Acceleration of soliton by nonlinear Landau damping of dust-helical waves

Ehsan, Zahida; Цинцадзе, Н. Л.; Vranjes, Jovo; Poedts, Stefaan

doi:10.1063/1.3127711

Cited by 7 publications

(16 citation statements)

References 26 publications

(23 reference statements)

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“…Now, to obtain the second Zakharov equation, which is also known as non‐linear Schrodinger equation, we start with the dispersion relation (7) and treat ω and k as operators given by

[ω = ω_{0} + i \frac{\partial}{\partial t}]

and

[k = k_{0} - i \frac{\partial}{\partial x}]

and obtain

i (\frac{\partial}{\partial t} + v_{g} \frac{\partial}{\partial x} - α \frac{\partial^{3}}{\partial x^{3}}) δ n_{normalp} + β \frac{\partial^{2} δ n_{normalp}}{\partial x^{2}} - Δ ω δ n_{normalp} - \frac{ℏ^{2}}{8 m_{normale} m_{normalp}} \frac{\partial^{4} δ n_{normalp}}{\partial x^{4}} + Ω_{normalLQ} \frac{δ n_{normali}}{n_{0 normalp}} δ n_{normalp} = 0,

where Ω LQ = ( n p0 / n e0 ( ω ce ω cp )) 1/2 , v g ( = ∂ω / ∂k the group velocity), and α , β and △ ω (the non‐linear frequency correction) are defined as:

v_{normalg} = {((), \frac{n_{e 0}}{n_{p 0}} ω_{ce} ω_{cp})}^{- 1 / 2} (U_{normalFS}^{2} + \frac{3 k^{2} ℏ^{2}}{2 m_{normalp} m_{normale}}) k

α = ((), \frac{n_{e 0}}{n_{p 0}} ω_{ce} ω_{})

…”

Section: Construction Of Zakharov Equationsmentioning

confidence: 99%

“…Now, we investigate the MI of the QLH waves, and to analyse the amplitude modulation of the QLH wave, we use Madelung's representation in the x direction only:

δ n_{normalp} \sim a (x, t) e^{iS (x, t)},

where the amplitude a and the phase S are real, and substitution of (22) into (16) and (17) gives real and imaginary parts, respectively.

- a_{0} (\frac{\partial}{\partial t} + {boldv}_{normalg} \cdot \frac{\partial}{\partial x}) δ italicS + β \frac{\partial^{2}}{\partial x^{2}} δ italica - γ \frac{\partial^{4}}{\partial x^{4}} δ italica + Ω_{normalLQ} a_{0} \frac{δ n_{normali}}{2 n_{0 p}} = 0

\frac{\partial}{\partial t} δ italica + {boldv}_{normalg} \frac{\partial δ italica}{\partial x} - α \frac{\partial^{3} δ italica}{\partial x^{3}} + 2 β a_{0} \frac{\partial^{2} δ italicS}{\partial x^{2}} = 0

and

(\frac{\partial^{2}}{\partial t^{2}} + Ω_{normalULQ}^{2} - \frac{n_{normali 0}}{n_{normalp 0}} V_{normalFS}^{2} \frac{\partial^{2}}{\partial x^{2}} + \frac{n_{i 0}}{n_{normalp 0}} \frac{ℏ^{2}}{4 m_{normalp} m_{...}})

…”

Section: Of Qlh Wavesmentioning

confidence: 99%

“…Ponderomotive force comes from the fast time scale in which positrons were involved, and it helps to excite the QULH wave on a slow time scale. Now, to obtain the second Zakharov equation, which is also known as non-linear Schrodinger equation, we start with the dispersion relation (7) and treat and k as operators given by [34] and obtain…”

Section: Construction Of Zakharov Equationsmentioning

confidence: 99%

“…This kind of instability has potential applications in non‐linear optics (lasers, self‐focusing, non‐linear radio waves, etc. ), hydrodynamics, electromagnetics, etc …”

