Nonlinear Plasma Research Articles

Non-Linear Plasma Wave Dynamics: Investigating Chaos in Dynamical Systems

This work addresses the significant issue of plasma waves interacting with non-linear dynamical systems in both perturbed and unperturbed states, as modeled by the generalized Whitham–Broer–Kaup–Boussinesq–Kupershmidt (WBK-BK) Equations. We investigate analytical solutions and the subsequent emergence of chaos within these systems. Initially, we apply advanced mathematical techniques, including the transform method and the G′G2 method. These methods allow us to derive new precise solutions and enhance our understanding of the non-linear processes dominating plasma wave dynamics. Through a systematic analysis, we identify the conditions under which the system transitions from orderly patterns to chaotic behavior. This investigation provides valuable insights into the fundamental mechanisms of non-linear wave propagation in plasmas. Our results highlight the dynamic interplay between non-linearity and variation, leading to chaos, which may be useful in predicting and potentially controlling similar phenomena in practical applications.

Soliton solutions of nonlinear coupled Davey–Stewartson Fokas system using modified auxiliary equation method and extended (G′/G2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(G'/G^{2})$$\\end{document}-expansion method

The captivating realm of the nonlinear coupled Davey–Stewartson Fokas system is explored in this research paper. As a powerful tool, the proposed system is utilized for the realistic representation of various non-linear dynamical mechanisms in different fields of sciences and engineering including non-linear optical fibers, plasma physics and water waves theory. Two distinct exact methods, namely the modified auxiliary equation method and the extended (G′/G2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(G'/G^{2})$$\\end{document}-expansion method, are utilized to acquire the exact soliton solutions of the non-linear coupled Davey–Stewartson Fokas system. A plethora of novel soliton solutions containing anti-kink, kink, bright, dark, dark-bright, bright-dark and some other singular soliton solutions, have been obtained using the employed exact methods. The significance of proposed manuscript lies in the novelty of obtained solutions. Kink, dark and bright solitons have wide applications in optical fiber communications, plasma physics and water waves dynamics. The acquired nontrivial exact solutions contain exponential, trigonometric, rational and hyperbolic functions. Some obtained solutions are visually represented through graphical simulations of 3D, 2D-contour and 2D-line plots, providing a comprehensive visualization of the soliton dynamics.The modulation instability of the proposed nonlinear system has been investigated, which ensures the stability of the system.

Studies of dynamic spatio-temporal processes of electrons in a 50 kHz/5 MHz dual-frequency dielectric barrier discharge plasma at atmospheric pressure

Dual-frequency excitation of dielectric barrier discharge (DBD) plasma reactors, where the plasma is generated by a low-frequency (LF) source and modulated by a radio-frequency (RF) source, have been widely adopted in the low-pressure regime. However, the impacts of the RF voltage and LF voltage amplitudes on the plasma parameters, including the spatiotemporal distributions of ion and electron densities, electron dynamics, and gas temperatures, remain poorly understood in the atmospheric pressure regime. The present work addresses this issue by conducting joint experimental and simulation studies for an atmospheric-pressure 50 kHz/5 MHz dual-frequency driven DBD plasma reactor based on phase-resolved optical emission spectra and a drift–diffusion model. The results demonstrate that the dynamic spatiotemporal behaviors of electrons change dramatically as the voltage of the RF component increases from 50 V to 300 V with the voltage of the LF component fixed at 1 kV. Moreover, the RF component is further demonstrated to modulate other plasma characteristics, such as particle densities, gas temperature, and argon emissions. These results contribute toward the tailoring of the non-equilibrium and nonlinear plasma parameters obtained under atmospheric pressure conditions.

The impact of standard Wiener process on the optical solutions of the stochastic nonlinear Kodama equation using two different methods

The stochastic nonlinear Kodama (SNLK) equation forced in the Stratonovich sense by multiplicative noise is considered here. New elliptic, hyperbolic, trigonometric, and rational stochastic solutions are acquired using ( G′/ G)-expansion method and mapping method. Because the SNLK equation is extensively used in is extensively used in nonlinear optics, fluid dynamics, and plasma physics, the obtained solutions may be used to study a broad range of relevant physical phenomena. In order to interpret the effects of multiplicative noise, the dynamic performances of the various obtained solutions are displayed utilizing 3D and 2D graphs. We infer that multiplicative noise impacts and stabilizes the solutions of SNLK equation.

In plasma physics and fluid dynamics: Symbolic computation on a (2+1)-dimensional variable-coefficient Sawada-Kotera system

Investigations on the real world have been facilitating the development of nonlinear science, and today, fluid dynamics and plasma physics attract people’s attention. This Letter studies a (2+1)-dimensional variable-coefficient Sawada-Kotera system in plasma physics and fluid dynamics. We build up a family of the similarity reductions, connecting that system with a known ordinary differential equation. Our similarity reductions depend on the plasma/fluid variable coefficients in that system, under certain variable-coefficient constraints.

