Simulating Damped Ion Acoustic Solitary Waves from Orbital Debris

Abstract

Nontrackable orbital debris has become a great risk to Earth-orbiting spacecraft. Subcentimeter debris is currently undetectable using ground-based radar and optical methods. Recent analytical, computational, and experimental work has shown that plasma density solitary waves, or solitons, will be produced by orbital debris due to their electrical charge, and propagate along the debris velocity vector. The amplitude and velocity of solitons that may be produced by millimeter–centimeter-scale orbital debris, as well as the orbital altitudes, latitudes, and velocities where solitons can be produced as a function of debris size, have been previously described. The Chan–Kerkhoven pseudospectral method is used now to apply the damped forced Korteweg–de Vries equation, calculate the damping rate of the solitons, and estimate the resulting soliton propagation distance. It is demonstrated that Landau damping dominates over collisional damping for these solitons. Pinned solitons, which travel with the debris, do not experience significant damping due to the presence of the persistent debris force at the soliton location, and will continue to propagate until the debris enters a region where pinned solitons cannot be created. The median propagation distance for precursor solitons, which advance ahead of the debris, is 10 km for 0.5-mm-radius debris and 6 km for 0.5-cm-radius debris. 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. It is necessary to understand the damping of solitons in order to assess the feasibility of on-orbit debris detection.