Sub-centimeter orbital debris is currently undetectable using ground-based radar and optical methods. However, pits in Space Shuttle windows produced by paint chips demonstrate that small debris can cause serious damage to spacecraft. Recent analytical, computational and experimental work has shown that charged objects moving quickly through a plasma will cause the formation of plasma density solitary waves, or solitons. Due to their exposure to the solar wind plasma environment, even the smallest space debris will be charged. Depending on the debris size, charge and velocity, debris may produce plasma solitons that propagate along the debris velocity vector and could be detected with existing sensor technology. Plasma soliton detection would be the first collision-free method of mapping the small debris population.

The first major contribution of this thesis is the identification of orbital locations where solitons will be produced, as a function of debris size and speed. Using the Chan & Kerkhoven pseudospectral method, we apply the Forced Korteweg-de Vries equation to describe the amplitude, width, and production frequency of solitons that may be produced by mm-cm scale orbital debris, as a function of the debris' size, velocity, and location (altitude, latitude, longitude) about Earth.

Analytical solutions result in solitons that propagate forever without damping, assuming a uniform plasma environment. However, Earth's space plasma is complex, with processes that could cause the solitons to dampen. Damped solitons will have a limit to the distance they will travel before becoming undetectable. For our second major contribution, we calculated the propagation distance of solitons in the presence of damping processes. We applied the Damped Forced Korteweg-de Vries equation to calculate the damping rate of the solitons, and estimate the resulting soliton propagation distance. We demonstrate that Landau damping dominates over collisional damping for these solitons. It is necessary to understand the damping of solitons in order to assess the feasibility of on-orbit debris detection.

In our first contribution, we demonstrate that one dimensional simulations are sufficient to model the orbital debris solitons that propagate along the debris velocity vector. However, in order to fully understand the soliton signatures in a 3D spatial environment, it is necessary to extend the Damped Forced Korteweg-de Vries model to three spatial dimensions. For our final major contribution, we apply the Damped Forced Kadomtsev-Petviashvili Equation, which is a natural extension for waves described by the Damped Forced Korteweg-de Vries equation. Transverse solitonic perturbations extend across the width of the debris, with predictable amplitudes and speeds that can be approximated by the one dimensional Damped Forced Korteweg-de Vries equation at the transverse soliton location. The transverse perturbations form soliton rings that advance ahead of the debris in the three dimensional simulations, allowing for additional opportunity for detection.

With the current absence of a dedicated, calibrated, on-orbit debris detection sensor, plasma soliton detection would be the first collision-free method of mapping the small debris population. The characteristics of plasma solitons described here are necessary to evaluate the feasibility of orbital debris detection via soliton detection with future debris detection systems.