Propagation Of Waves In Plasma Research Articles

Second Harmonic Generation of High Power Cosh-Gaussian Beam in Thermal Quantum Plasma: Effect of Relativistic and Ponderomotive Nonlinearity

Second harmonic generation (SHG) of high power Cosh-Gaussian(ChG) beam in thermal quantum plasma (TQP) is explored in current investigation. Relativistic and ponderomotive nonlinearities are taken together in present investigation. Combination of relativistic-ponderomotive nonlinearities causes modification in electron mass, thereby producing density gradients inside plasma. This further produces self-focusing of main beam. The well-known WKB and paraxial approaches are used for solving main beam’s wave equation and to obtain 2nd order ordinary differential equation (ODE). There is generation of electron plasma wave (EPW) due to these density gradients. Excited EPW interacts with main beam to generate 2nd harmonics in plasma. Effects of combined relativistic-ponderomotive nonlinearities and established laser - plasma parameters on beam’s waist and SHG yield are studied in present study.

Dynamic characterization of plasma and combustion wave interactions during millisecond-nanosecond combined laser-induced enhanced damage on fused silica

Fused silica, which is widely used in optical systems, limits the load capacity of the optical system when it is damaged by laser irradiation. In this paper, a combined millisecond-nanosecond pulsed laser induced triple combustion wave dynamics model for fused silica generation is developed. The relationship between pulse delay and the dynamic propagation of plasma and combustion waves induced by combined laser-induced fused silica was studied from three aspects: theory, simulation, and experiment. The results show that the energy deposition of the nanosecond laser injects energy into the dilute plasma, which increases the speed of the double-burning wave to form a triple-burning wave. In addition, it was found that the combined effect of viscous shear between the plasma plume and the air exacerbates the degree of imbalance in the Knudsen layer instantaneously releasing pressure and increasing the complexity of plasma and combustion wave propagation, recoil pressure produces a more complex crack network on the fused silica surface. The results provide a better understanding of the propagation properties of plasma and triple-burning waves during combined millisecond-nanosecond induced fused silica damage.

Multifluid Theory of Electrostatic Ion Cyclotron Waves in Partially Ionized Plasmas

Partially ionized plasmas universally exist in various astrophysical environments, such as the solar atmosphere and the E region of the ionosphere. In these contexts, the existence and propagation of waves in plasmas could be significantly influenced by effects of weakly ionized plasma (e.g., ion–neutral collisions). In this work, we investigate electrostatic ion cyclotron (EIC) waves in partially ionized plasmas based on the multifluid model with adiabatic electrons. Two distinct branches of EIC waves coexist in partially ionized plasmas: one branch is the conventional EIC waves; the other branch propagates around the “effective ion cyclotron frequency” which originates from self-consistent ion–neutral collisions. Furthermore, theoretical predictions in the new branch of EIC waves are qualitatively consistent with laboratory observations. In addition, a comparison between our theory and the previous work is also performed. This work can aid in understanding the acceleration and transverse heating of ions in partially ionized astrophysical plasmas where the ion–neutral collisions are frequent.

Analytical and dynamical analysis of nonlinear Riemann wave equation in plasma systems

The Riemann wave equation presents appealing nonlinear equations applicable in sea-water and tsunami wave propagation, ion and magneto-sound waves in plasmas, electromagnetic waves in transmission lines, and homogeneous stationary media. This study focuses on deriving soliton solutions in optics and exploring their physical properties. A wave transformation is used to convert a partial differential equation into an ordinary differential equation, from which soliton solutions are obtained using the generalized Riccati equation mapping approach. The solutions encompass various types of solitons, including bright, dark, periodic, and kink solitons. A comparison of solutions from this analytical method enhances the understanding of the nonlinear model’s behavior, with implications in plasma physics, fluid dynamics, optics, and communication technology. Additionally, 2D and 3D graphs illustrate the physical phenomena of the solutions using appropriate constant parameters. The qualitative analysis of the undisturbed planar system involves examining phase portraits in bifurcation theory, followed by introducing an outward force to induce disruption and reveal chaotic phenomena. Chaotic trajectories in the perturbed system are detected through various plots, including 3D, 2D, power spectrum, and chaotic attractor, alongside Lyapunov exponents. Stability analysis under different initial conditions is conducted, and sensitivity assessments are performed using the Runge–Kutta method. The findings are innovative and have not been previously explored for this system, highlighting the reliability, simplicity, and effectiveness of these techniques in analyzing nonlinear models in mathematical physics and engineering.

On some new travelling wave solutions and dynamical properties of the generalized Zakharov system.

