Plasma Theory Research Articles

Correlation functions of weakly inhomogeneous plasma

This article focuses on the kinetic theory of inhomogeneous plasma and explores the interaction between a high-frequency electric field and weakly inhomogeneous plasma. Particularly, it examines the impact of an external variable field on the kinetic and high-frequency properties of the plasma, including kinetic equations, correlation functions, and distribution functions of charged particles. The study derives expressions for the pair (two-particle) correlation function and the corresponding distribution function, taking into ac- count the spatial inhomogeneity of the plasma and electric field, as well as the collisions between charged particles. The results were obtained using the kinetic equation for the spatial-temporal spectral density of fluctuations and the method of successive approximations (separation of slow motions and fast oscillations). The field amplitude is considered a slowly varying function of time and coordinates. The calculations neglect the contribution of the magnetic component of the electromagnetic field, which is applicable to longitudinal electric fields. The results obtained in this article are primarily of theoretical interest, they reveal the picture of the interaction of a weakly inhomogeneous plasma with a high-frequency electric field and can be used in the construction of a kinetic theory of an inhomogeneous plasma located in high-frequency electromagnetic fields. Note that for charged particles of the same sign, the correlation function is negative, and for particles of different signs it is positive. In addition, the correlation function is exponentially small when the distance between the particles is greater than the Debye radius. In all calculations, the contribution of the magnetic component of the electromagnetic field is neglected, which is quite true for the longitudinal electric field.

Summary of the 11th Conference on Magnetic Confined Fusion Theory and Simulation

This conference report summarizes recent progress in plasma theory and simulation that was presented in contributed papers and discussions at the 11th Conference on Magnetic Confined Fusion Theory and Simulation (CMCFTS) held in Chengdu, China, 27–30 October, 2023. Progress in various fields has been achieved. For example, results on zonal flow generation by mode coupling, simulations of the key physics of divertor detachment, energetic particle effects on magnetohydrodynamic (MHD) modes in addition to ion- and electron-scale turbulence, physics of edge coherent modes and edge-localized modes, and the optimization of ion heating schemes as well as confinement scenarios using advanced integrated modeling are presented at the conference. In this conference, the scientific research groups were organized into six categories: (a) edge and divertor physics; (b) impurity, heating, and current drive; (c) energetic particle physics; (d) turbulent transport; (e) MHD instability; and (f) integrated modeling and code development. A summary of the highlighted progress in these working groups is presented.

Overview of T and D–T results in JET with ITER-like wall

Abstract In 2021 JET exploited its unique capabilities to operate with T and D–T fuel with an ITER-like Be/W wall (JET-ILW). This second major JET D–T campaign (DTE2), after DTE1 in 1997, represented the culmination of a series of JET enhancements—new fusion diagnostics, new T injection capabilities, refurbishment of the T plant, increased auxiliary heating, in-vessel calibration of 14 MeV neutron yield monitors—as well as significant advances in plasma theory and modelling in the fusion community. DTE2 was complemented by a sequence of isotope physics campaigns encompassing operation in pure tritium at high T-NBI power. Carefully conducted for safe operation with tritium, the new T and D–T experiments used 1 kg of T (vs 100 g in DTE1), yielding the most fusion reactor relevant D–T plasmas to date and expanding our understanding of isotopes and D–T mixture physics. Furthermore, since the JET T and DTE2 campaigns occurred almost 25 years after the last major D–T tokamak experiment, it was also a strategic goal of the European fusion programme to refresh operational experience of a nuclear tokamak to prepare staff for ITER operation. The key physics results of the JET T and DTE2 experiments, carried out within the EUROfusion JET1 work package, are reported in this paper. Progress in the technological exploitation of JET D–T operations, development and validation of nuclear codes, neutronic tools and techniques for ITER operations carried out by EUROfusion (started within the Horizon 2020 Framework Programme and continuing under the Horizon Europe FP) are reported in (Litaudon et al Nucl. Fusion accepted), while JET experience on T and D–T operations is presented in (King et al Nucl. Fusion submitted).

