Numerical Investigation of Two-Stream Instability in Magnetized Inhomogeneous Dusty Plasma Under the Influence of Ionization

Abstract

Dusty plasmas are multicomponent ionized media containing electrons, ions, neutral particles and charged dust grains. The simultaneous presence of dust, magnetic fields, plasma inhomogeneity and ionization modifies the collective response and affects electrostatic instability. In this study, a fluid model is formulated to investigate two-stream instability in a weakly ionized, magnetized and inhomogeneous dusty plasma. Electrons, singly charged positive ions and negatively charged dust grains are treated as interacting charged fluids, while ionization is represented by source terms in the continuity equations. A uniform magnetic field is applied along the z direction and a slowly varying equilibrium density gradient is included. Linear perturbation analysis with normal-mode dependence exp[i(k•r ? ?t)] gives a complex dispersion condition D(?,k,?I,B0,Ln?1,Zd,nd,V0)=0. The numerical analysis is performed in normalized variables to examine the effects of ionization frequency, magnetic-field strength, density-gradient parameter, dust density, dust charge and wave number. The calculated maximum growth rate increases from 0.20 to 0.37 as ?I/?pi increases from 0 to 0.6, and decreases from 0.42 to 0.18 as ?i/?pi increases from 0.2 to 2.5. The maximum growth rate also increases from 0.22 to 0.44 with the density-gradient parameter over the range 0.05–0.50. A non-monotonic dependence on dust density is obtained, with a maximum growth rate of 0.39 at nd/n0 = 0.10. Increasing dust charge from Zd = 500 to 5000 increases the maximum growth rate from 0.22 to 0.40. The wave-number spectrum has a maximum growth rate of 0.46 near k?D = 1.4 and decreases at larger wave numbers. The results demonstrate the combined influence of ionization, magnetic field, plasma inhomogeneity and dust parameters on the two-stream instability.

Introduction

The study investigates two-stream instability in a weakly ionized, magnetized, inhomogeneous dusty plasma. Dusty plasma contains electrons, ions, neutral particles, and negatively charged solid dust grains. The presence of dust adds inertia and charge density, significantly modifying plasma waves, electrostatic response, and instability behavior.

The model considers a uniform magnetic field, equilibrium density gradient, ionization, collisions, dust charging, and relative streaming between charged species. Electrons and ions are treated as mobile fluids, while massive negatively charged dust grains are assumed to have a constant equilibrium charge. The plasma satisfies the quasi-neutrality condition, and small perturbations are analyzed using a normal-mode approach. The resulting linearized fluid equations and Poisson equation produce a complex dispersion relation, whose imaginary part gives the instability growth rate.

Numerical calculations are performed using normalized parameters such as ionization frequency, magnetic-field strength, dust density, dust charge, wave number, density-gradient strength, and streaming velocity. The main results are:

• Ionization: Increasing normalized ionization frequency from 0 to 0.6 increases the maximum growth rate from 0.20 to 0.37.
• Magnetic field: Increasing magnetic-field strength from 0.2 to 2.5 decreases the growth rate from 0.42 to 0.18, indicating a stabilizing influence over the studied range.
• Density inhomogeneity: Increasing the density-gradient parameter from 0.05 to 0.50 raises the growth rate from 0.22 to 0.44.
• Dust density: The response is non-monotonic; growth reaches 0.39 at nd/n0=0.10n_d/n_0=0.10 and then decreases at higher dust density.
• Dust charge: Increasing dust charge from Zd=500Z_d=500 to 5000 increases the growth rate from 0.22 to 0.40.
• Wave number: The instability exists over a finite wave-number range, with maximum growth of 0.46 at kλD=1.4k\lambda_D=1.4 before decreasing at larger wave numbers.
• Combined instability: The instability map shows stronger growth at intermediate wave numbers and lower magnetic-field strengths.

Conclusion

A fluid model for two-stream instability in a weakly ionized, magnetized and inhomogeneous dusty plasma has been formulated and solved numerically. The model includes electron, ion and dust dynamics, an ionization source, effective collisions, an external magnetic field, a density gradient and electrostatic coupling through Poisson\'s equation. The calculated maximum growth rate increases with ionization frequency and density-gradient strength and decreases with magnetic-field strength over the parameter ranges studied. Dust density produces a non-monotonic response, while increasing dust charge increases the maximum growth rate. The wave-number spectrum exhibits a finite unstable interval with a maximum growth rate near k?D = 1.4. These results provide a quantitative description of the dependence of the two-stream instability on the principal plasma parameters included in the model.

References

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Copyright

Copyright © 2026 Vandana Kumari, Dr. Saurabh Kumar Jain. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.