Waves In Cold Plasma Research Articles

A study on solutions of fractional order equal-width equation using novel approach

The time-fractional equal-width equation plays a vital role in plasma physics, serving as an essential tool for elucidating the dynamics of hydromagnetic waves in cold plasma, a critical component for the comprehensive understanding of plasma-related phenomena. Furthermore, this equation finds application in fluid mechanics, which models the transmission of nonlinear waves across shallow waters. In this study, we employ an innovative technique to solve time-fractional equal-width equation, demonstrating the q-homotopy analysis transform technique. This considered technique was implemented to find the effective approximated solution of the considered equations. The obtained results are discussed through the 3D plots and graphs that express the physical representation. The results derived from the q-homotopy analysis transform method are presented in a series form, exhibiting swift convergence and capturing the behavior of the equal-width equation’s solution with minimal error, and the convergence analysis and uniqueness of the solution using the projected method have been secured using the fixed-point theory. The projected method we used does not require linearization, perturbations, or discretization, which significantly reduces computations. The results disclose that the proposed technique is highly effective, methodical, and easy to apply for complex and nonlinear systems, helping us to capture the associated behavior of diverse classes of phenomena. The numerical simulations presented ensure higher accuracy and are compared with other techniques to evaluate approximate errors. In comparison with other techniques, the considered method is a competent tool to get an analytical solution of an considered equation and the methodology employed herein for the considered equation is demonstrated to be both efficient and dependable, marking a significant advancement in the field.

Singularity formation of hydromagnetic waves in cold plasma

We study C1 blow-up of the compressible fluid model introduced by Gardner and Morikawa, which describes the dynamics of a magnetized cold plasma. We propose sufficient conditions that lead to C1 blow-up. In particular, we find that smooth solutions can break down in finite time even if the gradient of initial velocity is identically zero. The density and the gradient of the velocity become unbounded as time approaches the lifespan of the smooth solution. The Lagrangian formulation reduces the singularity formation problem to finding a zero of the associated second-order ODE.

RSM-Based Optimization Analysis for Cold Plasma and Ultrasound-Assisted Drying of Caraway Seed.

In this study, the hot-air drying of caraway seeds was enhanced using two nonthermal physical field technologies: cold plasma (CP) and ultrasonic waves (US). Air drying temperatures of 35, 45, and 55 °C with CP pretreatment exposure times (CPt) of 25 and 50 s were used. When convective drying was accompanied by US, power levels (USp) of 60, 120, and 180 W were applied. Experimentally, the most effective contribution was found by using both CP pretreatment (25 s) and US (180 W), in which the maximum decreases of 31% and 39% were estimated for the drying period and specific energy consumption, respectively. The total color change, the rupture force, TPC, TFC, and antioxidant capacity were also estimated for evaluating the quality of dried products. In a CP-US-assisted drying program (25 s, 180 W), the minimum change in color and the rupture force were found to be 6.40 N and 20.21 N, respectively. Compared to the pure air drying, the combined application of CP and US resulted in a mean increase of 53.2, 43.6, and 24.01% in TPC, TFC, and antioxidant capacity of extracts at the temperature of 35 °C. Based on the response surface methodology (RSM) approach and obtained experimental data, accurate mathematical predictive models were developed for finding the optimal drying condition. The optimization process revealed that 39 °C, 180 W, and 23 s resulted in a desirability of 0.78 for drying caraway seeds.

Analytic wave solutions to the beta-time fractional modified equal width equation based on two efficient approaches

By using the two distinct methods known as the exp(-ϕ(η))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\exp (-\\phi (\\eta ))$$\\end{document} and the Expa\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Exp_a$$\\end{document}-function methods, various forms of soliton solutions of the modified equal width wave equation (MEWE) with beta time derivative (BTD) are produced in this study. This model is used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. The obtained solutions are in the form of rational, trigonometry and hyperbolic trigonometry functions. Using Mathematica software, the resulting solitons are validated. Graphs are also used at the conclusion to explain the findings. These soliton solutions imply that these two methods are more dependable, simple and efficient than other methods. The findings can be used to explain how studious structures and other comparable non-linear physical structures are substantially understood. The obtained results are very helpful in the fields of optics, kinetics solid-state physics and hydro-magnetic waves in cold plasma.

