等离子体中德拜长度和德拜屏蔽

The Boltzmann–Gibbs statistics have been shown theoretically and experimentally to be inadequate for describing plasma thermodynamics, whereas nonextensive statistical mechanics offers a more suitable framework. The Debye length, a fundamental criterion for characterizing plasma behavior, remains poorly understood in nonextensive plasmas—particularly for systems with ion charge states beyond unity. This work presents the most general expression for the nonextensive Debye length in electron–ion plasmas with arbitrary ion charge states. By invoking nonextensive statistical mechanics (parameterized by electron and ion nonextensive exponents), we develop a self-consistent Debye shielding theory. Key findings include the nonextensive Debye length depends explicitly on electron nonextensive parameter, ion nonextensive parameter, and ion charge state; it recovers the classical Boltzmann–Gibbs limit as nonextensive parameters approach unity; and it decreases monotonically with increasing nonextensive parameters or ion charge state, highlighting the impact of non-Boltzmannian distributions and high-Z ions on plasma screening. These results establish a foundation for nonextensive plasma diagnostic theories, enabling deeper insights into sheath structures (e.g., ion sheath, electron sheath, and dust sheath thicknesses). The theory can be extended to incorporate magnetic fields, anisotropy, radio-frequency effects, relativistic corrections, and multi-component (double/triple/N-component) plasmas. Moreover, nonextensive electric probe methods rooted in this theory offer critical tools for studying plasma waves, instabilities, turbulence, and anomalous transport, while facilitating quantitative tests of nonextensive geodesic acoustic mode and disruption physics.

A simple similarity has been proposed for kinetic (e.g., particle-in-cell) simulations of plasma transport that can effectively address the long-standing challenge of reconciling the tiny Debye length with the vast system size. This applies to both transport in unmagnetized plasma and parallel transport in magnetized plasmas, where the characteristics length scales are given by the Debye length, collisional mean free paths, and the system or gradient lengths. The controlled scaled variables are the configuration space, x/L, and an artificial Coulomb Logarithm, L ln Λ, for collisions, while the scaled time, t/L, and electric field, LE, are automatic outcomes. The similarity properties are examined, demonstrating that the macroscopic transport physics is preserved through a similarity transformation while keeping the microscopic physics at its original scale of Debye length. To showcase the utility of this approach, two examples of 1D plasma transport problems were simulated using the VPIC code: the plasma thermal quench in tokamaks [Li et al., Nuclear Fusion 63, 066030 (2023)] and the plasma sheath in the high-recycling regime [Li et al., Physics of Plasmas 30, 063505 (2023)].

No abstract available

Abstract The dipole polarizabilities, dipole and quadruple oscillator strengths and relativistic energy corrections are calculated for plasma embedded C VI ion which is of relevance in astrophysics and plasma physics. Numerical simulation of Numerov method is used to find the energy eigenvalues and eigenfunctions by solving the time-independent Schrodinger equation. The dependence of dipole and quadruple polarizabilities, oscillator strengths and relativistic energy corrections on Debye length is shown.

No abstract available

The differential and transport cross sections (TCSs) for binary collision are fundamental parameters to depict the traversing of charged particles in matter, which are often obtained via classical mechanics. The Bohr criterion was proposed to judge when the treatment via classical mechanics is reliable. However, there are very few quantitative comparisons of the cross sections between classical and quantum methods under the Debye potential. In this work, such comparisons—using the partial wave method and the Wentzel-Kramers-Brillouin (WKB) approximation—are made for wide ranges of collision velocity, ion charge states and Debye length. For the differential cross section, a quantitative range of velocity is obtained for the Bohr criterion that is invalid for ion–ion collisions, and the criterion is found to be almost invalid for electron–ion collisions. For the TCS, the quantitative range of velocities is given for the criterion and found to be valid for both ion–ion and electron–ion collisions. Such ranges are related to the de Broglie wavelength of the collision system and Debye length, and they are also relevant to the complex classical trajectories due to the attractive Debye potential in electron–ion collisions. The reason for the failure of classical mechanics at low and high velocities is explored by reinterpreting the Bohr criterion.

