Comparative Evaluation of Streaming Instabilities in Homogeneous Fusion Dusty Plasma Under the Influence of Magnetic Field and Quantum Effects

Abstract

Dusty plasmas consisting of electrons, ions and charged dust grains are commonly encountered in astrophysical environments, laboratory plasma systems and magnetic confinement fusion devices. The presence of charged dust particles significantly modifies plasma behaviour by altering collective interactions, wave propagation characteristics and instability growth. Among the various instability mechanisms observed in plasma systems, streaming instabilities play an important role in determining plasma transport, turbulence generation and energy redistribution. The present study investigates the influence of magnetic fields and quantum effects on streaming instabilities in homogeneous fusion dusty plasma. A Quantum Magnetohydrodynamic (QMHD) framework incorporating Bohm potential and Fermi pressure is employed to describe plasma dynamics. The governing continuity, momentum and Poisson equations are linearized around an equilibrium state to obtain a generalized dispersion relation. The effects of magnetic confinement, streaming velocity, dust density and quantum corrections on instability growth are examined. The analysis indicates that increasing magnetic field strength suppresses instability growth whereas increasing streaming velocity enhances instability development. Quantum effects introduce additional dispersion and contribute to plasma stabilization. Comparative analysis between classical and quantum models demonstrates that quantum corrections significantly modify wave propagation characteristics and instability thresholds. The study provides theoretical insight into instability control mechanisms relevant to fusion plasma confinement and advanced dusty plasma research.

Introduction

The text investigates streaming instabilities in homogeneous, magnetized fusion dusty plasma and focuses on how magnetic fields, streaming velocity, dust concentration, and quantum effects influence plasma stability.

Plasma is described as a charged state of matter in which particles interact through electromagnetic forces. Dusty plasma contains electrons, ions, neutral particles, and charged dust grains. The presence of dust introduces additional charge and inertia, significantly changing plasma-wave propagation and instability behavior. Dust acoustic waves and streaming instabilities are important phenomena in such systems.

The study focuses on a homogeneous, collisionless, magnetized fusion dusty plasma containing electrons, ions, and negatively charged dust grains. The plasma is assumed to satisfy the equilibrium quasi-neutrality condition

ni0=ne0+Zdnd0

and to have a uniform magnetic field directed along the z-axis. The plasma species are assumed to stream along the magnetic field with an equilibrium velocity V0.

To account for high-density plasma effects, the study uses a Quantum Magnetohydrodynamic (QMHD) model. Quantum effects are represented mainly through the Bohm quantum potential and Fermi degeneracy pressure. The basic governing equations are the continuity equation, momentum equation, quantum correction terms, and Poisson's equation.

A linear perturbation analysis is then applied. Small perturbations are introduced into density, velocity, and electrostatic potential, with wave-like disturbances assumed to have the form

exp?[i(kz−ωt)].

Combining the resulting linearized equations produces a generalized dispersion relation

D(ω,k,B0,H,V0,nd0)=0.

The dispersion relation determines both wave propagation and stability. The real part of the frequency describes wave propagation, while the imaginary part represents growth or damping. Specifically:

• Im?(ω)>0: instability and exponential growth.

• Im?(ω)<0: damping and stability.

Main Results

1. Effect of magnetic field

The numerical results show that increasing magnetic-field strength reduces the instability growth rate:

Thus, stronger magnetic confinement suppresses streaming instability by restricting particle motion and reducing the transfer of streaming energy into unstable modes.

2. Effect of streaming velocity

In relevant in dense plasmas because the Bohm potential and Fermi degeneracy pressure modify the dispersion and stability characteristics contrast, increasing streaming velocity increases the instability growth rate:

This indicates that greater relative streaming provides more kinetic energy to unstable plasma waves, resulting in stronger instability.

Conclusion

This study investigated streaming instabilities in homogeneous fusion dusty plasma using a Quantum Magnetohydrodynamic (QMHD) framework. The analysis demonstrated that magnetic field strength and quantum effects play a significant role in controlling plasma stability, whereas increasing streaming velocity promotes instability growth. Variations in dust density were found to modify wave propagation characteristics and influence the overall instability behaviour. The comparison between classical and quantum models showed that quantum corrections reduce the instability growth rate, highlighting the stabilizing effects of Bohm potential and Fermi degeneracy pressure. Overall, the findings improve the theoretical understanding of streaming instabilities in magnetized fusion dusty plasmas and provide a useful basis for future analytical, numerical and experimental investigations aimed at enhancing plasma confinement in fusion devices.

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Copyright

Copyright © 2026 Neha Sharma, 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.