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.

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.

Consistent travelling wave characteristic of space–time fractional modified Benjamin–Bona–Mahony and the space–time fractional Duffing models

Study on solitary wave phenomenon are closely related on the dynamics of the plasma and optical fiber system, which carry on broad range of wave propagation. The space–time fractional modified Benjamin–Bona–Mahony equation and Duffing model are important modeling equations in acoustic gravity waves, cold plasma waves, quantum plasma in mechanics, elastic media in nonlinear optics, and the damping of material waves. This study has effectively developed analytical wave solutions to the aforementioned models, which may have significant consequences for characterizing the nonlinear dynamical behavior related to the phenomenon. Conformable derivatives are used to narrate the fractional derivatives. The expanded tanh-function method is used to look into such kinds of resolutions. An ansatz for analytical traveling wave solutions of certain nonlinear evolution equations was originally a power sequence in tanh. The discovered explanations are useful, reliable, and applicable to chaotic vibrations, problems of optimal control, bifurcations to global and local, also resonances, as well as fusion and fission phenomena in solitons, scalar electrodynamics, the relation of relativistic energy–momentum, electromagnetic interactions, theory of one-particle quantum relativistic, and cold plasm. The solutions are drafted in 3D, contour, listpoint, and 2D patterns, and include multiple solitons, bell shape, kink type, single soliton, compaction solitary wave, and additional sorts of solutions. With the aid of Maple and MATHEMATICA, these solutions were verified and discovered that they were correct. The mentioned method applied for solving NLFPDEs has been designed to be practical, straightforward, rapid, and easy to use.

Simulation of Electromagnetic Waves in Magnetized Cold Plasma by a Novel BZT-DGTD Method

This work presents a novel discontinuous Galerkin time domain (DGTD) approach based on second-order bilinear <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z</i> transform (BZT) to analyze the behavior of electromagnetic waves in a magnetized cold plasma. The Maxwell’s equations and current density equation are utilized to formulate the governing mathematical expressions of magnetized plasma, and the BZT approach is employed to construct the time domain iterative formula. The suggested technique outperforms existing methods in terms of stability, performance, and aliasing effect avoidance. The efficacy of the suggested BZT-DGTD approach is investigated by analyzing electromagnetic wave propagation in unmagnetized and magnetized cold plasmas, and a comprehensive comparison is performed with commercial software WCT and COMSOL to validate its practicality. Furthermore, the features of electromagnetic wave propagation in plasma are investigated under numerous circumstances, and these instances are compatible with plasma physics.

Solitary wave solutions and investigation the effects of different wave velocities of the nonlinear modified Zakharov–Kuznetsov model for the wave propagation in nonlinear media

The modified Zakharov-Kuznetsov (mZK) model convey a significant role to analyze the inner mechanism of physical compound phenomenon in the field of two-dimensional discrete electrical lattice, the electrical waves in cold plasmas, plasma physics, nonlinear optics, wave behaviors of deep oceans, etc. In this study, numerous new, advanced, and more general exact solitary travelling wave solutions are explored to the early stated nonlinear model by the aid of newly developed generalized exponential rational function (GERF) method through the traveling wave transformation. The established solutions are in terms of trigonometric functions, rational functions, hyperbolic functions, exponential rational functions, and complex-soliton solutions. The results reveal that the free parameters significantly influence the existence of traveling waves, as well as nature, shape, and stability. The established soliton solutions demonstrate that the method is effective, compatible, scientifically efficient and easily applicable to identify a variety of wave structures of nonlinear evolution models. The mathematical simulations of the results were conducted by sketching 3D and 2D structures for different values of the associated parameters by the aid of the Wolfram Mathematica program.

