Cataloging the nonlinear waves excited by moving a charged body in the dusty plasma medium

TL;DR

The study addresses how a moving charged body excites nonlinear waves in a dusty plasma and models this with the forced Korteweg–de Vries ($fKdV$) equation to balance nonlinearity, dispersion, and external forcing. It catalogs wakes and several soliton types (precursor, pinned) and introduces a novel lagging soliton that trails the source, with the dynamics governed by driver parameters ($A$, $G$, $v_d$) and the nonlinearity coefficient $b$, analyzed via a Fourier pseudo-spectral numerical scheme. The work provides a parametric map of transitions among linear and nonlinear structures and demonstrates that lagging solitons can mediate these transitions, offering new physical insight and potential debris-detection signatures. Overall, the findings extend the theoretical understanding of nonlinear wave excitation in dusty plasmas and suggest practical diagnostic applications for orbital debris tracking.

Abstract

The nonlinear waves excited by the movement of a charged body in the dusty plasma medium are studied. A charged body moving through a dusty plasma medium can generate diverse nonlinear waves, such as precursors and pinned solitons. These wave excitations under weakly nonlinear and dispersive limits are described theoretically by the forced Korteweg-de Vries (fKdV) type equation. We have examined the role of the driver in shaping and evolving these wave excitations. In particular we studied the effect of primarily three source parameters, namely, amplitude, width, and flow speed, on the evolution of nonlinear structures. The driver generates a perturbation in the stable system configuration, which couples with medium characteristics and eventually evolves into propagating excitations. Our finding shows that the excitation of nonlinear structure by a moving body in a plasma medium is not just dictated by the mach number but also the features of the source such as amplitude and width. As a novel finding apart from pinned and precursor solitons, we observe another nonlinear structure that lags behind the source term, maintaining its shape and speed as it propagates. These features are the first ever theoretical depiction of such lagging structures.

Figures (6)

• Figure 1: Keeping amplitude constant and increasing width.For velocity 1.5,Nonlinearity 6.2,Amplitude 0.5 (a) wakes [$G=0.5$], (b) wakes [$G=1$], (c) lagging structure [$G=2$], (d) pinned [$G=4$].
• Figure 2: Keeping width constant and increasing amplitude.For velocity 1.5,Nonlinearity 6.2,width 1 (a) wakes [$A=0.5$], (b) precursor [$A=2$].
• Figure 3: Lagging structure formed for velocity 2;Amplitude 2;Width 4;Nonlinearity 2.
• Figure 4: (a) Velocity , (b) AL$^2$ Value , for the lagging structure formed with ;A=2,G=4,vd=2,b=2.
• Figure 5: Keeping width constant and increasing amplitude.For Velocity 1.5,Nonlinearity 6.2,width 0.5 (a) Precursor [$A=6$], (b) Precursor [$A=10$].