In this paper, we investigated the extraordinarily complex nonlinear evolution equations [Formula: see text]- and [Formula: see text]-dimensional generalized Camassa–Holm–Kadomtsev–Petviashvili (g-CHKP) equations found in shallow water waves. We use the Jacobi Elliptic Function Expansion (JEFE) method to derive a variety of closed-form analytical soliton solutions, and traveling wave solutions for the nonlinear [Formula: see text]- and [Formula: see text]-dimensional generalized g-CHKP equations. Several new forms of soliton-like solutions to the governing equations, as well as the dynamics of various types of solutions, are shown graphically for selecting the relevant parameters via numerical simulation. The originality of this work arises from the fact that the results mentioned are entirely new and have not before been studied for the given equation. Furthermore, the applied mathematical approach is more efficient and trustworthy for developing newly constructed soliton solutions in various fields of complex nonlinear phenomena. We anticipate that the findings of this work will have important applications in plasma physics, ocean engineering, optical fibers, quantum mechanics, fluid dynamics, nonlinear dynamics, and soliton theory.
Ensuring the reliability of plasma diagnostic data is essential for both safe operation and accurate analysis in Magnetic confinement fusion (MCF) devices. However, diagnostic signals are often corrupted by electromagnetic interference, hardware faults, or neutron irradiation, resulting in erroneous diagnostic data. To address this issue, a novel Real-Time Time-Domain Global Similarity (RT-TDGS) method based on machine learning is proposed. RT-TDGS transforms the multi-label classification problem of identifying erroneous channels into a binary classification of physical similarity between pairs of channels, exhibiting intrinsic robustness against variations in discharge parameters. During feature extraction, multiple evaluation metrics are employed to quantify the similarity between pairs of channels after feature engineering, and a machine learning model is then used to classify and identify erroneous channels based on these features. In the training phase, a multi-scale temporal sampling strategy is introduced, which constructs an augmented dataset by extracting features at different temporal scales to enhance the classification accuracy across various temporal scales of the experiments. Applied to the Experimental Advanced Superconducting Tokamak POlarimeter-INTerferomete system, the method achieves an accuracy of 0.9647 with an average processing time of 0.59 ms, fully satisfying real-time requirements. The RT-TDGS method significantly improves the reliability of real-time plasma control data and shows broad application potential in MCF devices.
The purpose of this study is to investigate the effects of multiplicative noise on the exact solutions of the generalized nonlinear Schrödinger equation. By employing two direct methods, we derive precise solutions, including hyperbolic, trigonometric and Jacobi elliptic function solutions. The research aims to enhance understanding of how multiplicative noise influences the behavior of these solutions, providing valuable insights into the dynamics of stochastic systems. Graphical examples illustrate the impact of noise, contributing to the broader field of nonlinear dynamics and its applications in physics and engineering. This study employs a two-pronged approach to derive exact solutions of the generalized nonlinear Schrödinger equation influenced by multiplicative noise. Initially, a similarity transformation reduces the stochastic problem to a second-order cubic nonlinear ordinary differential equation. Subsequently, four mappings between the Riccati equation and the reduced ordinary differential equation are established using the generalized unified method. The solutions generated include hyperbolic, trigonometric and Jacobi elliptic functions. The behavior of these solutions under varying levels of multiplicative noise is analyzed, supported by graphical representations to illustrate the effects of noise on the derived solutions. The findings reveal that multiplicative noise significantly affects the exact solutions of the generalized nonlinear Schrödinger equation. The study successfully derives multiple families of solutions, including hyperbolic, trigonometric and Jacobi elliptic functions, demonstrating the versatility of the employed methods. The analysis shows that the introduction of noise alters the stability and dynamics of these solutions, leading to complex behaviors. Graphical examples illustrate the impact of varying noise levels, highlighting the importance of considering stochastic effects in nonlinear systems. These results contribute to a deeper understanding of noise-induced phenomena in mathematical physics and engineering applications. This study offers original contributions by exploring the effects of multiplicative noise on the exact solutions of the generalized nonlinear Schrödinger equation, an area that has received limited attention in existing literature. By employing innovative methods, including the generalized unified technique and Jacobi elliptic function method, the research generates a diverse set of solutions that enhance the understanding of stochastic dynamics in nonlinear systems. The findings provide valuable insights into the interplay between noise and soliton behavior, which can inform future research and applications in fields such as optics, plasma physics and complex systems.