Effect of temperature on the wave breaking amplitude of nonlinear relativistic strong plasma waves

Effect of temperature on the wave breaking amplitude of nonlinear relativistic strong plasma waves

Bifurcation study, phase portraits and optical solitons of dual-mode resonant nonlinear Schrodinger dynamical equation with Kerr law non-linearity

This study investigates the dynamic characteristics of the dual-mode resonant non-linear Schrodinger equation with a Bhom potential. Hydrodynamics, nonlinear optical fibre communication, elastic media, and plasma physics are just a few of the mathematical physics and engineering applications for this model. The study aims to achieve two main objectives: first, to discuss bifurcation analysis, and second, to extract optical soliton solutions using the extended hyperbolic function method. The study successfully derives various wave solutions, including bright, singular, periodic singular and dark solitons, based on the governing model. The findings conferred in this article show a crucial advancement in understanding the propagation of waves in non-linear media. Additionally, bifurcation of phase portraits of ordinary differential equation consistent with the partial differential equation under consideration is conducted. We also highlight specific constraint conditions that ensure the presence of these obtained solutions. The existing literature shows that these methods are first time applied on this model.

Influences of densities and thermal temperatures of electron and beam fluids on the characteristics of the electron acoustic electrostatic fields and fluid energies

A model of nonlinear electron acoustic electrostatic plasma waves having electron beams has been investigated. The structure of Korteweg–de Vries soliton energy and the corresponding electrostatic field have been discussed. The parametric regimes for wave existence of compressive and rarefactive structures have been examined via auroral zone data. The effects of densities and thermal temperature of electrons and beams on the nature of the electrostatic field and fluid energies have been taken into account.

Electromagnetic ion cyclotron emission from ion-scale magnetic holes

Ion-scale magnetic holes are nonlinear plasma structures commonly observed in the solar wind and Earth's magnetosphere. These holes are characterized by the magnetic field depletion filled by hot, transversely anisotropic ions and electrons and are likely formed during the nonlinear stage of ion mirror instability. Due to the plasma thermal anisotropy within magnetic holes, they serve as a host of electromagnetic ion cyclotron waves, whistler-mode waves, and electron cyclotron harmonic waves. This makes magnetic holes an important element of the Earth's inner magnetosphere, where electromagnetic waves generated within may strongly contribute to energetic ion and electron scattering. Such scattering, however, will modify the hot-ion distribution that is trapped within magnetic holes and responsible for the magnetic field stress balance. Therefore, hot ion scattering within magnetic holes likely determines the hole lifetime. In this study, we investigate how ion scattering by electromagnetic waves affects the stress balance and lifetime of magnetic holes. For illustration, we used typical characteristics of magnetic holes, ion populations, and ion cyclotron waves observed in the Earth's magnetosphere. We have demonstrated that ion distribution isotropization via scattering by waves does not change significantly magnetic hole magnitude, but ion losses due to scattering into the atmosphere may limit the hole life-times to 10–30 min in the Earth's inner magnetosphere.

Non-linear plasma protein binding of cannabidiol

BackgroundCannabidiol is highly bound to plasma proteins. Changes in its protein binding can lead to altered unbound plasma concentrations and result in alteration of pharmacological activity of cannabidiol-containing medications. This research has assessed non-linearity of cannabidiol plasma protein binding and the potential effect of tizoxanide on the binding.MethodCannabidiol protein binding was evaluated by ultrafiltration technique. Human plasma was spiked with cannabidiol stock solution to produce samples of various concentrations. For interaction study potential interactant tizoxanide was added in each sample. All samples were processed through Amicon Micropartition system and analyzed by HPLC.ResultsThe study has detected cannabidiol binding to borosilicate glass (9%) and polyethylene plastics (15%). In the interaction study the mean protein unbound fraction of cannabidiol was 0.05 (5%), indicating no binding interaction between cannabidiol and tizoxanide since cannabidiol unbound fraction without tizoxanide was also 5%. The cannabidiol fraction unbound was more than 2-fold greater at high concentrations compared to low concentrations.Conclusiona). At high concentrations cannabidiol plasma protein binding is non-linear. The non-linearity can affect elimination and medicinal effect of cannabidiol drugs. b). Borosilicate and polyethylene containers should be avoided in formulation, packing and administration of cannabidiol-containing medicines to guarantee correct doses. c). Cannabidiol medications can be co-administered with tizoxanide without caution.