This study examines the extended version of the Zakharov system characterizing the dispersive and ion acoustic wave propagation in plasma. The genuine, non-dispersive field depicts a shift in plasma ion density from its equilibrium state, whereas the complex, dispersive field depicts the fluctuating envelope of a highly oscillatory field of electricity. The main focus of the analysis is on employing the expanded Fan sub-equation approach to achieve some novel travelling wave structures including the explicit, periodic, linked wave, and other new exact solutions are developed for different values of this parameter. Three dimensional graphs are utilised to examine the properties of the obtained solutions. Furthermore, ideas from planar dynamical theory are applied in this work to analyse the intricate behaviour of the analysed model. Sensitivity analysis, multistability, quasi-periodic and chaotic patterns, Poincaré map, and the Lyapunov characteristic exponent are used to analyse the dynamical features.

On acoustic solitary waves in a multispecies degenerate relativistic magnetized plasma using physics informed neural networks

In this paper, we investigate the nonlinear electrostatic wave propagation in a two-dimensional magnetized plasma. The plasma consists of electron and positron components with relativistic degeneracy and stationary ions for neutralizing its background. Using the basic equations for this type of plasma in combination with the reductive perturbation method, we derived the Zakharov–Kuznetsov equation using the Lorentz transformation stretching method (LT). For the first time, we compared the results of the Galilean transformation stretching method (GT) and the LT method to investigate the effect of plasma parameters, such as the relativistic degeneracy parameter of electron particles (re0), the density ratio of ion to electrons (δ), and the normalized electron cyclotron (Ωe), on the amplitude and width of the wave solutions. The plasma parameters used in this research are representative of compact astrophysical objects. Numerical results showed that the amplitude of wave solutions obtained by the LT method is smaller than the GT method, but the width is greater. We provide a physical explanation for these differences. Furthermore, we present a physics-informed neural network (PINN) approach to directly recover the intrinsic nonlinear dynamics from spatiotemporal data. The PINN model uses a deep neural network constrained by the governing equations to learn the optimal parameters, with the aim of enhancing the predictive capabilities of the system. The results of this study provide valuable insight into the propagation of nonlinear waves in white dwarfs, where relativistic effects are significant. These findings could substantially advance the development of emerging machine learning applications in astrophysics.

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.

Interaction between the core and the edge for ion cyclotron resonance heating based on artificial absorption plasma model

In numerical simulations of the ion cyclotron range of frequencies (ICRF) wave heating scheme, core solvers usually focus on wave propagation and absorption mechanisms within the core plasma region. However, the realistic scrape-off layer (SOL) plasma is usually simplified, making it difficult to have deeper understanding of wave propagation and absorption within the SOL. In this work, we employ a cold plasma assumption and an artificial absorption mechanism based on the approach of reference (Zhang et al 2022 Nucl. Fusion 62 076032), to study wave propagation and absorption in the realistic SOL plasma of the EAST. During the exponential decay of the total coupled power with respect to the toroidal mode numbers, several fluctuations are observed in the case of low collisional frequencies. The fluctuations may be caused by the cavity modes associated with specific toroidal mode numbers. Due to the presence of cut-off densities, the edge power losses and the total coupled power exhibit different behaviors before and after the cut-off layer is “open”. Furthermore, the simulation results obtained from the kinetic model in reference (Zhang et al 2022 Nucl. Fusion 62 076032) is discussed. This suggests that both the core-edge combined model and the artificial mechanism are capable of simulating wave propagation and absorption.

Modelling of ICRH slow wave propagation and absorption in Wendelstein 7-X stellarator

Abstract The propagation and absorption of the slow waves in the three-ion plasma of the Wendelstein 7-X stellarator have been investigated by ray tracing. The aim of the study is to obtain a qualitative notion of the penetration into the plasma and absorption of the wave excited by the potential difference between the antenna conductors and the antenna box. It has been discovered that the rays propagate along the magnetic field lines over a significant distance, up to 6 m, from the antenna. They weakly, to a depth of 0.1 m, penetrate into the plasma. Absorption of the slow waves by electrons does not lead to the generation of the currents capable of affecting the plasma equilibrium. Most of the slow waves are absorbed beyond the region of ion-ion hybrid resonance in the zone of cyclotron resonance of He3 ions at the periphery of the plasma. The ICRH of the three-ion W 7-X plasma will be used to heat He3 ions to high energies and simulate the confinement of alpha particles in an optimized stellarator configuration. The presence of a source of hot He3 ions, which are poorly confined, at the periphery of the plasma can affect the experimental results.

