Propagation analysis method considering angular spread for random electromagnetic waves in magnetized cold plasma

Random waves can be described as the sum of numerous plane waves, and stochastic processes describe their properties. Various methods have been used to widely investigate the propagation characteristics of electromagnetic waves in magnetized cold plasma based on a single-plane wave approximation. On the other hand, the properties of random waves are difficult to analyze using these methods. Instead, a framework of the wave distribution function (WDF) should be employed. In this study, we provide an explicit expression for an integration kernel in a magnetized cold plasma used for the WDF method. We show that the kernel can be approximated in the case of ultralow frequency/very low frequency (ULF/VLF) parts of whistler-mode waves with quasi-parallel propagation. We also propose a method for estimating a WDF representing a directional distribution of the wave energy density based on the principle of maximum entropy using three-component spectral matrix data of the magnetic field. Based on the insights obtained from the proposed method, we define a quantity called "sharpness," which provides spreading of wave normal angles. The sharpness is particularly effective in showing the spread of the wave normal angles for random non-single-plane waves. Compared with the conventional methods which evaluate the propagation properties (such as planarity), the "sharpness" exhibited a low calculation load and can be implemented easily for onboard processing.