Generation of Realizations of Electron Density for Numerical Electromagnetic Propagation Simulations

Abstract

Numerical calculations of electromagnetic (EM) wave propagation that solve the parabolic wave equation generally require that the propagation medium consists of a number of phase-changing screens. In general, the screens can be random, deterministic, or a combination (Deshpande et al., 2014;Grimault, 1998;Knepp, 1983). Deterministic shapes include Gaussian lenses, elongated Gaussian striations, and more complicated shapes. Statistically based or random phase screens are usually generated using Fourier transform techniques where the phase of the screen is calculated as the FFT of the product of the square root of the desired power spectrum and white Gaussian noise. In related study, Rino et al. (2019Rino et al. ( , 2018) develop a configuration space model that utilizes successive bifurcation to compute the striation sizes and their number to generate realizations of a structured medium. The bifurcation rule is intimately related to the instability mechanism that generates ionospheric structure. Furthermore, the bifurcation rule can be constrained to produce a structure having ionospheric-like two-component power-law power spectral density (PSD). In contrast to the more general configuration-space approach, the current paper obtains closed-form solutions by imposing rigid constraints to the solution.A physically intuitive technique is considered here to generate random realizations of ionospheric structure. Consider the two-dimensional (2-D) problem, where the ionospheric structure is infinitely elongated in the y-direction. The z-direction is the direction of propagation. This geometry represents propagation in the equatorial region of the earth, where the magnetic field lines are elongated in the north-south direction. The ionization consists of a finite number of Gaussians with random locations in the x − z plane and with random radii. The radius of each Gaussian is drawn from a user-chosen probability density function. This simple description is sufficient to generate numerical realizations of a disturbed 2-D ionosphere. Furthermore, it is possible to analytically calculate the PSD of electron density fluctuations and the PSD and autocorrelation function of the phase of the phase screens used to represent the ionosphere. Two different probability density functions for the striation size distribution are considered. One yields a single-component power-law PSD with the inner and outer scale of the form often observed in the ionosphere. The other leads to a power-law form of the correlation function of in-situ ionospheric structure. Superposing Gaussians with Gaussian-distributed variances, as we detail below, also gives rise to the Castaing distribution.