Using the Stix finite element RF code to investigate operation optimization of the ICRF antenna on Alcator C-Mod

As the Ion Cyclotron Radio Frequency range (ICRF) heating becomes more favorable in fusion devices, the urgency of predicting and mitigating impurity generation that arises from it becomes more pressing. In the ICRF regime, rectified Radio Frequency (RF) sheaths are known to form at antenna and material edges that influence negative effects like sputtering and a decrease in heating efficiency. Methods to mitigate the formation of these RF sheaths through RF image currents cancellation have been experimentally studied. A power-phasing scan done on Alcator C-Mod in which the amount of power on the two inner straps (P in) versus the total 4 straps (P tot) was varied showed a minimization of enhanced potentials between Pin/Ptot∼ 0.7–0.9 while impurities were minimized for Pin/Ptot∼ 0.5–0.8. New capabilities in the realm of representing the RF sheath numerically now allow for these experiments to be simulated. Given the size of the sheath relative to the scale of the device, it can be approximated as a Boundary Condition (BC). A new parallelized cold-plasma wave equation solver called Stix implements a non-linear sheath impedance model BC formulated by Myra et al (2015 Phys. Plasmas 22 062507) through the method of finite elements using the MFEM library [http://mfem.org]. It is seen that Stix shows qualitative agreement with the measured C-Mod enhanced potentials.

Analysis of chaotic structures, bifurcation and soliton solutions to fractional Boussinesq model

In this work, we used the space-time fractional coupled Boussinesq (STFCB) model that is essential tools in the study of quantum optics, steady physics, the variational string’s acoustic waves, ion vibrational frequencies, hydro-magnetic waves in cold plasma and many other fields. In order to put such new precise solutions of the aforementioned model, the modified Sardar-sub equation (MSSE) technique has been suggested with inside the sense of conformable derivative and the fractional order partial differential equation that is capable of changing into an ordinary differential equation by using the travelling wave transform. The scoring of solitons and other solutions demonstrates the MSSE technique compatibility for different constant values, which are shown in 3-D, 2-D and contour plots. Additionally, we discussed the examined model chaotic and dynamical tendencies. The theory of plane dynamical system is used to examine the chaotic patterns of the systems. The investigations are novel and unexamined. They can be utilized to explain the physical phenomena which have been simulated to provide details on the brief dynamical characteristics. According to numerical simulations modifying the parameters of frequencies and amplitudes has an impact on the system of dynamical properties. We indicated that the MSSE technique for creating precise solutions offers new and significant mathematical tools in applied mathematics.

Vlasov equation, waves and dispersion relations in fractal dimensions: Landau damping and the toroidal ion temperature gradient instability problem

In this study, we have used the concept of ‘product-like fractal measure’ introduced by Li and Ostoja-Starzewski in their formulation of anisotropic and elastic media to introduce Vlasov equation in fractal dimension. We have been motivated by this new concept since it is safely applied to several systems with length scales bounded by lower and upper cutoffs via the dimensional regularization technique. We have considered through this study collisionless plasma in fractal dimension and we have analyzed the impacts of the Vlasov equation in some points in plasma physics starting from the Hamiltonian dynamics. Several results have been obtained and discussed accordingly. The main outcomes of the present study concern first the facts that waves in cold plasma are associated with low fractal dimensions and hence by low complexity and that the effective damping is affected by the sign of the fractal dimension and differs from the conventional Landau damping in magnitude and in sign for negative dimension. Besides, for a very low fractal dimension, the Landau damping is negligible or removed. This result was observed in kinetic turbulent plasmas and may solve the paradox problem emerging in the application of critical balance to a kinetic turbulence cascade.

A Parametric Study of Oxygen Ion Cyclotron Harmonic Wave Excitation and Polarization by an Oxygen Ring Distribution

AbstractOxygen ion cyclotron harmonic (OCH) waves are electromagnetic emissions with frequencies near the harmonics of the oxygen ion cyclotron frequency. These waves can be excited by an energetic O+ ring distribution. Here, we perform a parametric study of OCH waves by an O+ ring distribution. We investigate the effects of ring concentration (ηho), velocity (vr), temperature (Tr), total O+ concentration (ηo), and wave normal angles (WNAs) on the wave growth rate and polarization. We find that four‐wave modes are related to OCH waves. The growth rates and frequency range increase with ηho and ηo and decrease with Tr. The peak growth rate roughly follows the first peak of (square of the Bessel function corresponding to the O+ ring) or cold plasma wave modes, which can be used to explain the vr and WNA dependences. OCH waves shift from the transverse mode to the compressional mode as vr increases.

