Dust-Ion-Acoustic Rogue Waves in a Dusty Plasma Having Super-Thermal Electrons

Akib Al Noman,A A Mamun,Subrata Banik,Mehedi Hassan,Nure Alam Chowdhury,Md Khairul Islam,Abdul Mannan

doi:10.3390/gases1020009

Akib Al Noman, A A Mamun + Show 5 more

Open Access

https://doi.org/10.3390/gases1020009

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Abstract

The standard nonlinear Schrödinger Equation (NLSE) is one of the elegant equations to find detailed information about the modulational instability criteria of dust-ion-acoustic (DIA) waves and associated DIA rogue waves (DIARWs) in a three-component dusty plasma medium with inertialess super-thermal kappa distributed electrons, and inertial warm positive ions and negative dust grains. It can be seen that the plasma system supports both fast and slow DIA modes under consideration of inertial warm ions along with inertial negatively charged dust grains. It is also found that the modulationally stable parametric regime decreases with κ. The numerical analysis has also shown that the amplitude of the first and second-order DIARWs decreases with ion temperature. These results are to be considered the cornerstone for explaining the real puzzles in space and laboratory dusty plasmas.

Highlights

It can be seen that the plasma system supports both fast and slow DIA modes under consideration of inertial warm ions along with inertial negatively charged dust grains
We have numerically analyzed the variation of the modulational instability (MI) growth rate (Γ g ) of DIAWs with kfor different values of μ3 under consideration of fast mode shown in the left panel of Figure 3 by using these following plasma parameters: k = 1.3, Φ0 = 0.5, ρ = 1 × 103, μ = 3 × 10−6, and μ2 = 0.3, and it is clear from this figure that the Γ g, initially, increases with k, and becomes maximum for a particular value of k (i.e., k ' 18), decreases to zero (i.e., k ' 25)
We have numerically analyzed Equation (32) in the right panel of Figure 3 to observe the effects of ion temperature to the formation of first-order DIA rogue waves (DIARWs)

Summary

Governing Equations

Fully ionized, and collisionless three-component DPM comprising super-thermal electrons, positively charged inertial warm ions, and negatively charged dust grains. The overall charge neutrality condition of our plasma system can be written as ne0 + Zd nd0 = Zi ni0 , where ne0 , nd0 , and ni0 are the equilibrium electron, dust, and ion number densities, respectively, and Zd (Zi ) is the charge state of the negative (positive) dust grain (ion). Where nd (ni ) is the dust (ion) number density normalized by the equilibrium value nd0 (ni0 ); ud (ui ) is the dust (ion) fluid speed normalized by the ion sound speed Ci = ( Zi k B Te /mi )1/2. The expression for the number density of the super-thermal electrons (following the κdistribution) can be expressed as [36].

Derivation of the NLSE

Modulational Instability and Rogue Waves

Results and Discussion

Conclusions