Dynamics of transformed nonlinear waves for the (2+1)-dimensional pKP-BKP equation: interactions and molecular waves

In this paper, the dynamical behaviors of transformed nonlinear waves for the (2+1)-dimensional combined potential Kadomtsev-Petviashvili and B-type Kadomtsev-Petviashvili (pKP-BKP) equation are investigated, which can be used to reveal the nonlinear wave phenomena in nonlinear optics, plasma physics and hydrodynamics. The breath-wave and the lump solutions are constructed by means of the soliton solutions. The conversion mechanism for the breath-wave is systematically analyzed, which leads to several new kink-shaped nonlinear waves. The gradient relationships of these transformed waves are revealed by a Riemannian circle. Through the analysis of the nonlinear superposition between the periodic wave component and the kink solitary wave component, the dynamical characteristics including the formation mechanism, oscillation and locality for the nonlinear waves are investigated. The time-varying properties of transformed waves are shown by the study of time variables. By virtue of the two breath-wave solutions, several interactions including elastic and inelastic collisions between two nonlinear waves are studied. In particular, some transformed molecular waves encompassing the non-, semi- and full-transition modes are presented with the aid of velocity resonance. The results can help us further understand the complex nonlinear waves existing in the integrable systems.

Terahertz-frequency plasmonic-crystal instability in field-effect transistors with asymmetric gate arrays

We present a theory for plasmonic crystal instability in a semiconductor field-effect transistor with a dual grating gate array, designed with strong asymmetry in the elementary cell of this “crystal”. We demonstrate that, under the action of a dc current bias, the Bloch plasma waves in the plasmonic crystal formed in this transistor develop the Dyakonov–Shur instability. By calculating the energy spectrum and instability increments/decrements—which govern the growth/decay of excitations within the plasmonic crystal—we analyze the dependence of the latter on the electron drift velocity and the extent of the structural asymmetry. In contrast with the corresponding problem for gate arrays with symmetric unit cells, the presence of finite plasma instability increments across the entire Brillouin zone is established. This important difference points to the possibility of exciting sustained, radiating, non-linear electron plasma oscillations in the instability endpoint of the asymmetric array. These structures should be readily implementable in common semiconductor heterostructures, using standard nanofabrication techniques, enabling operation at room temperature. Long-range coherence of the unstable plasma oscillations, generated in the elementary cells of the crystal, should dramatically increase the radiated THz electromagnetic power, making this approach a promising pathway to the generation of THz signals.

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.

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.

Laser and Astrophysical Plasmas and Analogy between Similar Instabilities

Multipulse laser–matter interactions initiate nonlinear and nonequilibrium plasma fluid flow dynamics and their instability creating microscale vortex filaments, loop-soliton chains, and helically paired structures, similar to those at the astrophysical mega scale. We show that the equation with the Hasimoto structure describes both, the creation of loop solitons by torsion of vortex filaments and the creation of solitons by helical winding of magnetic field lines in the Crab Nebula. Our experiments demonstrate that the breakup of the loop solitons creates vortex rings with (i) quasistatic toroidal Kelvin waves and (ii) parametric oscillatory modes—i.e., with the hierarchical instability order. For the first time, we show that the same hierarchical instability at the micro- and the megascale establishes the conceptual frame for their unique classification based on the hierarchical order of Bessel functions. Present findings reveal that conditions created in the laser-target regions of a high filament density lead to their collective behavior and formation of helically paired and filament-braided “complexes”. We also show, for the first time, that morphological and topological characteristics of the filament-bundle “complexes” with the loop solitons indicate the analogy between similar laser-induced plasma instabilities and those of the Crab and Double-Helix Nebulas—thus enabling conceptualization of fundamental characteristics. These results reveal that the same rotating metric accommodates the complexity of the instabilities of helical filaments, vortex rings, and filament jets in the plasmatic micro- and megascale astrophysical objects.

Effects of gamma radiation on the optical properties of ultrafine iron particle/polystyrene composites

The present research studied the influence of gamma radiation doses on the optical properties and parameters of the tested composite samples consisting of polystyrene polymer as a matrix filled with different concentrations of ultrafine iron particles (0, 10, 20, and 30 wt.%) with an average thickness of 2 µm. Using a UV-1800 Shimadzu spectrophotometer, the optical absorbance and transmittance values of the tested composite samples were measured at room temperature in the wavelength range of 200–800 nm. Optical parameters such as the excitation energy for electronic transitions, optical energy gap, dispersion energy, static dielectric constant, static refractive index, moments of the optical spectrum, optical oscillator strengths, linear optical susceptibility, third-order nonlinear optical susceptibility, carrier concentration to the effective mass ratio, high-frequency dielectric constant, nonlinear refractive index, plasma frequency and long wavelength refractive index were calculated and discussed at different doses of gamma radiation (1, 2, and 6 kGy). The results demonstrate that the optical properties and parameters of the gamma-irradiated composites vary with increasing gamma doses. This variation in values was observed after increased irradiation due to enhanced metal–polymer bonding and due to an increase in the density of the free charges within the metal polymer composites.

