Modulational instability of ion-acoustic waves in plasmas with superthermal electrons

Gharaee, H.; Afghah, S.; Abbasi, H.

doi:10.1063/1.3566006

Cited by 27 publications

(32 citation statements)

References 19 publications

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“…To study the MI of DAWs, we will derive the NLSE by employing the standard multiple scale (reductive perturbation) technique . Let A be the state (column) vector ( n d , u d , ϕ ) T , describing the system's state at a given position x and instant t. We shall consider small deviations from the equilibrium state A (0) = (1, 0, 0) T by taking …”

Section: Derivation Of Nlsementioning

confidence: 99%

“…

A = A^{((), 0)} + ϵ A^{((), 1)} + ϵ^{2} A^{((), 2)} + \dots = A^{((), 0)} + {false\sum}_{n = 1}^{\infty} ϵ^{n} A^{((), n)},

where ϵ ≪ 1 is a smallness parameter. In the standard multiple scale (reductive perturbation) technique, the stretched (slow) space and time variables are commonly used by many authors as follows:

ξ = ϵ (x - v_{g} t), τ = ϵ^{2} t,

where v g is the group velocity in the x direction. We assume that all perturbed states depend on the fast scales via the phase θ 1 = kx − ωt only, while the slow scales enter the argument of the l th harmonic amplitude

A_{l}^{((), n)}

, which is allowed to vary along x ,

A^{((), n)} = {false\sum}_{l = - \infty}^{\infty} A_{l}^{((), n)} (ξ, τ) e^{il (kx - ω italict)} .

…”

Section: Derivation Of Nlsementioning

confidence: 99%

“…The reality condition

A_{- l}^{((), n)} = A_{l}^{(n) *}

is met by all state variables. According to these considerations, the derivative operators are treated as follows

\frac{\partial}{\partial t} \to \frac{\partial}{\partial t} - ϵ v_{g} \frac{\partial}{\partial ξ} + ϵ^{2} \frac{\partial}{\partial τ},

\frac{\partial}{\partial x} \to \frac{\partial}{\partial x} + ϵ \frac{\partial}{\partial ξ} .

…”

Section: Derivation Of Nlsementioning

confidence: 99%

“…According to these considerations, the derivative operators are treated as follows. [17][18][19][20][21][22][23][24][25][26][27]…”

Section: Derivation Of Nlsementioning

confidence: 99%

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Dust‐acoustic envelope solitons in super‐thermal plasmas

Noman

Chowdhury

Mannan

et al. 2019

Contributions to Plasma Physics

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The modulational instability (MI) of the dust‐acoustic waves (DAWs) in an electron‐positron‐ion‐dust plasma (containing super‐thermal electrons, positrons, and ions along with negatively charged adiabatic dust grains) is investigated by the analysis of the non‐linear Schrödinger equation (NLSE). To derive the NLSE, the reductive perturbation method was employed. Two different parametric regions for stable and unstable DAWs are observed. The presence of super‐thermal electrons, positrons, and ions significantly modifies both the stable and unstable regions. The critical wave number kc (at which MI sets in) depends on the super‐thermal electron, positron, and ion, and adiabatic dust concentrations.

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Section: Derivation Of Nlsementioning

confidence: 99%

“…

A = A^{((), 0)} + ϵ A^{((), 1)} + ϵ^{2} A^{((), 2)} + \dots = A^{((), 0)} + {false\sum}_{n = 1}^{\infty} ϵ^{n} A^{((), n)},

where ϵ ≪ 1 is a smallness parameter. In the standard multiple scale (reductive perturbation) technique, the stretched (slow) space and time variables are commonly used by many authors as follows:

ξ = ϵ (x - v_{g} t), τ = ϵ^{2} t,

A_{l}^{((), n)}

, which is allowed to vary along x ,

A^{((), n)} = {false\sum}_{l = - \infty}^{\infty} A_{l}^{((), n)} (ξ, τ) e^{il (kx - ω italict)} .

…”

Section: Derivation Of Nlsementioning

confidence: 99%

“…The reality condition

A_{- l}^{((), n)} = A_{l}^{(n) *}

is met by all state variables. According to these considerations, the derivative operators are treated as follows

\frac{\partial}{\partial t} \to \frac{\partial}{\partial t} - ϵ v_{g} \frac{\partial}{\partial ξ} + ϵ^{2} \frac{\partial}{\partial τ},

\frac{\partial}{\partial x} \to \frac{\partial}{\partial x} + ϵ \frac{\partial}{\partial ξ} .

…”

Section: Derivation Of Nlsementioning

confidence: 99%

“…According to these considerations, the derivative operators are treated as follows. [17][18][19][20][21][22][23][24][25][26][27]…”

Section: Derivation Of Nlsementioning

confidence: 99%

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Dust‐acoustic envelope solitons in super‐thermal plasmas

Noman

Chowdhury

Mannan

et al. 2019

Contributions to Plasma Physics

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“…We have employed the standard multiple-scale perturbation technique to derive the NLS equation. It was shown that in earlier investigations [30] that MI of ion acoustic waves is significantly influenced by the presence of superthermal electrons and growth rate is larger in the presence of more superthermal electrons. We have, however, investigated the combined effects of the external magnetic field, dust concentration and the superthermality of electrons on the MI of DIA wave packets.…”

Section: Introductionmentioning

confidence: 99%

Amplitude modulation of three-dimensional low-frequency solitary waves in a magnetized dusty superthermal plasma

2017

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The amplitude modulation of three-dimensional (3D) dust ion-acoustic wave (DIAW) packets is studied in a collisionless magnetized plasma with inertial positive ions, superthermal electrons and negatively charged immobile dust grains. By using the reductive perturbation technique, a 3D-nonlinear Schrödinger equation is derived, which governs the slow modulation of DIAW packets. The latter are found to be stable in the low-frequency ðx\x c

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Modulation of ion sound excitations in electron–ion plasmas with double spectral index distribution function

Ullah

Masood

Siddiq

2020

Contributions to Plasma Physics

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Theoretical investigation of amplitude modulation of ion sound waves is presented here for an electron–ion plasma where the electrons are dictated by the double spectral index (r, q) distribution function. Using the standard reductive perturbative technique, a non‐linear Schrödinger (NLS) equation is derived that describes the evolution of modulated ion sound envelope excitations. Stability analysis of the NLS equation shows that the ion sound waves remain stable for the flat‐topped and kappa‐like distributions, but they can become unstable for the spiky electron velocity distribution. It is shown that changing the electron population in regions of low and high phase space density regions results in remarkable features that have no equivalent in ion sound waves with Boltzmannian electrons. Different types of localized ion sound excitations are plotted for the different shapes of the distribution functions controlled by the double spectral indices, and the underlying physics is discussed in detail. The present investigation may be beneficial to understand ion sound excitations in space plasmas where the distribution functions of the shapes presented here are frequently encountered by the satellite missions.

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Modulational instability of ion-acoustic waves in plasmas with superthermal electrons

Cited by 27 publications

References 19 publications

Dust‐acoustic envelope solitons in super‐thermal plasmas

Dust‐acoustic envelope solitons in super‐thermal plasmas

Amplitude modulation of three-dimensional low-frequency solitary waves in a magnetized dusty superthermal plasma

Modulation of ion sound excitations in electron–ion plasmas with double spectral index distribution function

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