Plasma Waves Research Articles

Optical solitons for the Hirota–Ramani equation via improved G′G-expansion method

In this work, first it is shown that the Hirota–Ramani equation, which governs the nonlinear propagation of coupled Langmuir and dust-acoustec wave in a multicomponent dusty plasma, possesses kinds of wave profile such as singular periodic profile, periodic profile, singular soliton profile, M-shape rational profile, bright soliton profile, kink profile in the form of the trigonometric, hyperbolic, and rational solutions. With the aid of symbolic computation, we select the Hirota–Ramani equation with a source to investigate the validity and advantage of the improved [Formula: see text]-expansion method and construct some frames of the 3D profiles and the contour profiles to the equation along with the 2D profiles of some solutions to understand the traveling wave dynamics. Following the selection of appropriate values for the associated parameters, more generalized solutions are provided, along with certain patterns in the solutions that are examined. This improved method is effective, concise, reliable, and can be applied for further futuristic applications.

Electrostatic Surface Waves in Magnetized Quantum Plasma Half-Space with Application of Metallic Gold

Electrostatic Surface Waves in Magnetized Quantum Plasma Half-Space with Application of Metallic Gold

Ion acoustic solitary waves in an adiabatic dusty plasma: roles of superthermal electrons, ion loss and ionization

Abstract The propagation of dust ion acoustic solitary wave (DIASW) is investigated in the multicomponent dusty plasma with adiabatic ions, superthermal electrons and stationary dust. The reductive perturbation method is employed to derive the damped Korteweg-de Vries (DKdV) equation which describes DIASW. The result reveals that, the adiabaticity of ions significantly modifies the basic features of the DIASW. The ionization effect makes the solitary wave growing, while collisions reduce the growth rate and even lead to the damping. With the increase in ionization cross section $\frac{{\Delta \sigma }}{{{\sigma _0}}}$, ion-to-electron density ratio ${{\delta}_{\rm{ie}}}$ and superthermal electrons parameter $\kappa $, the effect of ionization on DIASW enhances.

Model expressions for refractive indices of electron waves in cold magnetoactive plasma of arbitrary density

Despite the undoubted importance of having fairly simple analytical expressions for the refractive indices of wave modes in a magnetoactive plasma, such expressions are known only in some particular cases. For electron waves with frequencies much higher than the lower hybrid resonance frequency, such an expression is known only for whistler waves in a dense plasma when the electron plasma frequency significantly exceeds the electron cyclotron frequency. In this Letter, we propose simple operational expressions for the refractive indices of all four electron modes in a magnetoactive plasma, namely, the fast magnetosonic, also called whistler mode, the slow extraordinary mode, the ordinary mode, and the fast extraordinary mode. The form of these expressions does not depend on the value of the ratio of plasma frequency to cyclotron frequency.

Exploring travelling wave solutions, bifurcation, chaos, and sensitivity analysis in the (3+1)-dimensional gKdV-ZK model: A comprehensive study using Lie symmetry methodology

This article presents a study on the generalized Korteweg-de Vries-Zakharov-Kuznetsov (gKdV-ZK) model, which is a nonlinear system that demonstrates the effect of magnetic fields on weak ion-acoustic waves in plasma consisting of cold and hot electrons. The research entails investigating the reduction of symmetry through Lie group analysis, scrutinizing the characteristics of the dynamic structure using bifurcation phase diagrams, and examining the dynamic behaviour of the perturbed dynamical system employing chaos theory. Methods such as 3D and 2D phase portraits, time series analysis, Poincaré maps, exploration of multistability in the autonomous structure across various initial conditions, Lyapunov exponents, and bifurcation diagrams are exercised to demonstrate chaotic behaviour. Additionally, the research establishes general forms of solitary wave solutions, encompassing hyperbolic, trigonometric, and rational soliton solutions, through the utilization of a modified auxiliary equation approach to analytically address the examined problem. These findings are visually depicted as 2D and 3D graphs with carefully selected parameters, accompanied by their corresponding constraint conditions. Furthermore, the sensitivity analysis of the studied equation is deliberated upon and visually illustrated. The uncovered findings are captivating, innovative, and potentially beneficial for comprehending various physical phenomena in engineering and science.