Equatorial ionospheric irregularities, particularly those associated with equatorial plasma bubbles (EPB), can significantly disrupt satellite navigation and communication systems. As the demand for reliable Global Navigation Satellite System (GNSS) and communication services grows, the prediction of ionospheric irregularities becomes critical. A key step in the prediction process is to identify distinct spatiotemporal patterns of irregularities, including day-to-day, longitudinal, and seasonal variations. However, with large datasets, manually classification or identification of these irregularities is a complex and challenging task. In this work, we propose unsupervised machine learning techniques to recognize and group irregularity patterns in large, unlabeled Rate of Total Electron Content (TEC) Index (ROTI) keograms. Specifically, two machine learning models: Gaussian Mixture Model and k-means clustering are employed. The ROTI keograms are constructed using GNSS data from two low-latitude receiver stations in Thailand. To reduce redundancy in the keogram images, three feature extraction techniques are applied before the clustering process. A comparative analysis is performed to determine the optimal number of clusters using these models. Based on the results, the optimal combination of feature extraction and clustering technique is determined for the proposed clustering model. The resulting k-means model with contour extractor classifies five distinct patterns of ionospheric irregularity patterns, providing valuable insights for enhancing EPB prediction models and deepening our understanding of ionospheric dynamics. Furthermore, these five irregularity patterns are analyzed in relation to space weather parameters such as the solar radio flux index (F10.7), and the geomagnetic index (Kp). The findings contribute to the development of robust prediction models, improving the reliability of satellite-based communication and navigation systems.
A recent proposal of accelerator based fusion reactor considers a scheme where an ion beam from the accelerator hits the target plasma on the resonance of the fusion reaction so that the reactivity ($σv$) can be an order of magnitude larger than that of a thermonuclear reactor. One of the important inputs is the stopping power which is needed to assess the energy loss of the beam in the plasma. In this work, we shall use the analytic formulation of Brown, Preston and Singleton~\cite{Brown:2005ji} to calculate the temperature dependence of the stopping power due to the target $t, {}^3H_e$, and ${}^{11}B$ plasmas in the resonance regions of their respective fusion reactions, i.e., $ d + t \rightarrow n + α, d + {}^3H_e \rightarrow p + α$, and $p + {}^{11}B \rightarrow 3 α$. It is found that the calculated stopping power, especially when the quantum corrections are included, does not go down with temperature as fast at $T^{-3/2}$. Instead it decreases slower, more like $T^{-x}$ with $x \le 1$ in the range of T from $\sim$ 5 to 50 keV for $d$ on $t$ and ${}^3H_e$ plasmas around their resonance energies.
Even though controlled non-thermal (low-temperature) electrical discharges have a wide range of applications from biomedicine to nanotechnology to environmental science, the electrical breakdown of insulation systems caused by discharges within the dielectrics is one of the most unwelcome events in the operation of high-voltage electrical apparatuses and power system components. A deeper understanding of non-thermal discharges is therefore of paramount relevance with reference to increasing levels of operating voltages and technological advancements. Particularly, the behavior of freely available atmospheric air, as the most commonly used gaseous dielectric, under applied high voltage calls for specific technical and analytical attention. This study set out to mathematically model, simulate, and analyze nonthermal plasma discharges in the insulation systems with air as the dielectric under normal atmospheric conditions. In this paper, a new hydrodynamic drift-diffusion model to simulate positive air discharge under atmospheric pressure is developed. This model contains a set of continuity equations for electron, positive, and negative ions (to include the dynamics and generation/loss of these charged particles and development of space charge) strongly coupled with Poisson's equation (to account for the mutual influence of space charge and interelectrode electric field). The model is validated with experimental results. The spatial and temporal evolution of charged particles and development of space charge, distribution of local electric field, and discharge current in the interelectrode air volume are presented and analyzed. Also, the effects of different parameters are studied. Simulations are carried out using COMSOL Multiphysics software. Comprehensive computer simulations enable it to gain a more profound insight into the behavior of atmospheric air as dielectric and non-thermal plasma discharges through this medium, which was not possible until some years ago. Therefore, this study not only corroborates the existing experimental findings but also facilitates further investigations in this area of study.