No abstract available

Decades of analytic and computational work have demonstrated that a charge immersed in a hot plasma is screened. For both Abelian and non-Abelian interactions, the characteristic screening length $1/m_D$ is set by the so-called Debye mass $m_D \sim g_s T$, proportional to the plasma temperature $T$ and the dimensionless gauge coupling $g_s$. One of the most interesting naturally occurring examples is the quark-gluon plasma (QGP) that filled the early universe prior to the QCD confinement phase transition at $t_{\rm QCD} \sim 10^{-5}\,{\rm s}$. During this early epoch, regimes of strong spacetime curvature are of significant cosmological interest, such as near primordial black holes (PBHs). However, the typical description of Debye screening only applies within Minkowski spacetime, and is therefore insufficient to describe the dynamics of charged plasmas near PBHs or other primordial features. We construct an effective field theory for soft modes of the gauge field $A_\mu^a$ to give a full description of Debye screening in non-Abelian plasmas within arbitrary curved spacetimes, recovering a temperature-dependent Debye mass that exhibits gravitational redshift. We then apply our results to some scenarios of cosmological interest: an expanding FLRW universe and the vicinity of a PBH immersed in a hot QGP.

   In this research, the effect of laser beam energy on the properties and behavior of plasma produced from aluminum and nickel alloy was studied using the Optical Stimulated Emission Spectroscopy method. The properties of the plasma were characterized by exposing the target material (the alloy) to high-energy laser pulses ranging from 500 to 900 mJ using a pulsed Nd:YAG laser with a pulse rate of up to 50 Hz. This ensures a balanced energy distribution and allows monitoring of the increasing effects in the plasma without strong thermal effects. This method allows for a detailed study of the physical properties of the plasma, including the spectral radiation intensity and associated emission peak as well as the study of various plasma properties such as temperature and electron density and other plasma parameters, including the plasma frequency, Debye length, and Debye number. The results obtained show that both temperature and density increase with increasing laser power, with both effects peaking at a laser power of 900 mJ. Calculations of the plasma frequency and Debye number also show a concomitant increase in these two effects with increasing laser power. This work demonstrates how laser power can increase plasma stability and significantly improve physical processes within plasma. It also demonstrates how diagnostic techniques can be useful in plasma analysis and have numerous medical, industrial, and technological applications.

Optical emission spectroscopy (OES) is used to analyze the main properties of aloe vera plasma, where the plasma is generated using a plasma jet. Several parameters of the plasma are measured, including electron temperature (Te), electron density (ne), plasma frequency (fp), Debye length (λD), and Debye number (ND). The study is based on the use of different laser energies ranging from 100 to 400 mJ. To evaluate the electron temperature, the Boltzmann scheme was applied, which is based on the analysis of the spectral intensity of optical emissions from the plasma. The electron density was calculated using Stark line broadening, which reflects the effect of electric fields generated by electrons in the plasma on the width of the spectral lines. In this experiment, the target (aloe vera material) was exposed to the laser from a distance of 8 cm, while the emitted radiation was measured using an optical fiber at a distance of 0.5 cm from the target. All measurements were performed in air, where the electron temperature was found to range between 0.793 and 1.124 eV. The results showed that both the electron temperature and the electron density increased with increasing laser power. This increase is in line with expectations, as higher laser power leads to greater detuning of matter and an increase in the number of electrons generated in the plasma, which increases the plasma density and temperature.

The electrostatic charging environment inside lunar lava tubes was investigated in laboratory experiments using a glass tube exposed to a simulated solar wind flow. A conducting surface was attached at the entrance of the tube and biased to various negative potentials to study the electron shielding effect on the charging conditions inside the tube. The electrical potential at the bottom of the glass tube was measured using a planar probe. It is shown that the bottom surface potential is positive and increases with the increasing ion beam energy, as well as with the increasing depth inside the tube, as a result of electron Debye shielding at the entrance and along the length of the tube due to the electron thermal motion. It is found that the bottom tube potential does not approach the ion kinetic energy even when the solar wind electrons are nearly fully shielded from entering the tube. We show that ion-generated secondary electrons from the sidewall of the tube partially neutralize the buildup of positive charges at the bottom of the tube. Our results provide insights into the plasma charging environment inside lunar lava tubes that may be used as natural habitats for future human exploration on the surface of the Moon.

