Quantum Treatment of Kinetic Alfv\'en Waves instability in a dusty plasma: Magnetized ions

TL;DR

This paper investigates the quantum effects on kinetic Alfvén wave instability in a dusty plasma with magnetized ions, deriving dispersion relations and analyzing how quantum corrections influence wave behavior and instability growth rates.

Contribution

It introduces a quantum-corrected dispersion relation for kinetic Alfvén waves in dusty plasmas, highlighting the impact of quantum effects and plasma parameters on wave stability.

Findings

Quantum correction suppresses Alfvén wave frequency.

Growth rates of instability are significantly affected by plasma parameters.

Derived analytical expressions for various propagation modes.

Abstract

The dispersion relation of kinetic Alfv\'en wave in inertial regime is studied in a three component non-degenerate streaming plasma. A lin- ear dispersion relation using fluid- Vlasov equation for quantum plasma is also derived. The quantum correction CQ raised due to the insertion of Bohm potential in Vlasov model causes the suppression in the Alfven wave frequency and the growth rates of instability. A number of analytical expressions are derived for various modes of propagation. It is also found that many system parameters, i.e, streaming velocity, dust charge, num- ber density and quantum correction significantly influence the dispersion relation and the growth rate of instability.