The transition from space exploration based on monolithic spacecraft to modular architectures requires overcoming severe challenges in robotic dynamics and advanced propulsion. This scientific article investigates the integration of Model Predictive Control (MPC) systems and mass-property simulators in In-Space Assembly and Manufacturing (ISAM) environments. The methodology is based on an analytical-deductive approach, exploring the equations of physical gas dynamics in rarefied flows applied to ion thrusters, as well as the kinematic modeling of electromechanical actuators in microgravity. The study is articulated around seven central axes: the ISAM infrastructure; the mathematical formulation of MPC and LQR control; closed-loop simulation via physics engines (MuJoCo); the analytical expansion of ion plumes; the mechatronic design of sensors and actuators; autonomous navigation based on mapping algorithms; and the strategic impact of these technologies on security and STEM education. The literature and models attest that the continuous variation of the inertia tensor during orbital assembly requires adaptive controllers capable of predicting structural dynamics in real-time. It is concluded that the advancement of space systems engineering depends on the inseparable fusion of plasma physics, autonomous robotics, and computational predictive control.
Negative Ion Source Neutral beam Injection (NNBI), as a critical auxiliary heating system for magnetic confinement fusion devices, directly affects the plasma heating efficiency of tokamak devices through the reliability of its beam source system. The single-shot experiment constitutes a significant experimental program for NNBI. This study addresses the frequent equipment failures encountered by the NNBI beam source system during a cycle of experiments, employing fault tree analysis (FTA) to conduct a systematic reliability assessment. Utilizing the AutoFTA 3.9 software platform, a fault tree model of the beam source system was established. Minimal cut set analysis was performed to identify the system’s weak points. The research employed AutoFTA 3.9 for both qualitative analysis and quantitative calculations, obtaining the failure probabilities of critical components. Furthermore, the F-V importance measure and mean time between failures (MTBF) were applied to analyze the system. This provides a theoretical basis and practical engineering guidance for enhancing the operational reliability of the NNBI system. The evaluation methodology developed in this study can be extended and applied to the reliability analysis of other high-power particle acceleration systems.
Md. Shafiqul Islam, M. Roshid, Mahtab Uddin
et al.
In this work, we study the modulation instability (MI) and closed‐form soliton solution of the modified Korteweg–de Vries–Zakharov–Kuznetsov (mKdV‐ZK) equation with a truncated M‐fractional derivative. The mKdV‐ZK equation can be used to describe the behavior of ion‐acoustic waves in plasma and the propagation of surface waves in deep water with nonlinear and dispersive effects in fluid dynamics. To execute a closed soliton solution, we implement two dominant techniques, namely, the improved F‐expansion scheme and unified solver techniques for the mKdV‐ZK equation. Under the condition of parameters, the obtained solutions exhibit hyperbolic, trigonometric, and rational functions with free parameters. Using the Maple software, we present three‐dimensional (3D) plots with density plots and two‐dimensional (2D) graphical representations for appropriate values of the free parameters. Under the conditions of the numerical values of the free parameters, the obtained closed‐form solutions provided some novel phenomena such as antikink shape wave, dark bell shape, collision of kink and periodic lump wave, periodic wave, collision of antikink and periodic lump wave, collision of linked lump wave with kink shape, periodic lump wave by using improved F‐expansion method and kink shape, diverse type of periodic wave, singular soliton, and bright bell and dark bell‐shape wave phenomena by using unified solver method. The comparative effects of the fractional derivative are illustrated in 2D plots. We also provided a comparison between the results obtained through the suggested scheme and those obtained by other approaches, showing some similar solutions and some that are different. Besides, to check of stability and instability of the solution, the MI analysis of the given system is investigated based on the standard linear stability analysis and the MI gain spectrum analysis. With the use of symbolic calculations, the applied approach is clear, simple, and elementary, as demonstrated by the more broad and novel results that are obtained. It may also be applied to more complex phenomena.