In this study, laser-induced breakdown spectroscopy (LIBS) was used to analyze the plasma generated from a Zn:Cu alloy (x = 0.9) using a Nd:YAG laser at 1064 nm. Plasma was generated at different laser pulse energies ranging from 400 to 800 mJ. The electron temperature (Te) was determined using the Boltzmann plot method, while the electron number density (ne) was calculated using Stark broadening. Other plasma parameters were also evaluated, including plasma frequency (fp), Debye length (λD), and Debye number (Nd). The results showed that Te increased from 0.846 eV at 400 mJ to 0.906 eV at 800 mJ, and ne increased from 1.000 × 10¹⁸ cm⁻³ to 1.121 × 10¹⁸ cm⁻³. Plasma frequency increased from 898.000 × 1010 Hz to 950,868 × 1010 Hz, while the Debye length slightly decreased from 0.683 × 10⁻5 cm to 0.668 × 10⁻5 cm. The Debye number showed modest variation around 1300, reflecting relatively stable collective behavior across the energy range. These findings indicate that higher laser energy leads to hotter and denser plasma, enhancing the emission intensity and plasma characteristics. The study contributes quantitative insights into Zn–Cu plasma behavior under varying laser energies, providing potential applications in material diagnostics using LIBS.

A recently developed three-dimensional version of the quasistatic code LCODE has a novel feature that enables high-accuracy simulations of the long-term evolution of waves in plasma wakefield accelerators. Equations of plasma particle motion are modified to suppress clustering and numerical heating of macroparticles, which otherwise occur because the Debye length is not resolved by the numerical grid. The previously observed effects of premature wake chaotization and wavebreaking disappear with the modified equations.

This study investigates the plasma parameters of a cadmium oxide (CdO) target using laser-induced breakdown spectroscopy (LIBS). The plasma spectra of CdO were observed after preparation using a pulsed laser with energies of (300, 500 and 700) mJ. The experiment used a high-power laser to ablate the Cd target, generating a plasma plume that emitted characteristic spectral lines. We extracted valuable information about the plasma parameters by analysing the emitted light, including electron temperature, electron density and ionisation degrees. The LIBS setup was carefully calibrated and optimised to ensure accurate and reliable measurements. The evaluation of electron density was achieved by employing Stark broadening analysis, plasma density and plasma frequency. Additionally, it is worth noting that the Debye length decreases as energy increases. The electron temperature values range from 0.770 eV–0.788 eV. While ‎the electron density ranged from (4.167–4.688) × 1017 cm–3. The remaining plasma properties were determined by the utilisation of mathematical formulae and the Boltzmann plot approach.‎ This study provides the first systematic correlation between laser energy 300 mJ–700 mJ and plasma parameters, the temperature and density of electrons, and other fundamental plasma properties in CdO targets, demonstrating a linear increase in electron density with energy. These findings optimise LIBS for Cd detection in environmental monitoring or thin-film diagnostics, utilising emission spectroscopy-based characterisation techniques. This is the first study to quantify Cd plasma parameters across a laser energy range 300 mJ–700 mJ using combined Stark broadening and Boltzmann plot methods.

A spherical-implosion platform diagnosed with the "beamlets" scattered-light detector provides high sensitivity to the impact of plasma screening on inverse bremsstrahlung absorption. Contrary to the more restrictive screening length suggested previously [D. Turnbull et al., Phys. Rev. Lett. 130, 145103 (2023)0031-900710.1103/PhysRevLett.130.145103; D. Turnbull et al., Phys. Plasmas 31, 063304 (2024)1070-664X10.1063/5.0203446], the beamlets data indicate that the electron-only Debye length is the relevant screening length for high-density inverse bremsstrahlung absorption. Using the updated absorption model, we simulate the OMEGA direct-drive inertial confinement fusion implosion database and show that bang times are well reproduced without any ad hoc multipliers.