Nonlinear behavior of dust acoustic periodic soliton structures of nonlinear damped modified Korteweg–de Vries equation in dusty plasma

In this article, the nonlinear plasma model known the damped modified Korteweg–de Vries equation under consideration on the base of analytical technique to know the novel behavior of this nonlinear model. We formulated the nonlinear plasma model by utilizing the RP (reductive perturbation) technique with basic set of fluid system which consisted on cold negative charge dust fluid, immobile background neutral charges, positive charge ion fluid, fast (ionized) electrons and thermally electrons. We also constructed various kinds of novel soliton solutions including kink wave solitons, periodic solitary waves, anti-kink wave solitons for the damped modified KdV equation. The determined soliton solutions are novel, interested and did not determined in the previous research. The physical interpretation of demonstrated solutions represent in contour, two-dim and three-dim with computational software. The study prove that our proposed approach is powerful, efficient and can also be fruitful for study of other nonlinear models.

Accelerating self-modulated nonlinear waves in weakly and strongly magnetized relativistic plasmas

It is known that a nonlinear Schrödinger equation describes the self-modulation of a large amplitude circularly polarized wave in relativistic electron–positron plasmas in the weakly and strongly magnetized limits. Here, we show that such an equation can be written as a modified second Painlevé equation, producing accelerated propagating wave solutions for those nonlinear plasmas. This solution even allows the plasma wave to reverse its direction of propagation. The acceleration parameter depends on the plasma magnetization. This accelerating solution is different to the usual soliton solution propagating at constant speed.

Impact of stalling events on microcirculatory hemodynamics in the aged brain.

The role of cerebral microvasculature in cognitive dysfunction can be investigated by identifying the impact of blood flow on cortical tissue oxygenation. In this paper, the impact of capillary stalls on microcirculatory characteristics such as flow and hematocrit (Ht) in the cortical angioarchitecture is studied. Using a deterministic mathematical model to simulate blood flow in a realistic mouse cortex, hemodynamics parameters, including pressure, flow, vessel diameter-adjustable hematocrit, and transit time are calculated as a function of stalling events. Using a non-linear plasma skimming model, it is observed that Ht increases in the penetrating arteries from the pial vessels as a function of cortical depth. The incidence of stalling on Ht distribution along the blood network vessels shows reduction of RBCs around the tissue near occlusion sites and decreased Ht concentration downstream from the blockage points. Moreover, upstream of the occlusion, there is a noticeable increase of the Ht, leading to larger flow resistance due to higher blood viscosity. We predicted marked changes in transit time behavior due to stalls which match trends observed in mice invivo. These changes to blood cell quantity and quality may be implicated in the development of Alzheimer's disease and contribute to the course of the illness.

Shot-to-shot electron beam pointing instability in a nonlinear plasma bubble.

Shot-to-shot electron beam pointing instability in the plasma bubble, defined here as electron beam pointing jitter (EBJ), is a long-standing problem that limits the potential of the laser wakefield accelerator (LWFA) in a range of demanding applications. In general, EBJ is caused by variations in laser and plasma parameters from shot to shot, although the exact physical mechanism by which EBJ grows in the plasma wave remains unclear. In this work we theoretically investigate the fundamental physics of EBJ inside the plasma bubble and show how the intrinsic betatron oscillation can act as an amplifier to enhance EBJ growth. The analytical formulas for electron trajectory, pointing angle, and EBJ are derived from the basic momentum equationof an electron and verified numerically. It is shown that the shot-to-shot fluctuations of the laser and plasma parameters, such as laser strength, focus, and carrier-envelope phase, as well as the ambient plasma density and profile, lead to EBJ. The evolution of EBJ is dictated by the dynamics of the plasma bubble. Two amplification processes of the betatron oscillation are found in the rapidly evolving bubbles and play important roles in EBJ growth. The first is driven by a linear resonance in the wobbling bubble due to the coupling of the betatron oscillation and the bubble centroid oscillation. The second is a parametric resonance seen in the breathing bubble, where EBJ grows exponentially due to the strong frequency modulation of the betatron oscillation. Their characteristic functions, growth rates, and resonance conditions are deduced analytically and validated numerically. Finally, we also studied how radiation reaction affects EBJ. Our research provides a clear understanding of the basics of EBJ dynamics in LWFA and will help improve the use of LWFA in demanding applications.