Painlevé analysis and Hirota direct method for analyzing three novel physical fluid extended KP, Boussinesq, and KP-Boussinesq equations: Multi-solitons/shocks and lumps

Due to the extensive and diverse connections of the Kadomtsev-Petviashvili (KP) equation with various physical phenomena, such as the propagation of waves in sea and ocean water and the propagation of nonlinear waves in plasmas when two-dimensional perturbations are considered, thus in this study and based on the original KP equation, we construct and investigate three extended models, which are called the extended KP (eKP) equation, the extended Boussinesq (eBO) equation, and the extended KP-Boussinesq (eKP-BO) equation. These equations are commonly observed in many physical contexts involving nonlinear and dissipative media. Our research begins with thoroughly verifying the complete integrability of the three extended models. Once this crucial step is accomplished, we will examine these three extended models using the simplified Hirota approach (SHA), leading us to derive multiple soliton/shock solutions. Furthermore, the Hirota bilinear form of each model will be employed to derive a set of lump solutions for these three extended models, utilizing different parameter values. We also analyze some derived solutions graphically by presenting some two- and three-dimensional graphics to understand the dynamic behavior of the waves described by these solutions. The obtained results are anticipated to benefit a broad spectrum of academics interested in studying fluid mechanics, water wave characterization, and other interdisciplinary domains. Additionally, these models are anticipated to be essential in describing and understanding the dynamics of several nonlinear phenomena that arise and propagate in different plasma systems when perturbations are considered in multidimensions.

Analytical solutions and soliton behaviors in the space fractional Heisenberg ferromagnetic spin chain equation

This study investigates soliton solutions to the (2 + 1)-dimensional space fractional Heisenberg ferromagnetic spin chain equation incorporating beta fractional derivatives that explain the nonlinear propagation of spin wave in the ferromagnetic material with magnetic interactions including the both classical and semi-classical frameworks. This model has applications in spintronics, plasma physics, magnet theory, and condensed matter physics. Employing the two-potential extended Kudryashov and (G′/G, 1/G)-expansion methods, we derive some original and generic solutions composed of trigonometric functions, hyperbolic functions, and their rational forms. For particular values of the parameters, these solutions offer V-shaped, bell-shaped, kink, periodic, flat kink, and singular periodic solitons. The physical behavior of these solitons is demonstrated through three-dimensional, contour, and two-dimensional plots. The results are important in the study of phase transitions in ferromagnetic materials, lattice vibrations in condensed matter, and the propagation of shock waves in plasma. This study also demonstrates the potential and reliability of the employed strategies.

Large-amplitude plasma wave generation by laser beating in inhomogeneous magnetized plasmas

Large-amplitude plasma wave is known to accelerate electrons to high energies. The electron energy gain mainly depends on plasma wave amplitude. In this paper, we investigate the excitation of large-amplitude plasma waves by laser beat-wave in an inhomogeneous plasma. The idea behind this work is to employ linear and radial plasma density profiles to enhance the plasma wave amplitude. PIC simulations are used to validate the numerical solution of the nonlinear wave equation in cylindrical dimensions through the finite difference method. Furthermore, the effects of the quadratic-radial plasma density profiles and magnetic field on the plasma wave excitation are investigated. The study shows that compared to the linear density profile of plasma, the plasma wave amplitude in the case of a linear-radial density profile is far more pronounced. For the linear-radial density profile, the plasma wave amplitude remains steady over greater distances of propagation compared to the linear density profile, resulting in reduced immediate damping effects. It can also be seen that the plasma wave amplitude is higher for the quadratic-radial than for the linear-radial density profiles. The effect of a longitudinal magnetic field on plasma wave amplitude is investigated. It can be seen that the plasma wave amplitude is increased by applying a magnetic field. This study may provide a way to enhance the plasma wave field for accelerating the electrons in laser-plasma accelerators.

Painlevé Analysis of the Traveling Wave Reduction of the Third-Order Derivative Nonlinear Schrödinger Equation

The second partial differential equation from the Kaup–Newell hierarchy is considered. This equation can be employed to model pulse propagation in optical fiber, wave propagation in plasma, or high waves in the deep ocean. The integrability of the explored equation in traveling wave variables is investigated using the Painlevé test. Periodic and solitary wave solutions of the studied equation are presented. The investigated equation belongs to the class of generalized nonlinear Schrödinger equations and may be used for the description of optical solitons in a nonlinear medium.

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.

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.