Section: Introductionmentioning

confidence: 99%

“…), hydrodynamics, electromagnetics, etc. [33][34][35][36][37][38][39][40][41] ; that is why a large amount of work has been devoted to this.…”

mentioning

confidence: 99%

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Modulation instability of lower hybrid waves leading to cusp solitons in electron–positron(hole)–ion Thomas Fermi plasma

Ehsan

Цинцадзе

Fedele

et al. 2019

Contributions to Plasma Physics

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Following the idea of three‐wave resonant interactions of lower hybrid waves, it is shown that quantum‐modified lower hybrid (QLH) wave in electron–positron–ion plasma with spatial dispersion can decay into another QLH wave (where electron and positrons are activated, whereas ions remain in the background) and another ultra‐low frequency quantum‐modified ultra‐low frequency Lower Hybrid (QULH) (where ions are mobile). Quantum effects like Bohm potential and Fermi pressure on the lower hybrid wave significantly reshaped the dispersion properties of these waves. Later, a set of non‐linear Zakharov equations were derived to consider the formation of QLH wave solitons, with the non‐linear contribution from the QLH waves. Furthermore, modulational instability of the lower hybrid wave solitons is investigated, and consequently, its growth rates are examined for different limiting cases. As the growth rate associated with the three‐wave resonant interaction is generally smaller than the growth associated with the modulational instability, only the latter have been investigated. Soliton solutions from the set of coupled Zakharov and NLS equations in the quasi‐stationary regime have been studied. Ordinary solitons are an attribute of non‐linearity, whereas a cusp soliton solution featured by nonlocal nonlinearity has also been studied. Such an approach to lower hybrid waves and cusp solitons study in Fermi gas comprising electron positron and ions is new and important. The general results obtained in this quantum plasma theory will have widespread applicability, particularly for processes in high‐energy plasma–laser interactions set for laboratory astrophysics and solid‐state plasmas.

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“…Now, to obtain the second Zakharov equation, which is also known as non‐linear Schrodinger equation, we start with the dispersion relation (7) and treat ω and k as operators given by

[ω = ω_{0} + i \frac{\partial}{\partial t}]

and

[k = k_{0} - i \frac{\partial}{\partial x}]

and obtain

i (\frac{\partial}{\partial t} + v_{g} \frac{\partial}{\partial x} - α \frac{\partial^{3}}{\partial x^{3}}) δ n_{normalp} + β \frac{\partial^{2} δ n_{normalp}}{\partial x^{2}} - Δ ω δ n_{normalp} - \frac{ℏ^{2}}{8 m_{normale} m_{normalp}} \frac{\partial^{4} δ n_{normalp}}{\partial x^{4}} + Ω_{normalLQ} \frac{δ n_{normali}}{n_{0 normalp}} δ n_{normalp} = 0,

where Ω LQ = ( n p0 / n e0 ( ω ce ω cp )) 1/2 , v g ( = ∂ω / ∂k the group velocity), and α , β and △ ω (the non‐linear frequency correction) are defined as:

v_{normalg} = {((), \frac{n_{e 0}}{n_{p 0}} ω_{ce} ω_{cp})}^{- 1 / 2} (U_{normalFS}^{2} + \frac{3 k^{2} ℏ^{2}}{2 m_{normalp} m_{normale}}) k

α = ((), \frac{n_{e 0}}{n_{p 0}} ω_{ce} ω_{})

…”

Section: Construction Of Zakharov Equationsmentioning

confidence: 99%

“…Now, we investigate the MI of the QLH waves, and to analyse the amplitude modulation of the QLH wave, we use Madelung's representation in the x direction only:

δ n_{normalp} \sim a (x, t) e^{iS (x, t)},

where the amplitude a and the phase S are real, and substitution of (22) into (16) and (17) gives real and imaginary parts, respectively.

