另一类是电迴旋介质。对于磁迴旋介质,如铁氧体,取μ为张量而ε为标量。而对电迴旋介质,如等离子体,取ε为张量而μ为标量。其次,由于矩阵μ_p非常小(在(15)式中定义),我们可以把解展为μ_p的冪级数,并计算出一级近似。具体结果在式(23)、(25)、(28)、(32)和(33)中表示。最后对Г函数的物理意义和它的渐近展开式的有效范围作了讨论。

ABOUT ONE METHOD OF FINDING THE GREEN TENSOR FUNCTIONS OF ELECTROMAGNETIC FIELD IN ANISOTROPIC MEDIA

In this paper, we suggest one method of finding the Green tensor functions in whole space, which are defined in formula (3). Some times it is also called the elementary solution of the corresponding differential equation. All this method is based on Fourier transform. Owing to complexity, we are obliged to make some simplifications. Magneto-gyrotropic media and electric-gyrotropic media are considered separately. For magneto-gyrotropic medium, such as ferrite, μ, is a tensor while ε remains scalar. Conversely, for electric-gyrotropic medium, such as plasma, ε is tensor and μ remains scalar. Taking advantage of the smallness of matrix μ_p (defined in (15)) we make an expansion in power series of μ_p, and carry out the calculations in first order approximation. The concrete results are expressed in formulae (23)、(25)、(28)、(32) and (33). The physical meaning of Γ and the effective region of the asymptotic expansions are discussed.