Abstract Garay-Avendaño and Zamboni-Rached defined two classes of axisymmetric solutions of the free Maxwell equations. We prove that the linear combinations of these two classes of solutions cover all totally propagating time-harmonic axisymmetric free Maxwell fields – and hence, by summation on frequencies, all propagating axisymmetric free Maxwell fields. It provides an explicit representation for these fields. This will be important, e.g., to have the interstellar radiation field in a disc galaxy modeled as an exact solution of the free Maxwell equations.

中文翻译：

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自由麦克斯韦方程轴对称解的显式表示

摘要 Garay-Avendaño 和Zamboni-Rached 定义了两类自由麦克斯韦方程的轴对称解。我们证明这两类解的线性组合涵盖了所有完全传播的时谐轴对称自由麦克斯韦场——因此，通过频率求和，所有传播轴对称自由麦克斯韦场。它为这些字段提供了明确的表示。这将很重要，例如，将盘状星系中的星际辐射场建模为自由麦克斯韦方程的精确解。