- a_{0} (\frac{\partial}{\partial t} + {boldv}_{normalg} \cdot \frac{\partial}{\partial x}) δ italicS + β \frac{\partial^{2}}{\partial x^{2}} δ italica - γ \frac{\partial^{4}}{\partial x^{4}} δ italica + Ω_{normalLQ} a_{0} \frac{δ n_{normali}}{2 n_{0 p}} = 0

\frac{\partial}{\partial t} δ italica + {boldv}_{normalg} \frac{\partial δ italica}{\partial x} - α \frac{\partial^{3} δ italica}{\partial x^{3}} + 2 β a_{0} \frac{\partial^{2} δ italicS}{\partial x^{2}} = 0

and

(\frac{\partial^{2}}{\partial t^{2}} + Ω_{normalULQ}^{2} - \frac{n_{normali 0}}{n_{normalp 0}} V_{normalFS}^{2} \frac{\partial^{2}}{\partial x^{2}} + \frac{n_{i 0}}{n_{normalp 0}} \frac{ℏ^{2}}{4 m_{normalp} m_{...}})

…”

Section: Of Qlh Wavesmentioning

confidence: 99%

Section: Construction Of Zakharov Equationsmentioning

confidence: 99%

“…This kind of instability has potential applications in non‐linear optics (lasers, self‐focusing, non‐linear radio waves, etc. ), hydrodynamics, electromagnetics, etc …”

Section: Introductionmentioning

confidence: 99%

“…), hydrodynamics, electromagnetics, etc. [33][34][35][36][37][38][39][40][41] ; that is why a large amount of work has been devoted to this.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Modulation instability of lower hybrid waves leading to cusp solitons in electron–positron(hole)–ion Thomas Fermi plasma

Ehsan

Цинцадзе

Fedele

et al. 2019

Contributions to Plasma Physics

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Acceleration of dust particles by vortex ring

et al. 2010

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It is shown that nonlinear interaction between large amplitude circularly polarized EM wave and dusty plasma leads to a nonstationary ponderomotive force which in turn produces a vortex ring, and magnetic field. Then the ensuing vortex ring in the direction of propagation of the pump wave can accelerate the micron-size dust particles which are initially at rest and eventually form a non relativistic dust jet. This effect is purely nonstationary and unlike linear vortices, dust particles do not rotate here. Specifically, it is pointed out that the vortex ring or closed filament can become potential candidate for the acceleration of dust in tokamak plasmas.

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Dust-acoustic waves and stability in the permeating dusty plasma. I. Maxwellian distribution

Gong

Liu

2012

Physics of Plasmas

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The dust-acoustic waves and their stability in the permeating dusty plasma with the Maxwellian velocity distribution are investigated. We derive the dust-acoustic wave frequency and instability growth rate in two limiting physical cases that the thermal velocity of the flowing dusty plasma is (a) much larger than, and (b) much smaller than the phase velocity of the waves. We find that the stability of the waves depend strongly on the velocity of the flowing dusty plasma in the permeating dusty plasma. The numerical analyses are made based on the example that a cometary plasma tail is passing through the interplanetary space plasma. We show that, in case (a), the waves are generally unstable for any flowing velocity, but in case (b), the waves become unstable only when the wave number is small and the flowing velocity is large. When the physical conditions are between these two limiting cases, we gain a strong insight into the dependence of the stability criterions on the physical conditions in the permeating dusty plasma. a) Corresponding

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Acceleration of soliton by nonlinear Landau damping of dust-helical waves

Cited by 7 publications

References 26 publications

Modulation instability of lower hybrid waves leading to cusp solitons in electron–positron(hole)–ion Thomas Fermi plasma

Modulation instability of lower hybrid waves leading to cusp solitons in electron–positron(hole)–ion Thomas Fermi plasma

Acceleration of dust particles by vortex ring

Dust-acoustic waves and stability in the permeating dusty plasma. I. Maxwellian distribution

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