Cylindrical freak waves in a non-Maxwellian dusty bulk-sheath plasma: An approximate solution for the cylindrical nonlinear Schrödinger equation

El-Tantawy, S. A.; Elgendy, Abdelfattah T.; Ismail, Safaa Salah

doi:10.1016/j.physleta.2017.08.054

Cited by 30 publications

(7 citation statements)

References 41 publications

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“…Mathematical Problems in Engineering method gives excellent results compared to the traditional method with many physical applications. For the future work, it is well known that most physical experiments that take place in the laboratory, especially experiments of plasma physics, are carried out in a cylindrical/spherical vessel [62][63][64]. erefore, to describe the modulated envelope waves that can propagate in the cylindrical/spherical vessel, the basic equations of the physical problem must be designed in the curved coordinates/nonplanar (cylindrical and spherical) coordinates.…”

Section: Discussionmentioning

confidence: 99%

The Hybrid Finite Difference and Moving Boundary Methods for Solving a Linear Damped Nonlinear Schrödinger Equation to Model Rogue Waves and Breathers in Plasma Physics

Salas

El-Tantawy

Castillo

2020

Mathematical Problems in Engineering

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In this paper, the dissipative and nondissipative modulated pulses such as rogue waves (RWs) and breathers (Kuznetsov-Ma breathers and Akhmediev breathers) that can exist and propagate in several fields of sciences, for example, plasma physics, have been analyzed numerically. For this purpose, the fluid dusty plasma equations with taking the kinematic dust viscosity into account are reduced to the linear damped nonlinear Schrödinger equation using a reductive perturbation technique. It is known that this equation is not integrable and, accordingly, does not have analytical solution. Thus, for modelling both dissipative RWs and breathers, the improved finite difference method is introduced for this purpose. It is found that FDM is a good numerical technique for small time interval but for large time interval it becomes sometimes unacceptable. Therefore, to describe these waves accurately, the new improved numerical method is considered, which is called the hybrid finite difference method and moving boundary method (FDM-MBM). This last and updated method gives an accurate and excellent description to many physical results, as it was applied to the dust plasma results and the results were good.

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Section: Discussionmentioning

confidence: 99%

The Hybrid Finite Difference and Moving Boundary Methods for Solving a Linear Damped Nonlinear Schrödinger Equation to Model Rogue Waves and Breathers in Plasma Physics

Salas

El-Tantawy

Castillo

2020

Mathematical Problems in Engineering

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“…Equation 29is equivalent to equation (26), by comparing the coefficients, we obtain the Lagrangian multiplier b i (i � 1, 2, 3, 4, 5), i.e.,…”

Section: F R θ T P P R P θ P T P Rrmentioning

confidence: 99%

“…Compared with the integer order model, the fractional order model can better describe the dynamic response of the actual system, improve the performance of the dynamic system, and solve practical problems. However, in the research of plasma physics, most of the models are established in integer order [26,27]. is makes it necessary to establish a fractional order model to describe and study the propagation of solitary waves in plasma.…”

Section: Introductionmentioning

confidence: 99%

Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas

Liu

Chen

2020

Complexity

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In this paper, the fractional order models are used to study the propagation of ion-acoustic waves in ultrarelativistic plasmas in nonplanar geometry (cylindrical). Firstly, according to the control equations, (2 + 1)-dimensional (2D) cylindrical Kadomtsev–Petviashvili (CKP) equation and 2D cylindrical-modified Kadomtsev–Petviashvili (CMKP) equation are derived by using multiscale analysis and reduced perturbation methods. Secondly, using the semi-inverse method and the fractional variation principle, the abovementioned equations are derived the time-space fractional equations (TSF-CKP and TSF-CMKP). Furthermore, based on the fractional order transformation, the 1-decay mode solution of the TSF-CKP equation is obtained by using the simplified homogeneous balance method, and using the generalized hyperbolic-function method, the exact analytic solution of TSF-CMKP equation is obtained. Finally, the effects of the phase speed λ, electron number density (through β3) and the fractional order α,β,ω on the propagation of ion-acoustic waves in ultrarelativistic plasmas are analyzed.

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“…The driven voltage waveform may contain low or intermediate RF, which is smaller or comparable to the ion plasma frequency, i.e. 1 MHz [8][9][10][11]. These low and intermediate frequencies allow ions accelerated in the sheath to be partially modulated with the time-dependent sheath electric field.…”

Section: Introductionmentioning

confidence: 99%

Ion transit effects on sheath dynamics in the intermediate radio-frequency regime: excitations of ion-acoustic waves and solitons

Shihab

Elbadawy

El-Siragy

et al. 2022

Plasma Sources Sci. Technol.

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The capacitively coupled plasma is investigated kinetically utilizing the particle- in-cell technique. The Argon (Ar) plasma is generated via two radio-frequencies. The plasma bulk density increases by increasing the voltage amplitude of the high frequency (≥ 13.56 MHz) which is much greater than the ion plasma frequency. The intermediate radio-frequencies ( ≈ 1 MHz) which are comparable to the ion plasma frequency causes a broadening of the ion energy distribution considerably, i.e., ions gain energies above and lower than the time-averaged energy. The good agreement between published experimental results and our theoretical calculations via the Ensemble- in-Spacetime model confirms the modulation of ions around time-averaged values. Intermediate frequencies allow ions to respond partially to the instantaneous electric field. The response of ions to the instantaneous electric field is investigated semi- analytically. The dispersion relation of the plasma sheath and bulk are derived. Stable ion acoustic modes are found. The ion-acoustic modes have two different velocities and carry energy from the sheath edge to the electrode. Also, intermediate frequencies excite solitons in the plasma sheath; the results may help to explain the ion density, flux, and energy modulation, and, consequently, the broadening of the ion energy distribution.

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Cylindrical freak waves in a non-Maxwellian dusty bulk-sheath plasma: An approximate solution for the cylindrical nonlinear Schrödinger equation

Cited by 30 publications

References 41 publications

The Hybrid Finite Difference and Moving Boundary Methods for Solving a Linear Damped Nonlinear Schrödinger Equation to Model Rogue Waves and Breathers in Plasma Physics

The Hybrid Finite Difference and Moving Boundary Methods for Solving a Linear Damped Nonlinear Schrödinger Equation to Model Rogue Waves and Breathers in Plasma Physics

Time-Space Fractional Model for Complex Cylindrical Ion-Acoustic Waves in Ultrarelativistic Plasmas

Ion transit effects on sheath dynamics in the intermediate radio-frequency regime: excitations of ion-acoustic waves and solitons

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