This study used two custom dielectric barrier discharge plasma (DBDP) systems designs to produce non-thermal plasma and investigate its properties. The setup included two identical parallel copper electrodes with specific design dimensions (16cm length, 3mm diameter) and two similar glass tubes (13cm length, 5.5mm outer diameter, and 5mm inner diameter) as a dielectric barrier. In the first design, only one of the copper electrodes was covered with a glass tube, while in the second, each one was covered with a glass tube. The optical emission spectroscopy (OES) technique was employed to analyze the produced plasma spectrum and then calculate the plasma parameters (electron temperature, electron density, frequency of electron, Debye length, and Debye number) at different conditions of Ac applied voltage (18-22 kV) and discharge gap distance is fixed (4 mm) for both designs. For all operating conditions, electron temperature was 4.177- 4.273 eV, while electron density was 1.582×1018-1.942×1018 cm-3. The results reveal a novel and significant effect of electrode configurations on the properties of the produced plasma due to the distribution of the electric field in the discharge region, sparking new avenues for research in this field.

In this paper, the influencing mechanisms of the initial operating parameters including the initial plasma density, electron temperature, plasma width and the externally applied voltage on the ion extraction characteristics are studied based on a simplified one-dimensional analytical model for a double-wall bounded decaying plasma system. Firstly, a criterion of the dimensionless plasma width (L min) which is normalized with the Debye length for evaluating the state of the sheath expansion is proposed for the first time. Secondly, if the plasma width is larger than the value of L min, a complete sheath expansion process including both the supersonic and subsonic sheath expansion phases occurs during plasma decaying. Consequently, on the one hand, the total ion extraction time and the fraction of the extracted ions at the end of Stage II, i.e., the sheath expansion and ion rarefaction wave propagation stage during the whole ion extraction process, can be determined by the initial operating parameters; and on the other hand, it is estimated that about 70% of ions can be extracted at the end of the second stage from the bulk plasma with a consumption of about 62.5% of the total ion extraction time within the parameter ranges studied in this paper. This research is helpful for a deep understanding to the physical mechanisms of the charged-particle transport, as well as for guiding parameter optimizations with better ion extraction performances in practice.

The study used the optical emission spectroscopy method to present the effect of changing doping ratios and laser energy on plasma parameters. Plasma spectra were acquired across energy levels by zinc oxide combined with nickel oxide (ZnOX: NiO1-X) at x = 0.3, 0.5, and 0.7. The analysis of these airborne mixtures was carried out through the application of spectroscopy. The electron temperature results indicated that the range for x=0.3 was 0.446-0.491 eV, for x=0.5 was 0.470-0.486 eV, and for x=0.7 it was 0.474-0.489 eV. Differences in electron temperatures between compositions can lead to new technological applications and comprehension of physical phenomena. It was found that when the proportion of doping was increased, the intensities of the spectral lines, electron temperature (Te), Debye number (ND), and Debye length (λD) increased. In contrast, electron density (ne) and plasma frequency (fp) decreased with the increase of the laser energy; doped material's emission lines occurred more frequently in the mixed material. With these results, we obtain the best conditions for solar cell applications for zinc oxide elements combined with nickel oxide. 

In this work, the optical emission spectroscopy technique was employed to diagnose the plasma and solar wind parameters of Comet C/2020 F3 from July 21 to July 31, 2020. Datasets of comet C2020 F3 (NEOWISE) were gathered using the Cassegrain telescope camera CTK-II providing information within the visible spectrum, particularly emission lines within the wavelength range of 560 to 636 nanometers. The investigation utilized a two-line ratio method to scrutinize the spectrum of the comet over a five-day period from July 21 to July 31, 2020. Furthermore, various plasma parameters such as electron temperature, electron density, Debye length, and plasma frequency were determined. The study also delved into solar wind parameters that align with the comet plasma parameters, including solar wind temperature (in Kelvin), proton density (measured in 1/cm³), solar wind speed (in kilometers per second), and magnetic field strength (denoted as Bx, By, and Bz) in nT. The findings obtained from the analysis of the spectrum were employed to identify the chemical composition of the comet plasma. The results of this study are evident in a correlation between the intensity of these emissions and the distance of the comet from the Sun. It was observed that the heightened values of solar wind speed and temperature, particularly between the 25th and 28th of July, influenced the temperature and electron density of the plasma. During the 30th and 31st days of July, there was a decrease in both electron temperature and electron density as the comet moved farther away from the Sun.

