Ion-beam driven dust-cyclotron and dust-lower-hybrid instabilities in nonthermal dusty magnetoplasmas with dust-charge fluctuation

TL;DR

The paper addresses how an ion beam can induce and couple dust-cyclotron and dust-lower-hybrid-like modes in nonthermal dusty magnetoplasmas with dust-charge fluctuations. By employing two-fluid ions and dust, κ-distributed electrons and ions, and OML dust charging, the authors derive a general linear dispersion relation and show a novel dispersive DLH-like mode that couples to DC through beam effects, with a frequency below $\widetilde{\omega}_{\rm{dl}}$. Growth rates are obtained for both Cerenkov and beam-cyclotron resonances, revealing that maximum growth occurs near resonances and saturates at high wavenumbers; these instabilities are sensitive to $\\sigma_i$, $Z_e$, $\\kappa_e$, $\\kappa_i$, $\\delta_e$, and magnetic field strength. The findings have implications for energy transfer and cross-field transport in space environments (e.g., magnetospheres) and laboratory dusty plasmas, offering insight into beam-driven heating and confinement loss and suggesting avenues for nonlinear follow-up studies.

Abstract

We reveal a new dispersive dust-lower-hybrid (DLH)-like mode that can couple to modified dust-cyclotron (DC) waves in a dusty magnetoplasma by the influence of a streaming ion beam. Previous studies have overlooked such hybrid modes and the coupling in the study of resonant cyclotron instabilities in dusty magnetoplasmas. Using two-fluid models for positive ion beams and charged dust grains, nonthermal $κ$-density distributions for electrons and positive ions, and orbital motion limited (OML) models for dust-charge fluctuations, we derive a general linear dispersion relation for the coupled DLH and DC modes in the limit of when the hydrodynamic time scale is much longer than the dust-charging time scale. The hybrid mode propagates with a frequency lower than the typical dust-lower-hybrid frequency, $\widetildeω_{\rm{dl}}\equivω_{\rm{pd}}Ω_d/\sqrt{ω^2_{\rm{pd}}+Ω^2_d}$, where $ω_{\rm{pd}}$ is the dust-plasma oscillation frequency and $Ω_d$ is the dust-cyclotron frequency. We obtain the growth rates of instabilities due to Cerenkov and cyclotron interactions and analyze them, taking into account the influences of the static magnetic field, ion-to-electron temperature ratio, electron-to-dust number density ratio, dust-charge fluctuation, and superthermal electrons and ions. We find that the maximum growth rates tend to increase but reach steady states as the wave number increases. The instabilities reported here could be relevant to various plasma environments, including space plasmas (e.g., Earth's magnetosphere) and laboratory dusty plasma experiments.

Figures (4)

• Figure 1: In Cerenkov interactions, the profiles of the maximum growth rates (normalized by $\omega_{\rm{pd}}$) are shown against the parallel component of the wave number (normalized by $\lambda_{\rm{D}}^{-1}$) for different values of the parameters $\sigma_i$, $Z_e$, and $\kappa_e$ as in the legends. Subplots (a) and (b) correspond to instabilities associated with dust-cyclotron [Eq. \ref{['eq-growth-dc1-max']}] and dust-lower-hybrid [Eq. \ref{['eq-growth-dl1-max']}] modes respectively. The other fixed parameter values are $T_e/T_b=100$, $\rm{v}_{\rm{te}}/\rm{v}_{\rm{b0}}=0.01$, $\delta_e=2.5$, $\delta_i=1.4$, $\kappa_i=3$, $r_{d}/\lambda_{\rm{De}}=1.6$, and $\Omega_{\rm{dp}}\equiv\Omega_d/\omega_{\rm{pd}}=2$.
• Figure 2: The same as in Fig. \ref{['fig_1']} but with the variation of the parameters $\Omega_{\rm{dp}}\equiv\Omega_d/\omega_{\rm{pd}}$, $\delta_e$, and $\kappa_i$ as in the legends. The other fixed parameter values are $T_e/T_b=100$, $\rm{v_{te}}/\rm{v_{b0}}=0.01$, $\sigma_i=0.05$, $\delta_i=1.4$, $\kappa_e=9$, $r_{d}/\lambda_{\rm{De}}=1.6$, and $Z_e=4$.
• Figure 3: In beam-cyclotron interactions, the profiles of the maximum growth rates (normalized by $\omega_{\rm{pd}}$) are shown against the perpendicular component of the wave number (normalized by $\lambda_{\rm{D}}^{-1}$) for different values of the parameters $\sigma_i$, $Z_e$, and $\kappa_e$ as in the legends. Subplots (a) and (b) correspond to instabilities associated with dust-cyclotron [Eq. \ref{['eq-growth-dc2']}] and dust-lower-hybrid [Eq. \ref{['eq-growth-dl2']}] modes respectively. The other fixed parameter values are the same as in Fig. \ref{['fig_1']}.
• Figure 4: The same as in Fig. \ref{['fig_3']} but with the variation of the parameters $\Omega_{\rm{dp}}\equiv\Omega_d/\omega_{\rm{pd}}$, $\delta_e$, and $\kappa_i$ as in the legends. The other fixed parameter values are $T_e/T_b=100$, $\rm{v_{te}}/\rm{v_{b0}}=0.01$, $\sigma_i=0.05$, $\delta_i=1.4$, $\kappa_e=9$, $r_{d}/\lambda_{\rm{De}}=1.6$, and $Z_e=4$.