Effect of green technologies of cold plasma and airborne ultrasound wave on the germination and growth indices of cumin (Cuminum cyminum L.) seeds

AbstractCurrent research is considered to study the effect of nonthermal physical field technologies of atmospheric cold plasma (CP) and ultrasound waves (US) on the germination and seedling indices of cumin seeds. In this regard, different drying strategies were planned in a single and combined form using a lab‐scale cold plasma unit and ultrasound‐assisted air dryer. Various duration of CP pretreatment (CPt: 0, 15, and 30 s), ultrasound power (P: 0, 60, 120, and 180 W), and air temperature (T: 30, 35, and 40°C) were practiced to investigate the changes in germination traits and microstructure characteristics of cumin seeds. It was found that CP pretreatment and ultrasound treatment in a single form significantly increased germination percentage, germination index, and germination rate as well as seeding vigor of cumin seeds. The morphological alteration in the surface of the seeds, which modifies the seed surface hydrophilicity and accelerates water uptake, may be the leading cause of CP and US‐induced modification in the germination power. The highest stimulatory effect belonged to the combined application of cold plasma and ultrasound wave when the cumin seeds were treated with an appropriate CP dose and ultrasound energy. So that, the maximum germination percentage (92%), germination index (14.91), and germination rate (21.33%), as well as the highest values of seedling vigor index I (178.67 mm) and vigor index II (420.72 mg), were in possession of pretreatment with CPt: 15 s before ultrasound‐assisted drying at T ≤ 35°C and P ≤ 120 W.Practical ApplicationsThis study demonstrates the potential of cold plasma and ultrasound wave before and during air drying of cumin seeds, respectively. Cold plasma was used as a nonthermal and nonchemical pretreatment strategy before air drying of cumin seeds in ultrasound‐assisted dryer. A single application of cold plasma caused a significant increase in germination percentage, germination index, and germination rate of cumin seeds. The positive effect of cold plasma on the studied parameter of cumin seeds intensified when it was supported by airborne low‐power ultrasound waves during air drying.

Soliton Solutions and Sensitive Analysis of Modified Equal-Width Equation Using Fractional Operators

In this manuscript, the novel auxiliary equation methodology (NAEM) is employed to scrutinize various forms of solitary wave solutions for the modified equal-width wave (MEW) equation. M-truncated along with Atangana–Baleanu (AB)-fractional derivatives are employed to study the soliton solutions of the problem. The fractional MEW equations are important for describing hydro-magnetic waves in cold plasma. A comparative analysis is utilized to study the influence of the fractional parameter on the generated solutions. Secured solutions include bright, dark, singular, periodic and many other types of soliton solutions. In compared to other methods, the solutions demonstrate that the proposed technique is particularly effective, straightforward, and trustworthy that contains families of solutions. In addition, the symbolic soft computation is used to verify the obtained solutions. Finally, the system is subjected to a sensitive analysis. Integer-order results calculated by the symmetry method present in the literature can be addressed as limiting cases of the present study.

The dispersion and propagation of topological Langmuir-cyclotron waves in cold magnetized plasmas

The topological Langmuir-cyclotron wave (TLCW) is a recently identified topological surface excitation in magnetized plasmas. We show that TLCW originates from the topological phase transition at the Langmuir wave-cyclotron wave resonance. By isofrequency surface analysis and two- and three-dimensional time-dependent simulations, we demonstrate that the TLCW can propagate robustly along complex phase transition interfaces in a unidirectional manner and without scattering. Because of these desirable features, the TLCW could be explored as an effective mechanism to drive current and flow in magnetized plasmas. The analysis also establishes a close connection between the newly instituted topological phase classification of plasmas and the classical Clemmow-Mullaly-Allis (CMA) diagram of plasma waves.