During reentry, the high temperatures experienced by near-space hypersonic vehicles result in surface ablation, generating ablative particles. These particles become part of a plasma, commonly referred to as a “dusty plasma sheath” in radar remote sensing. The dusty plasma model, integral in radar studies, involves extensive charge and dynamic interactions among dust particles. Previous derivations assumed that the dust particle radius significantly surpassed the Debye radius, leading to the neglect of dust radius effects. This study, however, explores scenarios where the dust particle radius is not markedly smaller than the Debye radius, thereby deducing the charging process of dusty plasma. The derived equations encompass the Debye radius, charging process, surface potential, and charging frequency, particularly considering larger dust particle radii. Comparative analysis of the dusty plasma model, both before and after modification, reveals improvements when dust particles approach or exceed the Debye length. In essence, our study provides essential equations for understanding dusty plasma under realistic conditions, offering potential advancements in predicting electromagnetic properties and behaviors, especially in scenarios where dust particles closely align with or surpass the Debye radius.

This study explores the generation of electrostatic (ES) electron Kelvin–Helmholtz instability (EKHI) in collisionless plasma with a step-function electron velocity shear akin to that developed in the electron diffusion region in magnetic reconnection. In incompressible plasma, ES EKHI does not arise in any velocity shear profile due to the decoupling of the electric potential from the electron momentum equation. Instead, a fluid-like Kelvin–Helmholtz instability (KHI) can arise. However, in compressible plasma, the compressibility couples the electric potential with the electron dynamics, leading to the emergence of a new ES mode EKHI on Debye length λDe, accompanied by the co-generation of an electron acoustic-like wave. The minimum threshold of ES EKHI is ΔU>2cse, i.e., the electron velocity shear is larger than twice the electron acoustic speed cse. The corresponding growth rate is Im(ω)=((ΔU/cse)2−4)1/2ωpe, where ωpe is the electron plasma frequency.

The microwave induced plasma jet (MIPJ) system was built using local materials and based on a tapered waveguide. The parameters of this plasma were determined like electron temperature Te, electron density ne. the other parameters such as plasma frequency( fp), the Debye length( λD), and the number of particles in the Debye sphere( Nd) It has also been studied. The study were done at different Ar flow rate ranging from (2-10) l/m and a discharge tube diameter ranging from (2-10) mm. all of these parameters were determined depending on the MIPJ spectrum. it turned out that there is a high possibility of controlling the parameters of MIPJ through manipulating these parameters.

We show that galaxy-cluster virial (i.e., structure-formation accretion) shock observations, in particular of synchrotron emission, imply ≳ 1% magnetization of a macroscopic, ≳ 1016 Debye-length layer downstream, challenging high Alfvén-Mach collisionless-shock modelling. Unlike similar shocks in supernova remnants or relativistic shocks in γ-ray burst afterglows, where macroscopic magnetized layers were attributed to preexisting or non-resonant cosmic-ray streaming-seeded substructure, virial shock upstreams are both weakly magnetized and pristine. Hence, some mechanism must generate macroscopic sub-structure out of the accreted primordial plasma, and may similarly dominate additional high-Mach shock systems.

We present a numerical study on the electron and ion density perturbation in low-temperature plasmas driven by the frequency detuning of two intense laser beams. Our study is performed in the hydrodynamic regime, which becomes applicable when the plasma grating period induced by the beating of the laser beams is greater than the Debye length and collective processes such as plasma oscillations can be excited. Our findings show a resonance in electron density perturbation as the frequency detuning approaches a value consistent with the Bohm–Gross dispersion relation in low- and high-pressure plasmas. We discuss the potential of this resonance as a diagnostic tool for precisely measuring electron temperature and density in low-temperature plasmas through coherent scattering.

Whereas the conventional wisdom suggests that the force between non-magnetized homogeneous, stationary, isotropic plasma, and the dust grain is only possible for the case of relative plasma–grain velocity, it is shown that stationary non-spherical asymmetric dust grain immersed in stationary, non-magnetized, isotropic plasma can experience a force caused by the grain–plasma interactions. The component of the force due to scattering of plasma particles in the limit of infinite Debye length is considered analytically. Both the particle scattering and absorption force components are modeled numerically in the limits of infinite and finite Debye length using a newly developed 2D3V Aspherical Particle-in-Cell code. The code simulates interactions of dust grain of selected non-spherical asymmetric shape with plasmas using dust shape conforming coordinates. The simulations confirm the existence of the force on non-spherical asymmetric grain in stationary non-magnetized plasma and show that the plasma screening effects can lead to reversal of the force direction.