Research on arc evolution law of arc extin‐ction device under high‐speed large current

AbstractThe lifespan of the guide rail is a bottleneck restricting the operational life of electromagnetic railguns. A well‐designed arc extinguishing device can reduce the arcing erosion caused by residual currents within the guide rail. The CuW alloy is widely used in the high‐pressure arc extinction field due to its excellent electrical and thermal conductivity, high strength, and hardness. Based on the theory of equilibrium state arc plasma, a finite element model of the air arc‐CuW electrode coupling in the arc extinction device was established to study millisecond‐level arc initiation, evolution, extinguishing characteristics, and distribution patterns under extreme and harsh operational conditions with a current input of 110 kA. The highest temperature in the arc column region was found to exceed 50,000 K. The study elucidated the influence of arc extinction device parameters on arc evolution, breakdown time, and breakdown voltage. Consequently, it established that the R70 spherical electrode exhibits optimal arc extinguishing characteristics. The aim of this research is to provide theoretical support for optimizing the arc suppression device. Additionally, experiments on high‐speed and high‐current arc extinction device discharges were conducted to validate the finite element analysis results regarding arc diffusion patterns and electrode erosion.

Sampling of plasma plume from atmosphere into vacuum for reliable Langmuir probe diagnostics

Langmuir probes cannot be used to diagnose cold atmospheric plasma jet, because their presence in the high electric field after-glow region modifies the plasma parameters that they are intended to measure. Here, we propose a system to sample the plasma plume from ambient conditions into a low-pressure region, where probe analysis can be accomplished. The effect of such a sampling process on the number density and velocity of the gas has been studied through simulations and using analytical equations. Simulation results regarding the effect of chamber and orifice dimensions on these parameters, have been presented. Based on this study an experimental chamber was fabricated and Langmuir probe analysis of the sampled plasma was done. Continuum flowing plasma theory was applied and the plasma density and electron temperature were estimated to be 1.8 × 1020m−3 and 4.7 eV respectively for the operating condition of 3 W plasma power at 12 kHz.

To plasma electrons motion theory in high-frequency fields

The article is dedicated to the kinetic theory of plasma, where the problem of interaction of high-frequency electric fields with weakly non-uniform plasma is investigated using kinetic equations with binary collision integrals for plasma particles. A new methodology for determining the expression of the averaged highfrequency pressure force is proposed based on solving the kinetic equation and using the method of successive approximations (separation of slow motions and fast oscillations) under the limiting conditions. An expression for the averaged quasi-potential force is derived based on the kinetic equation for the electron distribution function in weakly inhomogeneous magnetoactive plasma, taking into account electrons collisions with fixed ions and the presence of a longitudinally inhomogeneous high-frequency electric field using wellknown methods of theoretical and mathematical physics, such as successive approximations, averaging over the effective field oscillation period, and integration over trajectories. The amplitude of the field is a slowly varying function in both time and space coordinates. The obtained expression allows us to estimate the influence of collisions of plasma particles on the Miller force, and under limiting conditions it coincides with the known expressions for the high-frequency pressure force derived from the equation of plasma electrons motion in high-frequency fields. In all calculations, the contribution of the magnetic component of the electromagnetic field is neglected, which is quite justified for the longitudinal electric field.

Derivation of dirac exchange interaction potential from quantum plasma kinetic theory

The Dirac exchange interaction is derived from recent quantum kinetic theory for collisionless plasmas. For this purpose, the kinetic equation is written in the semiclassical and long wavelength approximations. The validity of the model for real systems is worked out, in terms of temperature and density parameters. Within the region of applicability, the correlation potential energy is shown to be always smaller than the exchange contribution. From the moments of the quantum kinetic equations, macroscopic, hydrodynamic equations are found, for an electron-ion plasma. The Dirac exchange term is explicitly derived, in the case of a completely degenerate electron gas. These results show, within quantum kinetic theory for charged particle systems, a new view of the Dirac exchange interaction frequently used in density functional theory parametrization. Finally, a simpler form of the quantum plasma exchange kinetic theory is also found.

