Signal Processing and Forward Modeling of Space Debris Detection via Plasma Solitons

Abstract

The nonlinear interaction of objects in low Earth orbit with the space plasma environment has been hypothesized to cause precursor soliton plasma waves. These plasma-object interactions may lead to unique engineering applications, especially the detection of hazardous sub-centimeter orbital debris that is undetectable by conventional methods. This nonlinear perturbation is currently modeled by the forced Korteweg - de Vries (fKdV) equation. This thesis aims to understand and characterize these waves through simulation beyond the fKdV model while progressing space-based and ground detection schemes. Ultimately this technique may play an important role in the problem of detecting small space debris. Three aspects of this detection scheme are developed. This includes two unconventional methods of detecting solitons. First the inverse scattering transform (IST), a mathematical spectral technique for decomposing a time series, is shown to automatically detect solitons from data. A numerical experiment using the fKdV model is performed to demonstrate this ability. The IST is suitable as an in situ detection method. It could be the basis of a debris collision early warning system for spacecraft. Second, the existing technique of ionospheric sensing using Global Navigation Satellite System (GNSS) is extended to detecting spacecraft plasma wakes. Traditionally, it is used for global scale space weather monitoring. An experiment is carried out using a known target, the International Space Station, on existing GNSS receivers that measure the ionospheric irregularity associated with the spacecraft. This experiment shows that there is a modification to the total electron content (TEC) when the ISS flies through the radio line-of-sight. Using models that are compared to the experiment, a multi-point sensor is proposed that would resolve the diffraction pattern from these plasma structures. This work uses multi-fluid plasma simulation to refine the fKdV model of soliton generation from debris. In particular, we find that the range of ion acoustic Mach numbers that are conducive to precursor soliton generation is larger than predicted by the fKdV equation. A new theory that matches the multi-fluid simulation results is derived using pressure balances to predict the supercritical Mach number. This new theoretical understanding of the critical Mach numbers predicts a wider range of orbits that will create precursor solitons than in previous studies. In addition, several new details of precursor solitons are discovered and characterized with multi-fluid simulation. This includes changes in the amplitude scaling of the periodicity of soliton generation (the "intersoliton interval"). Importantly, corrections to the first order results of the fKdV equation which couple fluid velocity, density, and electrostatic potential are identified. A theory that explains this in the small amplitude limit is derived. For debris detection, this effect impacts how the soliton is detected. The same soliton will manifest different amplitudes in each plasma species, contrary to the result of the fKdV equation. Thus, a model error in inferring debris properties from solitons has been discovered.