Filipe S. Ribeiro, Pedro D. S. Silva, Manoel M. Ferreira
Unmagnetized cold plasma modes are investigated in the context of the chiral Maxwell-Carroll-Field-Jackiw (MCJF) electrodynamics, where the axion chiral factor acts retrieving some typical properties of magnetized plasmas. The Maxwell equations are rewritten for a cold, uniform, and collisionless fluid plasma model, allowing us to determine the dispersion relation, new refractive indices, and propagating modes. We find four distinct refractive indices modified by the purely timelike CFJ background that plays the magnetic conductivity chiral parameter role associated with right-circularly polarized (RCP) and left-circularly polarized (LCP) waves. For each refractive index, the propagation and absorption zones are determined and illustrated for some specific parameter values. Modified RCP and LCP helicons are found in the low-frequency regime. The optical behavior is investigated, revealing that the chiral factor induces birefringence, measured in terms of the rotatory power (RP). The dichroism coefficient is carried out for the absorbing zones. The negative refraction zones may enhance the involved rotatory power, yielding RP sign reversion, a feature of rotating plasmas and MCFJ chiral plasmas. Charge density oscillations and Langmuir waves are also discussed, revealing no modified dispersion relation due to the chiral axion factor.
AbstractUnusual thermal self‐focusing of two‐dimensional beams in plasma which axis is parallel to the equilibrium straight magnetic field is considered. The equilibrium parameters of plasma determine scenario of a beam divergence (usual or unusual) which is stronger as compared with a flow without magnetic field. Nonlinear thermal self‐action of a magnetosonic beam behaves differently in the ordinary and unusual cases. Damping of wave perturbations and normal defocusing in gases leads to reduction of the magnitude of initially planar perturbations at the axis of a beam. Additional thermal self‐focusing nonspecific for gases occurs in plasma under some condition which counteracts this reduction. The theory and numerical examples concern thermal self‐action of initially focused (defocused) magnetosonic beam. Dynamics of perturbations in a beam is determined by dimensionless parameters responsible for diffraction, damping of the wave perturbations, initial radius of a beam's front curvature, and the ratio of viscous to thermal damping coefficients.
The slowing down of a charged particle beam passing through the dusty plasma with a non-thermal velocity alpha-distribution is studied. By using the Fokker-Planck collision theory, we derive the deceleration factor and slowing down time and make the numerical analyses. We show that the non-thermal velocity alpha-distributions of the plasma components have a significant effect on the slowing down. With increase of the mean velocity, the deceleration factor increases rapidly, reaches a peak and then decreases gradually. And the entire peak of the deceleration factor moves generally to the right with the increase of the alpha-parameter. The slowing down time decreases with the increase of the non-thermal alpha-parameter, and so the slowing down time in the non-thermal dusty plasma is generally less than that in a Maxwellian one.
Due to the highly nonlinear nature of the beam-loading, it is at present not possible to analytically determine the beam parameters needed in a two-bunch plasma wakefield accelerator for maintaining a low energy spread. Therefore in this paper, by using the Broyden-Fletcher-Goldfarb-Shanno algorithm for the parameter scanning with the code QuickPIC and the polynomial regression together with k-fold cross-validation method, we obtain two fitting formulas for calculating the parameters of tri-Gaussian electron beams when minimizing the energy spread based on the beam-loading effect in a nonlinear plasma wakefield accelerator. One formula allows the optimization of the normalized charge per unit length of a trailing beam to achieve the minimal energy spread, i.e. the optimal beam-loading. The other one directly gives the transformer ratio when the trailing beam achieves the optimal beam-loading. A simple scaling law for charges of drive beams and trailing beams is obtained from the fitting formula, which indicates that the optimal beam-loading is always achieved for a given charge ratio of the two beams when the length and separation of two beams and the plasma density are fixed. The formulas can also help obtain the optimal plasma densities for the maximum accelerated charge and the maximum acceleration efficiency under the optimal beam-loading respectively. These two fitting formulas will significantly enhance the efficiency for designing and optimizing a two-bunch plasma wakefield acceleration stage.