Stochastic Equations of Hydrodynamic Theory of Plasma

Stochastic Equations of Hydrodynamic Theory of Plasma

Equivalence of measures and stochastic equations of hydrodynamic theory of plasma

Equivalence of measures and stochastic equations of hydrodynamic theory of plasma

Kinetic theory of weakly ionized plasma and electrolyte mixtures including Onsager matrix and frequency dispersion effects

AbstractWe summarize the method of hydrodynamic approximation for weakly ionized plasmas developed with Klimontovich in 1962 and give a generalization to many—component systems using Onsagers matrix theory and including dispersion effects. We develop the conductivity theory of complex plasma and electrolyte mixtures based on the model of charged hard spheres with given non‐additive contact distances, including frequency‐dependent electric fields. These generalizations are made with the aim to allow applications to complex natural systems as atmospheric plasmas and seawater. Finally, we give as an example a numerical calculation of the single ion conductivities of a six‐component seawater model.

Novel method for identifying the stages of discharge underwater based on impedance change characteristic

It is difficult to determine the discharge stages in a fixed time of repetitive discharge underwater due to the arc formation process being susceptible to external environmental influences. This paper proposes a novel underwater discharge stage identification method based on the Strong Tracking Filter (STF) and impedance change characteristics. The time-varying equivalent circuit model of the discharge underwater is established based on the plasma theory analysis of the impedance change characteristics and mechanism of the discharge process. The STF is used to reduce the randomness of the impedance of repeated discharges underwater, and then the universal identification resistance data is obtained. Based on the resistance variation characteristics of the discriminating resistance of the pre-breakdown, main, and oscillatory discharge stages, the threshold values for determining the discharge stage are obtained. These include the threshold values for the resistance variation rate (K) and the moment (t). Experimental and error analysis results demonstrate the efficacy of this innovative method in discharge stage determination, with a maximum mean square deviation of S cr less than 1.761.

Non-Thermal Solar Wind Electron Velocity Distribution Function.

The quiet-time solar wind electrons feature non-thermal characteristics when viewed from the perspective of their velocity distribution functions. They typically have an appearance of being composed of a denser thermal "core" population plus a tenuous energetic "halo" population. At first, such a feature was empirically fitted with the kappa velocity space distribution function, but ever since the ground-breaking work by Tsallis, the space physics community has embraced the potential implication of the kappa distribution as reflecting the non-extensive nature of the space plasma. From the viewpoint of microscopic plasma theory, the formation of the non-thermal electron velocity distribution function can be interpreted in terms of the plasma being in a state of turbulent quasi-equilibrium. Such a finding brings forth the possible existence of a profound inter-relationship between the non-extensive statistical state and the turbulent quasi-equilibrium state. The present paper further develops the idea of solar wind electrons being in the turbulent equilibrium, but, unlike the previous model, which involves the electrostatic turbulence near the plasma oscillation frequency (i.e., Langmuir turbulence), the present paper considers the impact of transverse electromagnetic turbulence, particularly, the turbulence in the whistler-mode frequency range. It is found that the coupling of spontaneously emitted thermal fluctuations and the background turbulence leads to the formation of a non-thermal electron velocity distribution function of the type observed in the solar wind during quiet times. This demonstrates that the whistler-range turbulence represents an alternative mechanism for producing the kappa-like non-thermal distribution, especially close to the Sun and in the near-Earth space environment.

Nonlinear structure and growth rate of solitary waves for extended Zakharov-Kuznetsov equation in plasma having (r, q) distribution electrons

The Reductive Perturbation Technique (RPT) is used to investigate ion acoustic waves (IAWs) in magnetized plasmas made up of electrons obeying the generalized form of ( r,q ) distribution. The analysis makes use of the Extended Zakharov-Kuznetsov (EZK) equation and the hydrodynamic theory of plasmas. The study investigates the effects of electron flatness ( r ) at low energy and superthermal ( q ) at high energy on the characteristics of IAWs, and the solutions to the EZK equation are plotted for different values of the plasma characteristics, such as the total ion cyclotron frequency, the ion to electron temperature ratio, and the ion-specific heat. The research goes into great detail to estimate the instability threshold and growth rate of these waves by applying a small-k perturbation technique. Overall, this investigation contributes to the better understanding of ion acoustic structures in space plasmas.

