Full-Path Nonlinear Modeling of Microwave Power Transmission Through Ionospheric Plasma for Space Solar Power Station

Abstract

Space Solar Power Station (SSPS) concepts rely on gigawatt-class microwave beams to carry orbital solar energy through the ionosphere, where the beam and the plasma form a coupled nonlinear system: the field heats electrons, the heating alters the collision frequency and plasma density, and the modified medium in turn reshapes the field. To our knowledge, this work is the first study to quantify this two-way interaction between microwave power transmission and the ionospheric plasma environment through full-path nonlinear modeling. The 340 km path from 400 km to 60 km altitude is reconstructed by 34 cascaded two-dimensional axisymmetric finite-element full-wave segments with complex-field transfer, using International Reference Ionosphere (IRI) electron-density and NRLMSISE-00 neutral-atmosphere inputs. A Shallow Neural Network (SNN) surrogate replaces the implicit electron energy balance with an explicit closure that maps altitude and local field magnitude to electron temperature and effective collision frequency, enabling stable nonlinear iteration. For 1 GW beams at 2.45 GHz and 5.8 GHz, the volume-integrated Ohmic deposition is 29.4 kW and 5.11 kW, respectively -- fractional losses of order $10^{-5}$ -- and the ratio between the two bands follows the $ω^{-2}$ scaling of collisional absorption. The deposition concentrates near 95 km altitude, where the product of electron density and collision frequency peaks, whereas the electron-temperature perturbation (up to 3815 K) maximizes in the F region, where cooling is weakest; ponderomotive density depletion remains below 0.02\%. The ionosphere is therefore effectively transparent to the SSPS power budget but not to the beam phase: localized heating and refractive perturbation accumulate phase-front distortion relevant to phased-array beam control, rectenna phase compensation, and environmental assessment.