Plasma wave propagation conditions analysis using the warm multi-fluid model

Although an accurate description of wave propagation and absorption in plasmas requires complicated full-wave solutions or kinetic simulations, local dispersion analysis can still be helpful to capture the main physics of wave properties. Plasma wave propagation conditions or accessibility informs whether a wave can propagate to a region, which usually depends on the wave frequency, wave vector, the local plasma density, and magnetic field. We demonstrate a warm multi-fluid eigenvalue model and a matrix approach to rapidly calculate plasma wave accessibility diagrams, where thermal effects are also included via an isotropic pressure term. All cold plasma waves, from high-frequency electron cyclotron waves, intermediate-frequency lower hybrid waves, to low-frequency ion cyclotron waves, are presented. By comparing with the kinetic model, it is interesting to find that the warm multi-fluid model, though incapable of reproducing the Bernstein modes, can provide a quick way to determine whether thermal effects are important.

Numerical Simulation for Solitary Waves of the Generalized Zakharov Equation Based on the Lattice Boltzmann Method

The generalized Zakharov equation is a widely used and crucial model in plasma physics, which helps to understand wave particle interactions and nonlinear wave propagation in plasma. The solitary wave solution of this equation provides insights into phenomena such as electron and ion acoustic waves, as well as magnetic field disturbances in plasma. The numerical simulation of solitary wave solutions to the generalized Zakharov equation is an interesting problem worth studying. This is crucial for plasma-based technology, as well as for understanding nonlinear wave propagation in plasma physics and other fields. In this study, a numerical investigation of the generalized Zakharov equation using the lattice Boltzmann method has been conducted. The lattice Boltzmann method is a new modeling and simulating method at the mesoscale. A lattice Boltzmann model was constructed by performing Taylor expansion, Chapman–Enskog expansion, and time multiscale expansion on the lattice Boltzmann equation. By defining the moments of the equilibrium distribution function appropriately, the macroscopic equation can be restored. Furthermore, the numerical experiments for the equation are carried out with the parameter lattice size m=100, time step Δt=0.001, and space step size Δx=0.4. The solitary wave solution of the equation is numerically simulated. Numerical results under different parameter values are compared, and the convergence and effectiveness of the model are numerically verified. It is obtained that the model is convergent in time and space, and the convergence orders are all 2.24881. The effectiveness of our model was also verified by comparing the numerical results of different numerical methods. The lattice Boltzmann method demonstrates advantages in both accuracy and CPU time. The results indicate that the lattice Boltzmann method is a good tool for computing the generalized Zakharov equation.

Exploring plasma phenomena with the Nizhnik–Novikov–Veselov formula: Analyzing ion-acoustic waves, solitons, and shocks

This paper delves into the intricacies of the ([Formula: see text])-dimensional asymmetric Nizhnik–Novikov–Veselov ([Formula: see text]) model, a nonlinear partial differential equation governing ion-acoustic wave propagation in plasma. By employing advanced analytical and numerical approaches, the study explores innovative solitary wave solutions, particularly focusing on the dynamics of isochoric flow. Isochoric flow analysis is crucial for unraveling the complex behaviors exhibited by incompressible fluids like elastomers and bio-elastomers, which maintain a constant density. The derivation of the ([Formula: see text])-dimensional [Formula: see text] equation stems from fluid equations governing plasma dynamics. This model serves as a valuable tool for simulating experimental observations of plasma waves. The computational methodology applied in this research demonstrates a commendable level of precision and consistency, yielding novel solitary wave solutions previously unreported in the [Formula: see text] model. These results underscore the study’s importance and novelty. The outcomes not only contribute to our understanding of incompressible fluid dynamics, but also lay the groundwork for future investigations in this domain. The revealed solitary wave solutions have the potential to inform the development of more accurate models for predicting fluid dynamics, thereby advancing the field.

An overview of the evolution of the modeling of reflectometry diagnostics in fusion plasmas using finite-difference time-domain codes

Microwave reflectometry, having its origins in ionosphere probing techniques to evaluate electronic density, has become one of the most important diagnostics for the same quantity in fusion plasmas. Reflectometry will play a major role in next-generation machines, in particular in DEMO, where it is expected to provide plasma positioning, shaping, and tracking data. The ability to have an ever-increasing comprehensive description of reflectometry is particularly important since it allows us to assess the measuring capabilities of existing experimental systems and to predict the performance of new diagnostic concepts based on probing waves. Furthermore, wave propagation in a thermonuclear plasma with fluctuating electronic densities is far from straightforward and the need for a numerical full-wave treatment becomes fundamental. We will present the reader with the fundamentals of this technique and introduce the usage and evolution of FDTD in reflectometry, using as an example, the synthetic diagnostics setup that uses the family of REFMUL* codes, which is employed in the assessment of the performance of several reflectometry systems in different fusion machines.

Retraction: “Modeling of plasma wave propagation and crystal lattice theory based on computational simulations” [AIP Adv. 13, 045223 (2023)

Retraction: “Modeling of plasma wave propagation and crystal lattice theory based on computational simulations” [AIP Adv. 13, 045223 (2023)