An iterative method for solving one class of non-linear integral equations with Nemytskii operator on the positive semi-axis

A class of non-linear integral equations with monotone Nemytskii operator on the positive semi-axis is considered. This class of integral equations appears in many areas of modern natural science. In particular, such equations, with various restrictions on non-linearity and the kernel, arise in the dynamic theory of $p$-adic strings for the scalar field of tachyons, in the kinetic theory of gases and plasma within the framework of the usual and modified non-linear Bhatnagar-Gross-Crook models for the Boltzmann kinetic equation. Equations of similar nature appear also in the non-linear radiative transfer theory in inhomogeneous media and in the mathematical theory of the spread of epidemic diseases within the framework of the modified Diekmann-Kaper model. A constructive theorem for the existence of a bounded positive and continuous solution is proved. As a result, we get a uniform estimate of the difference between the previous and subsequent iterations, the corresponding successive approximations converge uniformly to a bounded continuous solution to the equation. The asymptotic behaviour of the constructed solution at infinity is studied. In particular, it is proved that the limit of this solution at infinity exists and is positive, and is uniquely determined from a certain characteristic equation. It is also proved that the difference between the limit and the solution is a summable function on the positive semi-axis. Using some geometric estimates for convex and concave functions, and employing the theorem on integral asymptotics obtained here, we prove the uniqueness of the solution in a certain subclass of non-negative non-trivial continuous and bounded functions. The results obtained are also applied to the study of a special class of non-linear Urysohn type integral equations on the positive semi-axis. In particular, the existence of a positive bounded solution to this class of equations is verified, and some qualitative properties of the constructed solution are studied. We also give specific applied examples of the corresponding kernels and non-linearities to illustrate the importance of the results obtained.

Recent development and prospect on heavy-ion collisions in colliders

Heavy ion collisions play a key role in advancing our understanding of the universe. These are collisions in which two atomic nuclei collide at high energy, releasing large amounts of energy and creating new elements. One of the fundamental theories of heavy-ion collisions is the quark-gluon plasma (QGP) theory. It suggests that in collisions at sufficiently high energies, the quarks and gluons of the colliding nuclei are no longer confined to individual particles, but form a new state of matter. In some heavy-ion collisions, the QGP may exhibit properties similar to those found in the early universe. In addition, studying heavy ion collisions could help answer some fundamental questions, such as the origin of mass and the nature of dark matter. This article focuses on the experimental setups related to Heavy-ion collisions and the results obtained by the researchers so far. The focus is on the more cutting-edge research built on Relativistic Heavy-ion Colliders. This article provides a partial summary of these results and an outlook on their future development.

Backstreaming ions at a high Mach number interplanetary shock

Context.Solar Orbiter, a mission developed by the European Space Agency, explores in situ plasma across the inner heliosphere while providing remote-sensing observations of the Sun. The mission aims to study the solar wind, but also transient structures such as interplanetary coronal mass ejections and stream interaction regions. These structures often contain a leading shock wave that can differ from other plasma shock waves, such as those around planets. Importantly, the Mach number of these interplanetary shocks is typically low (1–3) compared to planetary bow shocks and most astrophysical shocks. However, our shock survey revealed that on 30 October 2021, Solar Orbiter measured a shock with an Alfvén Mach number above 6, which can be considered high in this context.Aims.Our study examines particle observations for the 30 October 2021 shock. The particles provide clear evidence of ion reflection up to several minutes upstream of the shock. Additionally, the magnetic and electric field observations contain complex electromagnetic structures near the shock, and we aim to investigate how they are connected to ion dynamics. The main goal of this study is to advance our understanding of the complex coupling between particles and the shock structure in high Mach number regimes of interplanetary shocks.Methods.We used observations of magnetic and electric fields, probe-spacecraft potential, and thermal and energetic particles to characterize the structure of the shock front and particle dynamics. Furthermore, ion velocity distribution functions were used to study reflected ions and their coupling to the shock. To determine shock parameters and study waves, we used several methods, including cold plasma theory, singular-value decomposition, minimum variance analysis, and shock Rankine-Hugoniot relations. To support the analysis and interpretation of the experimental data, test-particle analysis, and hybrid particle in-cell simulations were used.Results.The ion velocity distribution functions show clear evidence of particle reflection in the form of backstreaming ions several minutes upstream. The shock structure has complex features at the ramp and whistler precursors. The backstreaming ions may be modulated by the complex shock structure, and the whistler waves are likely driven by gyrating ions in the foot. Supra-thermal ions up to 20 keV were observed, but shock-accelerated particles with energies above this were not.

