Multi-dimensional Instability of Dust Acoustic Waves in Magnetized Quantum Plasmas with Positive or Negative Dust

Abstract

A survey of dust acoustic waves (DAWs) in magnetized dusty plasmas composed of negatively or positively charged mobile dust and 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 or 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 temperature ratio between electrons and ions, and quantum diffraction parameter are discussed for both cases. The implications of these results to the interior of white dwarf stars and magnetars have been briefly discussed.