Role of gas composition in weakened nonlinear standing wave excitation and improved plasma radial uniformity in very-high-frequency asymmetric capacitive Ar/CF4 discharges

The higher harmonics generated by nonlinear sheath motion would enhance the standing wave effect, and thus lead to center-peaked plasma density profile in very-high-frequency (VHF) capacitive discharges. In this work, a nonlinear transmission line (NTL) model introduced in Zhou et al (2021 Plasma Sources Sci. Technol. 30 125017) has been extended, with radial transport of various particles and nonlinear sheath motion into account, to investigate the effects of CF4 fraction α on the nonlinear standing wave excitation and plasma radial uniformity in VHF (60 MHz) capacitively coupled Ar/CF4 plasmas at 3 Pa. The results indicate that for pure Ar discharges (i.e. α= 0%), the nonlinearly excited harmonics with short wavelength significantly enhance the electron power absorption at the radial center, resulting in a pronounced central-high plasma density profile. As α increases, the high-order harmonics are gradually damped due to the increase of resistance, as well as the longer wavelength caused by thicker sheath thickness. Thus, the radial profile of the electron absorbed power density shifts from center-peak to edge-high. Besides, at the radial center, the electron density and Ar+ ion density decrease with α , CF3 + ion density shows an increasing trend, while F− ion density initially rises and then decreases. Moreover, the density profiles of all the species become more uniform at higher CF4 fraction, due to the suppressed nonlinear standing wave excitation and the longer wavelength of the nonlinear harmonics.

Effects of dust size distribution and non-Maxwellian electrons on shock waves in a dusty plasma

We present a study of dust acoustic shock waves in a non-Maxwellian plasma with dust charge fluctuations, which are seen to cause a dissipation term in fluid model, and consequently shocks are generated. In particular, we focus on dust acoustic waves as affected by various dust size distributions. Two distinct dust size distributions—the polynomial and the power law distributions—have been used. For analytical investigation of nonlinear wave propagation in complex plasmas, a reductive perturbation approach is used to obtain the Burgers equation. A dusty plasma system with non-Maxwellian Kappa distribution is considered and it is shown that the amplitude of a shock wave, for the dust size distribution is larger than that for the mono-sized counterpart, while the shock width manifests an opposite trend. Furthermore, the shock wave speed is also affected by the dust size distributions as well as by the nature of velocity distribution function. To benchmark our findings, we apply the proper limit on the spectral index, i.e., κ→∞, and retrieve the Maxwellian results. The current findings are crucial for comprehending respective shock distributions for a plasma system exhibiting non-thermal characteristics and having dust size distributions.

Evolution of Subsonic Shock Waves Associated with Reconnection Jets in Earth’s Magnetotail

Motivated by the signatures of nonlinear electrostatic waves observed by the Magnetospheric Multiscale spacecraft mission in reconnection jet regions of Earth's magnetotail, we have explored the dynamical features of ion-acoustic shock waves in the magnetotail. In this investigation, we have examined the dynamics and characteristics of ion-acoustic subsonic shock waves in non-Maxwellian space plasma comprising of two counterstreaming ion beams with suprathermal electrons, assumed to follow a kappa (κ) distribution. A reductive perturbation technique has been adopted to establish an evolution equation for small amplitude electrostatic shock structures. Importantly, subsonic waves only exist when the beam velocity exceeds a certain threshold, beyond which supersonic and subsonic waves may coexist. The combined effects of the beam velocity and the non-Maxwellian electron statistics have been analyzed to examine the characteristics of subsonic shock waves. Both symmetric and asymmetric (in relative beam density) models have been considered, leading to distinct possibilities in the evolution of subsonic shock waves. The findings of the investigation will help unfold the relatively unexplored dynamical characteristics of subsonic shock waves that may form and propagate in the magnetosphere.

Prompt extinction of bump-on-tail energy spectra for radiation belt electron phase space density

The bump-on-tail electron flux energy spectral distributions in the Earth's radiation belt are widely observed and have been proven to be generated by plasmaspheric hiss-led wave–particle interactions. Here, we report and discuss the prompt disappearance of them induced by the high solar wind dynamic pressure (Pdyn) combined with substorms on 12–13 March 2014. To remove the potential adiabatic influence, the electron fluxes are all converted to phase space density in the TS04 geomagnetic coordinate. Immediately after the Pdyn reached its maximum accompanied by the intensifying of substorms, the initial bump-on-tail spectra of the phase space density at L* (the third adiabatic invariant) from 3.8 to 4.4 were destroyed and rapidly smoothed to the exponential distributions, with a distinct ascent for lower energy electrons and a sharp decline for higher energy electrons. The balance line between the source and loss processes was located at μ = 50–200 MeV/G (μ is the first adiabatic invariant), which is sensitive to the spatial location. Further investigation of the temporal evolution of the phase space density along with L* and the plasma wave distributions provided evidence that the loss processes dominated at higher L* for electrons at μ ≳ 100 MeV/G, while the source processes became stronger at lower L* for electrons at μ ≲ 10 MeV/G. Our study provides new insight into the rapid change of the radiation belt electron spectral types in response to solar wind disturbances, which could be fully considered in further radiation belt particle modeling.

