Weakly dissipative dust-ion acoustic wave modulation

Abstract

The modulational instability of dust-ion acoustic (DIA) waves in an unmagnetized dusty plasma is investigated in the presence of weak dissipations arising due to the low rates (compared to the ion oscillation frequency) of ionization recombination and ion loss. Based on the multiple space and time scales perturbation, a new modified nonlinear Schrödinger equation governing the evolution of modulated DIA waves is derived with a linear damping term. It is shown that the combined action of all dissipative mechanisms due to collisions between particles reveals the permitted maximum time for the occurrence of the modulational instability. The influence on the modulational instability regions of relevant physical parameters such as ion temperature, dust concentration, ionization, recombination and ion loss is numerically examined. It is also found that the recombination frequency controls the instability growth rate, whereas recombination and ion loss make the instability regions wider.

Breather structures in degenerate relativistic non-extensive plasma

“…Without reproducing the whole of the existing theory (El-Labany et al. 2003; Dauxois & Peyrard 2005; El-Taibany & Kourakis 2006; Shahmansouri & Farokhi 2012; Alinejad, Mahdavi & Shahmansouri 2014, 2016; El-Labany, El-Taibany & Zedan 2014; Rahman et al. 2015; Shahmansouri & Misra 2016), we shall provide the basic information needed to understand in what follows.…”

Comment on Weakly dissipative dust-ion acoustic wave modulation (J. Plasma Phys.82, 905820104, 2016)

“…In the recent article Alinejad, Mahdavi & Shahmansouri (2016) (henceforth to be referred to as Paper 1) an investigation was undertaken of the mechanism of weakly dissipative dust-ion acoustic wave modulation in dusty plasmas. It will be shown in the following that the analysis presented in that paper contains a number of intrinsic flaws, which render the results of doubtful value.…”

“…From a fundamental point of view, it appears that Alinejad et al. (2016) have taken into account the effects of ion recombination on the dust particles, and that of ionic momentum loss due to recombination on the dust particles and also due to electrostatic collisions between ions and dust grains, but they have neglected the effect of dust charging. The frequency scales characterizing these effects are typically of the same order of magnitude (Mamun & Shukla 2002), and therefore these should have been considered on an equal footing in the model.…”

“…Although dust charging implies precisely a variation of the electron and ion population density, this is not taken into account properly through the specific fluid model considered in Paper 1 (Alinejad et al. 2016).…”

“…The procedure outlined in Paper 1 is then pursued in third order, leading to a dissipative nonlinear Schrödinger equation (NLSE) in the form: where is now redefined as the first-order correction to the electrostatic potential, and and are space and time coordinates, consistently defined in the process (Alinejad et al. 2016). Not unexpectedly, the (linear) dispersion coefficient in the NLSE – see (3.12)–(33 a ) in Paper 1 – is left unaffected by the artificial dissipation mechanism discussed above.…”