Quantum Treatment of Kinetic Alfvén Waves Instability in a Dusty Plasma: Magnetized Ions

Kinetic Alfvén wave instability is examined rigorously in a uniform nondegenerate quantum dusty plasma. A linear dispersion relation of kinetic Alfvén wave in inertial regime is derived by incorporating Bohm potential in the linearized Vlasov model. It is found that the quantum correction CQ appears due to the insertion of Bohm potential in Vlasov model and causes the suppression in the Alfvén wave frequency and the growth rates of instability. A number of analytical expressions for various modes of propagation are derived. It is also found that the system parameters, that is, streaming velocity, dust charge, number density, and quantum correction, significantly influence the dispersion relation and the growth rate of instability