Dust magnetoacoustic waves in an inhomogeneous cylindrical four-component dusty plasma in the presence of polarization force

Abstract Dust magnetoacoustic waves have been examined in an inhomogeneous, bounded, cylindrical dusty plasma containing oppositely polarized dust particles. Considering polarization force, dust dynamics in r − θ plane is studied in the presence of inhomogeneous external magnetic field along z axis. At equilibrium, the dusty plasma components are supposed to follow Gaussian density distribution. Using reductive perturbation method (RPM), a variable coefficient cylindrical Kadomtsev–Petviashvili (VCCKP) equation has been derived. For weak azimuthal perturbation, an analytical solution, obtained by Zhang (“Exact solutions of a kdv equation with variable coefficients via exp-function method,” Nonlinear Dynam., vol. 52, nos. 1–2, pp. 11–17, 2008) using Exp-function method, is chosen. Phase velocity of dust magnetoacoustic wave is found to be modified by the density inhomogeneities, polarization force, dust charge state ratio and ion-to-electron temperature ratio. Spatio-temporal evolution of the dust number densities has been noticed. Existence of the compressive electromagnetic solitary waves is observed numerically for the chosen dusty plasma parameter range. The impacts of the inhomogeneity, polarization force, dust charge state ratio and ion-to-electron temperature ratio on the relative amplitude of the dust magnetoacoustic wave are also discussed.

Analysis of High-Order Bright–Dark Rogue Waves in (2+1)-D Variable-Coefficient Zakharov Equation via Self-Similar and Darboux Transformations

This paper conducts an in-depth study on the self-similar transformation, Darboux transformation, and the excitation and propagation characteristics of high-order bright–dark rogue wave solutions in the (2+1)-dimensional variable-coefficient Zakharov equation. The Zakharov equation is instrumental for studying complex nonlinear interactions in these areas, with specific implications for energy transfer processes in plasma and nonlinear wave propagation systems. By analyzing bright–dark rogue wave solutions—phenomena that are critical in understanding high-energy events in optical and fluid environments—this research elucidates the intricate dynamics of energy concentration and dissipation. Using the self-similar transformation method, we map the (2+1)-dimensional equation to a more tractable (1+1)-dimensional nonlinear Schrödinger equation form. Through the Lax pair and Darboux transformation, we successfully construct high-order solutions that reveal how variable coefficients influence rogue wave features, such as shape, amplitude, and dynamics. Numerical simulations demonstrate the evolution of these rogue waves, offering novel perspectives for predicting and mitigating extreme wave events in engineering applications.This paper crucially advances the practical understanding and manipulation of nonlinear wave phenomena in variable environments, providing significant insights for applications in optical fibers, atmospheric physics, and marine engineering.

Energy Transport and Conversion Within Earth's Supercritical Bow Shock: The Role of Intense Lower‐Hybrid Whistler Waves

AbstractDetailed analysis of a high Mach number quasiperpendicular Earth bow shock crossing by the Magnetospheric Multiscale (MMS) spacecraft fleet reveal that lower‐hybrid (LH) whistler waves generated in the shock foot region transport energy predominately along the shock surface and slightly toward the shock ramp in the shock normal incidence frame, where wave energy accumulates and is dissipated into the plasma. This suggests the LH whistlers play an integral role in energy reconfiguration at high Mach number collisionless shocks with ramifications to plasma heating. The multipoint observations are used to quantify the wave characteristic parameters (via interferometry), Poynting fluxes, and energy conversion rates D, and to assess their scale dependencies and spatial and temporal properties. The whistler associated energy transport and conversion are found to depend on scale and location within the layer. High‐frequency electrostatic waves yield largest values of D. However, the dominant net energy exchange contribution is from the LH whistlers. In the foot spatially temporally coherent net energy exchange from the plasma to whistlers is observed, whereas deeper in the ramp net wave energy dissipation to the plasma is observed exhibiting significant space‐time variability. These results are consistent with the modified two stream instability driven by the relative drift between reflected ions and electrons as the mechanism for wave growth in the foot. Owing to strong electron heating, whistler energy dissipation in the ramp is attributed to Landau damping, which out‐competes the destabilizing effect of the reflected ion and electron drift.

