We consider the solutions of two integrodifferential equations in this work. These equations describe the ultra-low frequency waves in the dipol-like model of the magnetosphere in the gyrokinetic framework. The first one is reduced to the homogeneous, second kind Fredholm equation. This equation describes the structure of the parallel component of the magnetic field of drift-compression waves along the Earth’s magnetic field. The second equation is reduced to the inhomogeneous, second kind Fredholm equation. This equation describes the field-aligned structure of the parallel electric field potential of Alfvén waves. Both integral equations are solved numerically.

中文翻译：

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近地等离子体波传播问题的积分方程

我们在这项工作中考虑两个积分微分方程的解。这些方程描述了陀螺动力学框架中磁层类似偶极子模型中的超低频波。第一个被简化为齐次的第二类 Fredholm 方程。该方程描述了沿地球磁场的漂移压缩波磁场的平行分量的结构。第二个方程简化为非齐次的第二类 Fredholm 方程。该方程描述了阿尔文波平行电场势的场对齐结构。两个积分方程都进行了数值求解。