This paper presents quasilinear theory (QLT) for classical plasma interacting with inhomogeneous turbulence. The particle Hamiltonian is kept general; for example, relativistic, electromagnetic, and gravitational effects are subsumed. A Fokker--Planck equation for the dressed 'oscillation-center' distribution is derived from the Klimontovich equation and captures quasilinear diffusion, interaction with the background fields, and ponderomotive effects simultaneously. The local diffusion coefficient is manifestly positive-semidefinite. Waves are allowed to be off-shell (i.e. not constrained by a dispersion relation), and a collision integral of the Balescu--Lenard type emerges in a form that is not restricted to any particular Hamiltonian. This operator conserves particles, momentum, and energy, and it also satisfies the H-theorem, as usual. As a spin-off, a general expression for the spectrum of microscopic fluctuations is derived. For on-shell waves, which satisfy a quasilinear wave-kinetic equation, the theory conserves the momentum and energy of the wave--plasma system. The action of nonresonant waves is also conserved, unlike in the standard version of QLT. Dewar's oscillation-center QLT of electrostatic turbulence (1973, Phys. Fluids 16, 1102) is proven formally as a particular case and given a concise formulation. Also discussed as examples are relativistic electromagnetic and gravitational interactions, and QLT for gravitational waves is proposed.
Mladen Mitov, Alexander Blagoev, Stanislav Zapryanov
et al.
Recent experiments using 15 frame interferometry on PF-1000 facility in Warsaw confirm the association between neutron emission and spontaneously self-organized, relatively long lasting, finite plasma structures. A crucial aspect of this association is the simultaneous observation of an axial magnetic field, which can allow magnetic flux lines to densely cover closed surfaces creating "magnetic flux surfaces". Evolution of such 3-dimensional (3-D) magnetic field structures is necessarily accompanied by induced electric field that can provide a very long (theoretically infinite) acceleration path length along a trajectory enclosed within the magnetic structure leading to high ion kinetic energy, resulting in a high reaction rate. Associated charge and current densities can be related to electric scalar potential and magnetic vector potential measured outside the plasma. We report our first observations of these fields outside the plasma focus and discuss their general features. The reported technique is capable of unambiguous first-principles interpretation of signals in terms of quantities related to distributions of charge density and rate of change of azimuthal current density ("electromagnetic structure") in the plasma focus. It is non-intrusive and completely insensitive to non-axisymmetric aspects of plasma. Our first results show that axial magnetic field generated by azimuthal current density distribution symmetric about the axis exists before, during and after the pinch phase.
The formation mechanisms of hydrogen peroxide due to the interaction of oxygen atom from the cold atmospheric plasmas in contact with water are not fully understood. Previous work on molecular dynamics (MD) simulations of interactions of O atoms in bulk water based on reactive force field and density-functional tight-binding method did not observe the formation of H2O2. In this work we applied density functional theory in MD simulations of 192 trajectories considering 63H2O−O system to explore the reaction mechanisms for atomic oxygen radical in water. Our calculations revealed that triplet (ground) state oxygen was not reactive. Oxywater-similar structure O−OH2 was a transient product. Perhydroxyl anion O−OH− and its counterpart hydronium H3O+ were formed. In most of simulated cases, hydrogen peroxide was observed as a final product. The formation pathways of hydrogen peroxide exhibited large complexities for the simple hydrogen bonded system. According to the sources and pathways of the hydrogen atom being bonded in hydrogen peroxide molecule, mechanisms can be classified into (1) hydrogen-abstraction, (2) hydrogen-transfer n (n = 3, 4, 5, 6, 7, 8), (3) proton-delivery n = 2, 3, (4) proton-transfer. It was confirmed that for correct prediction of reaction mechanisms is better to use quantum molecular dynamic simulations.