Langmuir wave dynamics and plasma instabilities: Insights from generalized coupled nonlinear Schrödinger equations

This study aims to tackle the generalized coupled nonlinear Schrödinger ([Formula: see text] – [Formula: see text]) equations, with a focus on understanding their physical significance and stability, especially in the realm of plasma physics. These equations are crucial for grasping the complex dynamics of wave interactions within plasma systems, which are fundamental for phenomena like wave-particle interactions, turbulence, and magnetic confinement. We employ analytical methods such as the generalized rational ([Formula: see text]at) and Khater II ([Formula: see text]hat.II) techniques, along with characterizing the system using Hamiltonian principles, to carefully examine the stability of solutions. The relevance of this model extends across various plasma phenomena, including electromagnetic wave propagation, Langmuir wave dynamics, and plasma instabilities. By applying these analytical techniques, we derive solutions and investigate their stability using Hamiltonian dynamics, providing valuable insights into the fundamental behavior of nonlinear plasma waves. Our findings reveal the existence of stable solutions under specific conditions, thus advancing our understanding of plasma dynamics significantly. This research carries significant implications for fields such as plasma physics, astrophysics, and fusion research, where a deep understanding of plasma wave stability and dynamics is crucial. Essentially, our study represents a scholarly effort to offer fresh perspectives on the behavior of [Formula: see text] – [Formula: see text] equations within plasma systems, contributing to the academic discourse on plasma wave phenomena.

Photothermal effects induced by laser radiation in a 2D axi-symmetric generalized thermoelastic semiconducting half space using MGL model

In this paper, a novel model based on the strain-temperature rate-dependent theory is investigated to study the coupling influences of thermal, elastic, and plasma waves during the photothermal process in a 2D axi-symmetric semiconducting half space. The surface absorption technique is used to illuminate the surface of the medium by a laser beam whose temporal and spatial profiles are Gaussian, moreover, the surface is also considered traction free. Integral transform method is applied using Laplace and Hankel transformations to obtain a general solution to the considered problem. Inverse Laplace transform is obtained computationally using Rimann-Sum approximation. Silicon element is chosen as an application to show the compatibility of the results of the MGL model with GL and CTE models, moreover the relaxation times effects of the new model were studied.

SEEING IS NOT UNDERSTANDING: Vygotsky, Halliday and Metaphor in Forming and Forgetting Middle School Science Concepts.

When teachers explain science concepts-for example, the solar wind, or plasma waves-some methods seem to be quick-acting and others long-lasting. Still others pose as many problems as they seem to solve. How, for example, does a parent explain how there can be solar wind without any air in space? How does a teacher explain how there can be plasma waves without any water? Locating metaphor between thinking and speech rather than within one or the other, we work out a single scheme to analyze two conversations with adult Koreans. These suggest that a text studied some ten years ago in middle school science class, replete with striking visual images, has left little more than everyday concepts. Instead of trying to use the striking visual images to refill gaps in the memory, however, the questions asked by a skilled science teacher suggest ways in which thinking could be freed from the middle school dogma of only three matter phases (solid, liquid, gas). To understand a metaphor like "solar wind", we need to replace fixed matters of fact with some more elusive facts of matter.

Electrostatic supersolitary waves: A challenging paradigm in nonlinear plasma science and beyond – State of the art and overview of recent results

A comprehensive overview is presented of recent theoretical advancements and observational manifestations of a relatively new type of electrostatic solitary wave (ESW), known as supersoliton or supersolitary wave (SSW). These nonlinear structures are characterized by a distorted pulse-shaped electrostatic potential excitations, deviating from the standard (“sech2”-like) form generally expected from solitonic pulses. In Space plasmas, in particular, e.g. in magnetospheric observations, SSWs may be associated with a characteristic wiggly bipolar electric field waveform. It has been shown that a three-component configuration is essential, as a minimum requirement for SSWs to occur in a plasma.Various spacecraft missions have recorded evidence of “non-conventional” electrostatic solitary waves (pulses) such as wiggly bipolar pulses, offset bipolar pulses, and monopolar pairs. This review article aims to present the current state of the art in this fascinating new theme, first outlining the basic framework for the modeling of such “exotic” ESWs and then putting forward a correlation between SSW structures with certain non-standard bipolar electric field forms observed in planetary magnetospheres.

