Multi-dimensional instability of dust acoustic waves in magnetized quantum plasmas by two-fluid quantum hydrodynamics model

Abstract

Study on dust acoustic waves (DAWs) described by two-fluid quantum hydrodynamics model (QHM) in a magnetized dusty plasmas composed of negatively and positively charged mobile dust, intertialess quantum electrons as well as ions is presented. The Zakharov-Kuznetsov (ZK) equation is derived via reductive perturbation technique. The solitary wave solution of ZK equation is given and the numerical analysis of the solution with parameters in dust crystals is performed to study the properties of the DAWs with positive and negative dust. The multi-dimensional instability of these solitary waves is investigated via small-k perturbation method. The instability criterion and growth rate relying on obliqueness, the density ratio between ions and dust, the dust cyclotron frequency, the Fermi temperatures ratio between electrons to ions, quantum diffraction parameter and the ratio between charge-to-mass ratio of positive dust and that of negative dust are discussed for compressive solitary waves (CSWs) and rarefactive solitary waves (RSWs). The implications of these results to the interior of white dwarf stars and magnetars have been briefly discussed.