Quantum signal processing for simulating cold plasma waves

Numerical modeling of radio-frequency waves in plasma with sufficiently high spatial and temporal resolution remains challenging even with modern computers. However, such simulations can be sped up using quantum computers in the future. Here, we propose how to do such modeling for cold plasma waves, in particular, for an X wave propagating in an inhomogeneous one-dimensional plasma. The wave system is represented in the form of a vector Schr\"odinger equation with a Hermitian Hamiltonian. Block encoding is used to represent the Hamiltonian through unitary operations that can be implemented on a quantum computer. To perform the modeling, we apply the so-called quantum signal processing algorithm and construct the corresponding circuit. Quantum simulations with this circuit are emulated on a classical computer, and the results show agreement with traditional classical calculations. We also discuss how our quantum circuit scales with the resolution.

Inelastic soliton wave solutions with different geometrical structures to fractional order nonlinear evolution equations

The general time fractional Burger- Fisher (TF-BF) and the space–time regularized long-wave (STF-RLW) equations are considered as examples of gravitational water waves in cold plasma as well as so many areas. The above equations are used in nonlinear science and engineering to study long waves in seas and harbors that travel in just one direction. First, the two equations are transformed to ODEs by applying a fractional complex transform along with characteristics of confirmable fractional derivative (CFD). Then, the extended tanh-function (ET-F) approach is investigated to find a variety of analytical solutions with different geometrical wave structures the mentioned models. The results are in the form of kink, one-, two-, multiple-solitons solutions, and other types sketched in 2D, 3D, and contour patterns.

New dynamical soliton propagation of fractional type couple modified equal-width and Boussinesq equations

The space–time fractional coupled modified equal-width equation and the coupled Boussinesq equation are a category of fractional partial differential equations, which might be crucial mathematical feathers in nonlinear optics, solid-state physics, vibrations in the nonlinear string, ion sound waves in plasma, hydro-magnetic waves in cold plasma and many more. To assemble such new exact solutions of the mentioned equations, the Sine-Gordon expansion (SGE) technique has been proposed with inside the sense of conformable derivative and the fractional order partial differential equation that is capable to change into an ordinary differential equation by using the traveling wave transform. In this article, the SGE technique has been employed to search the higher-dimensional fractional nonlinear evolution equations and hooked up consistent soliton solutions to the faster thought fractional nonlinear evolution equations through installing use of the prolonged higher-dimensional SGE technique. The compatibility of the extended SGE technique confirms through the scoring of soliton solutions. Moreover, we explored a couple of varieties of solutions over the maple calculations, including soliton, kink types, bell types, single soliton type, dark soliton, singular kink type, and anti-bell type solutions for distinct values of constants, which have been illustrated by the usage of 3D, list-point, contour analysis, and vector plotting. It is far incredible to understand that the feature of the solutions relies upon the selection of the parameters from the figures. This takes a look at an impactful position in studying higher-dimensional fractional nonlinear evolution equations through the prolonged SGE technique.

RF-transpond: A 1D coupled cold plasma wave and plasma transport model for ponderomotive force driven density modification parallel to B0

The RF-Transpond code couples a fluid plasma transport solver with a frequency domain cold plasma RF wave solver in a 1D domain parallel to a strong background magnetic field. A ponderomotive force term proportional to parallel gradients in the electric field strength is included in the transport model in order to describe ponderomotive effects in the scrape-off layer (SOL) of fusion plasmas. The transport and wave codes are verified independently and a coupled case corresponding to experimental parameters from the LArge Plasma Device (LAPD) is presented. The density perturbation ratio Rn, calculated to describe ponderomotive force driven modifications, is up to 20% for the simulation inputs used. Program summaryProgram Title: rf-transpondCPC Library link to program files:https://doi.org/10.17632/xn3y2yx9wj.1Developer's repository link:https://github.com/rhealbarnett/rf-transpond.gitLicensing provisions: MITProgramming language: MatlabNature of problem: Self consistent coupled model describing ponderomotive force driven density modification in the near field of RF antennas.Solution method: The density and velocity solutions are calculated from the continuity and momentum transport equations, solved using a finite difference time domain method, which include a ponderomotive force term that depends on the radio frequency electric field. The frequency domain electric field solution is calculated from the cold plasma wave equation, solved using a finite difference frequency domain method, where the cold plasma dielectric tensor is a function of the density. The electric field and density couple the two models, providing self consistency.