Dynamics of ion-acoustic solitary waves in three-dimensional magnetized plasma with thermal ions and electrons: a pseudopotential analysis

Dynamics of ion-acoustic solitary waves in three-dimensional magnetized plasma with thermal ions and electrons: a pseudopotential analysis

Instability analysis and face‐to‐face collision of dust acoustic waves in dusty plasmas: Perspective Jupiter environment

AbstractThe collisionless unmagnetized five components dusty plasmas have been considered to study the significance of the face‐to‐face collision of single‐ and multi‐solitons, phase shifts due to face‐to‐face collision, and instability of the dust acoustic waves in Jupiter's environment. To study the consequence of face‐to‐face collision extended Poincaré–Lighthill–Kuo method is used to derive the two‐sided nonlinear Korteweg–De Vries (KdV) equation. Besides, to investigate the dust acoustic wave's instability, the nonlinear Schrödinger equation has been derived following the procedure of Slathia et al. The multi‐soliton solutions are determined by employing the Hirota bilinear method. The concerned parameters in the issue play a crucial role in the phase shift (generated by the face‐to‐face collision); the collisional process of single‐, double‐, triple‐, and quadruple‐soliton; and the generation of dust acoustic solitons. Furthermore, the plasma parameters are crucial in the formation of dark solitons and envelop shocks.

The fractional soliton solutions of dynamical system arising in plasma physics: The comparative analysis

In light of fractional theory, this paper presents several new effective solitonic formulations for the Langmuir and ion sound wave equations. Prior to this study, no previous research has presented the comparision and obtained the generalized fractional soliton solutions of this kind with power law kernel and Mittag-Leffler kernel. The ion sound and Langmuir wave equations are essential in plasma physics, offering insights into the collective behavior of charged particles in plasmas and enabling diagnostics and control of these complex, ionized gas systems. The two distinct fractional order differential operators are substituted for the traditional order derivative to reshape the examined model. The Atangana-Baleanu non-singular and non-local operator and conformable fractional operator are the fractional-order operators that are used to create the fractional complex system equations for Langmuir waves and ion sound. A constructive approach new auxiliary equation method utilizes to obtain the exact analytical soliton solutions for ion sound and Langmuir wave equation. A wide range of soliton solutions is obtained, including mixed complex solitary shock solutions, singular solutions, mixed shock singular solutions, mixed trigonometric solutions, mixed singular solutions, exact solutions, mixed periodic solutions, and mixed hyperbolic solutions, dark soliton, bright soliton, trigonometric solutions, periodic results, and hyperbolic results. The solitons solution of the ion sound and Langmuir wave equations lies in their ability to maintain wave stability, their role in modeling wave propagation and nonlinear effects, their potential use as diagnostic tools, and their relevance in wave-particle interactions in plasma physics. The solitons provide a valuable framework for understanding the behavior of waves in plasmas and offer insights into the complex dynamics of these charged particle systems. A graphical comparison analysis of a few solutions is also shown here, taking into account appropriate parametric values through the use of the software package. Moreover, the results of this study have important implications for Hamilton's equations and generalized momentum, where solitons are employed in long-range interactions.

Numerical calculation of N-periodic wave solutions of the negative-order Korteweg-de Vries equations

Abstract In this paper, the N-periodic wave solutions of the negative-order Korteweg-de Vries equations are presented, which can be used to describe wave phenomena in the water waves and plasma waves. Combining the bilinear Bäklund transformation with the Riemann-theta function, the N-periodic wave solutions can be obtained. Employing the parity of the bilinear forms for the Bäklund transformation, the complexity of the calculation can be reduced. The difficulty of solving N-periodic wave solutions can be transformed into solving least square problems. The Gauss-Newton numerical algorithm is employed to solve this kind of problem. Furthermore, the characteristic lines are used to analyze quantitatively the quasi-periodic solutions. The characteristic line analysis method is specifically demonstrated in the case of N=3. Some examples of numerical simulations for the 3-periodic and 4-periodic waves are presented. It is proved that this method can be further extended to the N-periodic wave solutions.