Resonance cones in cold plasma: Origin, singularities, and power flow

In magnetized tenuous plasma, typical at the plasma edge of fusion devices, a nearly electrostatic wave mode with relatively enhanced electric field can propagate along a specific angle with the magnetic field. For this characteristic, it is known as a “resonance cone.” For instance, these waves can be excited by radio frequency antennas in the ion-cyclotron and lower-hybrid range of frequencies. We consider the resonance cones emitted by idealized spatially extended sources. In 2D, we use a novel geometric construction which generalizes the d'Alembert solution to curved boundaries/moving sources, and show, for the first time, that singular electric fields arise under these conditions, thereby bringing the resonance cones in line with the other resonances of the cold plasma theory. Still in 2D, we give an expression for the amount of power radiated by resonance cones in terms of surface quantities on the source, which is finite despite the singular electric field. We generalize the conclusions regarding the presence and location of singular electric fields to the 3D electromagnetic case.

On the Role of the Displacement Current and the Cattaneo’s Law on Boundary Layers of Plasma

In the present paper, we aim to mathematically analyse the role of the displacement current and the Cattaneo’s law on the boundary-layer theory of plasma, when the corresponding characteristic speed is relativistic. We restrict our analysis to two-dimensional flows and we study the asymptotic limit of the Navier–Stokes–Maxwell equations with Cattaneo’s law near a bounding flat line, when the Hartmann, Reynolds and magnetic Reynolds numbers proportionally diverge to infty . The goal of this paper is twofold. We first show that the extended version of the Navier–Stokes–Maxwell equations leads to a new family of boundary layers, which are hyperbolic both on the momentum equation and the Ampere’s law. Secondly, we address the well-posedness of the derived equations and show the existence of global-in-time analytic solutions for small initial data. Our modelling highlights which conditions on the dimensionless parameters allow to interpret the proposed system as boundary layers with thickness typical of Prandtl or Hartmann. Furthermore, our development shows that the conditions related to Hartmann might be more physically acceptable. Finally, our analysis suggests that the Cattaneo’s law and the displacement current might indeed stabilize the derived system in terms of existence of global-in-time analytic solutions.

Kinetic theory for spin-polarized relativistic plasmas

The investigation of spin and polarization effects in ultra-high intensity laser–plasma and laser–beam interactions has become an emergent topic in high-field science recently. In this paper, we derive a relativistic kinetic description of spin-polarized plasmas, where quantum-electrodynamics effects are taken into account via Boltzmann-type collision operators under the local constant field approximation. The emergence of anomalous precession is derived from one-loop self-energy contributions in a strong background field. We are interested, in particular, in the interplay between radiation reaction effects and the spin polarization of the radiating particles. For this, we derive equations for spin-polarized quantum radiation reaction from moments of the spin-polarized kinetic equations. By comparing with the classical theory, we identify and discuss the spin-dependent radiation reaction terms and radiative contributions to spin dynamics.

Thinking about the Wave-Particle Duality with Plasma Theory and Explaining it based on the Oscillator and Qseudo-Oscillator Models

It is the first time for us to observe the quantum world with the plasma theory. Mean-while, many new concepts, such as the discrete quantum, precise quantum and the non-linear quantum, etc., and new horizons, i.e., cutting off the connection of interaction, or equivalently introducing destructive disturbance, are supposed into the quantum mechanics at the first. The normal and pseudo-oscillator models are introduced and used to explain the wave and particle duality of quantum field. By adding such new content, it is hoped that people can understand the physics behind the quantum mechanics, rather than recognizing it with the pure mathematic knowledge. It is suggested that the quantum world is better to consider the influence of outside environment, and then the quantum mechanics is turned into the quantum dynamics. The establishment of quantum dynamics is helpful for people better understand and hence utilize the quantum mechanics, such as the quantum optics, quantum communication and quantum computer, etc.