Dust-ion-acoustic solitons in an ion-beam-driven dusty magnetoplasma with adiabatic and nonadiabatic dust charge variations

TL;DR

This work analyzes small-amplitude dust-ion-acoustic solitons in a magnetized, ion-beam-driven dusty plasma with both adiabatic and nonadiabatic dust-charge variations. By applying reductive perturbation, the authors derive damped KdV equations that incorporate collision-enhanced currents, ion creation/loss, and dust charging dynamics, yielding explicit nonlinear, dispersive, and damping coefficients. They show that soliton energy decays over time and that beam and charging effects strongly influence amplitude, width, and polarity: nonadiabatic charging supports both compressive and rarefactive solitons, while adiabatic charging supports only compressive ones. The results highlight how magnetic field strength, obliquity, beam parameters, and dust-charge fluctuations modulate DIA solitons, with implications for energy transport and stability in laboratory and astrophysical dusty plasmas.

Abstract

We study the characteristics of small-amplitude nonlinear dust-ion-acoustic (DIA) solitary waves in active magnetized positive-ion-beam-driven dusty plasmas with the effects of nonadiabatic and adiabatic dust charge variations. In the model, we consider the ion-neutral collision and thereby consider the collision enhanced ion current to the dust-charging process and dust charge fluctuations. We show that the streaming of the positive-ion beam significantly affects the dust-charging process in which the dust charge number decreases (increases) with an increased beam velocity (number density). Using the standard reductive perturbation technique, we derive the evolution equations in the form of Korteweg-de Vries (KdV) equations for DIA solitary waves for two different cases: nonadiabatic and adiabatic dust charge variations. We study the effect of positive ion beam, dust charge variation, magnetic field, ion creation, and ion-neutral collision enhanced current on the wave characteristics. We find that the soliton energy decays with time and is affected by the beam velocity. Also, the solitary waves get damped by the effects of ion creation, ion loss, ion-neutral collision enhanced current, and dust charge variation. Although the ion beam does not change the polarity of solitary waves in the case of adiabatic dust charge variation, a transition from rarefactive to compressive solitary waves occurs in the presence of an ion beam with nonadiabatic dust charge variation.

Figures (14)

• Figure 1: Profiles of the dust charge number, $Z_{\textrm{d}0}$ [Eq. (\ref{['eqn_dust_charging_equation']})] is shown against the ion-beam to ion density ratio, $\delta_{\textrm{b}}$ in two different cases: Absence and presence of collision enhanced ion current.
• Figure 2: Profiles of the dust charge number, $Z_\textrm{{d}0}$ [Eq. (\ref{['eqn_dust_charging_equation']})] is shown against the ion-beam to ion density ratio, $\delta_{\textrm{b}}$ with different values of the positive ion-beam velocity, $u_{\textrm{b}0}$.
• Figure 3: Profiles of the phase velocity of DIAWs, $\text{v}_{0}$ [Eq. (\ref{['eqn_phase_velocity_adiabatic']}), the case of adiabatic dust charge variation] is shown against the ion-beam to ion density ratio, $\delta_{\textrm{b}}$ with different values of the positive ion-beam velocity, $u_{\textrm{b}0}$ and the dust to ion number density ratio, $\delta_{\textrm{d}}$ as in the legends. The value, $\delta_{\textrm{d}} = 0$ corresponds to the phase velocity in the case of nonadiabatic dust charge variation [Eq. \ref{['eqn_phase_velocity_weakly']}], which is independent of the ion-beam velocity.
• Figure 4: Decay of the soliton energy $(E_g)$ with time $\tau$ is shown with different values of the positive ion-beam streaming velocity $u_{b0}$ corresponding to Eqs. (\ref{['eqn_integral_conserved']}) [Subplot (a), Case of noadiabatic dust-chare variation] and (\ref{['eqn_integral_conserved_adiabatic']}) [Subplot (b), Case of adiabatic dust charge variation].
• Figure 5: Profiles of DIA solitons are shown for different values of the beam to ion density ratio, $\delta_b$. Subplots (a) and (b), respectively, correspond to solutions (\ref{['eqn_time_dependence_analytical']}) and (\ref{['eqn_time_dependence_analytical_adiabatic']}) obtained in the cases of nonadiabatic and adiabatic dust charge variations.