Simulation of Forced Korteweg De Vries Equation as Applied to Small Orbital Debris
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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.
This code uses the Chan & Kerkhoven pseudospectral method to solve the Forced Korteweg-de Vries equation to simulate 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. The Damped Forced Korteweg-de Vries equation is solved to calculate the damping rate of the solitons, and estimate the resulting soliton propagation distance. Finally, the Damped Forced Kadomtsev-Petviashvili Equation is solved to simulate transverse solitonic perturbations across the width of the debris.