Three-Dimensional Kadomtsev–Petviashvili Damped Forced Ion Acoustic Solitary Waves from Orbital Debris

Abstract

Subcentimeter debris has been proven to cause significant damage to Earth-orbiting spacecraft sensors and subsystems; however, they are currently undetectable using ground-based radar and optical methods. Orbital debris will produce plasma density solitary waves, or solitons, due to their electrical charge, which propagate along the debris velocity vector, with amplitudes within the range of detectability by existing ground- and space-based sensors. Previously, using the damped forced Korteweg–de Vries equation, the orbital altitudes, latitudes, and velocities, where solitons can be produced by millimeter- to centimeter-sized debris, were identified in the presence of Landau damping and considering one spatial dimension. The soliton amplitude, width, speed, wavelength, and propagation distance were also modeled as a function of debris size and speed. Now, the full 3-D signature of orbital debris solitons is simulated using the damped forced Kadomtsev–Petviashvili equation. Transverse solitonic perturbations extend across the width of the debris, with predictable amplitudes and speeds that can be approximated by the 1-D 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 3-D simulations, allowing for additional opportunity for detection. The presented 3-D soliton predictions will facilitate design of future detection methods. Orbital debris solitons would enable the first collision-free mapping of the small debris population.