The effect of dust size distribution on quantum dust acoustic wave

Abstract

Based on the quantum hydrodynamics theory, a proposed model for quantum dust acoustic waves (QDAWs) is presented including the dust size distribution (DSD) effect. A quantum version of Zakharov–Kuznetsov equation is derived adequate for describing QDAWs. Two different DSD functions are applied. The relevance of the wave velocity, amplitude, and width to the DSD is investigated numerically. The quantum effect changes only the soliton width. A brief conclusion is presented to the current findings and their relevance to astrophysics data is also discussed.

The impacts of dust size distribution on the head-on collision of quantum dust-acoustic solitary waves in ultradense astrophysical objects

“…Before going to the discussion, it should be mentioned here that our model is focused on quantum dusty plasmas of ultradense astrophysical objects (Ali and Shukla 2006;El-Taibany and Wadati 2007;El-Labany et al 2009b), in which the mass density is of order 10 6 g/cm 3 or more, like the case of white dwarfs or neutron stars, giving rise to k m ≈ 4 × 10 6 or more. Therefore, within the following numerical investigations, we will use (Ali and Shukla 2006;El-Taibany and Wadati 2007;El-Labany et al 2009b) r min = 10 −4 cm, k = 10 −6 , k z = 10 7 , k m = 4 × 10 6 , σ e ≈ 2, σ i ≈ 0.01, Fig. 1 Variation of phase shift with R for different values of the power law index β and r m = 10 −4 , k = 10 −6 , k z = 10 7 , k m = 4 × 10 6 n e0 = 5 × 10 23 cm −3 , n i0 = 2 × 10 24 cm −3 , H e ≈ 10 −1 , H i ≈ 10 −3 , and H d ≈ 10 −8 .…”

“…Z dj 0 is the number of electrons residing on the j th dust grain surface. The QDASWs dynamics can be described by the following normalized equations (El-Labany et al 2009b):…”

“…Mathematically, the differential form of the power law DSD can be written as (Meuris 1997;El-Labany et al 2009b)…”

“…They found that the soliton amplitude in case of a power law distribution is smaller than that of mono-sized dust grains. On the other hand, El-Labany et al (2009b) studied the effect of DSD on a quantum dust acoustic wave. They reported that only the velocity decreases as the power law index increases, although both the amplitude and the width increase.…”

“…They reported that only the velocity decreases as the power law index increases, although both the amplitude and the width increase. All of these works (Aslaksen and Havnes 1992;Meuris 1997;Duan and Shi 2003;El-Labany et al, 2007b, 2009b were beyond the scope of the interaction between two QDASWs in a dusty plasma. It is well known that the excitation, propagation, and interaction of solitary waves are important issues in our research.…”