Abstract: In this work, we measure the plasma parameters by using an AC high-voltage power supply that generates a non-thermal plasma jet system at atmospheric pressure. A nickel (Ni) metal strip, with dimensions of 1.5 × 10 cm2, was connected to the anode electrode of the AC power supply. This nickel strip was immersed in a flask with a small amount of distilled water positioned below the plasma plume nozzle. Optical emission spectroscopy (OES) was used to diagnose the plasma system at different argon gas flow rates (1-5 L/min) and varying applied voltage values (11-15 kV). It is significant to know the processes accompanying plasma generation to measure their parameters which include the electron temperature (Te), electron number density (ne) of the plasma, Debye length (λD), and plasma frequency (fp). Our results showed an increase in the intensity of spectral lines with the increase in applied discharge voltage (11-15 kV). The maximum peak for ArI was observed at a wavelength of 811.531 nm, and the maximum peaks for nickel (Ni) were observed at wavelengths of 285.21 and 519.70 nm. Also, the results indicated a gradual increase in electron temperature (Te) and electron density (ne) values at the applied voltage of 0.403-0.468 eV. Likewise, the electron density (ne) was in the range of (11.486-13.851) × 1017 cm-3. Keywords: Atmospheric plasma jet, Nickel (Ni) plasma parameters, Electron temperature, Spectroscopic optical emission (OES).

We present a new model for current collected by a spherical Langmuir probe in magnetized plasmas. Data are obtained using state-of-the-art fully 3D kinetic particle-in-cell simulations. We perform a dimensional analysis and use it to determine the appropriate model function. The model is then empirically derived based on the simulation data for a range of probe potentials and magnetic field values with respect to the Debye length. The final model function is applicable to most space plasmas and can easily be generalized.

The basics of the stability theory have been developed for a plasma diode, in which flows of relativistic electrons and positrons come from opposite electrodes and move without collisions in a self-consistent electric field. The regime is studied when all particles reach opposite electrodes. As an example, the stability of steady states of such a diode is considered. An integrodifferential equation for the amplitude of the electric field perturbation is derived. For the case of a uniform stationary field, an analytical solution of this equation is found. Plasma dispersion and the effect of the relativistic factor γ0 on it are studied. It is shown that there is a threshold for the electron current density, above which the solutions become unstable, and an aperiodic instability develops in the plasma. The value of the inter-electrode distance corresponding to the threshold is equal to [γ0(γ0+1)]1/2πλD, where λD is the relativistic Debye–Hückel length. This coincides with the known result for the non-relativistic case at γ0→1.

A formulation for the parametric instability of electromagnetic (EM) waves in magnetized pair plasma is developed. The linear growth rate of induced Compton scattering is derived analytically for frequencies below the cyclotron frequency for the first time. We identify three modes of density fluctuation: ordinary, charged, and neutral modes. In the charged mode, the ponderomotive force separates charges (electrons and positrons) longitudinally, in contrast to the nonmagnetized case. We also recognize two effects that significantly reduce the scattering rate for waves polarized perpendicular to the magnetic field: (1) the gyroradius effect due to the magnetic suppression of particle orbits, and (2) Debye screening for wavelengths larger than the Debye length. Applying this to fast radio bursts (FRBs), we find that these effects facilitate the escape of X-mode waves from the magnetosphere and outflow of a magnetar and neutron star, enabling 100\% polarization as observed. Our formulation provides a foundation for consistently addressing the nonlinear interaction of EM waves with magnetized plasma in astrophysics and laser physics.

No abstract available

The plasma screening effect on Shannon entropy values is studied for atomic states of hydrogen under the more general exponential cosine screened Coulomb (MGECSC) potential, which can be used to model Debye and quantum plasmas. The wavefunctions used in the calculation of Shannon entropy are obtained by solving the Schrödinger equation employing the efficient Numerov technique. Shannon entropy is calculated for hydrogen atom quantum levels using various sets of screening parameters to account for the four different potential forms present in the MGECSC potential. The electron density distributions are considerably altered due to the plasma shielding influence on the embedded hydrogen atoms, and this effect is measured by the shift in Shannon entropy. A greater screening influence on entropy is observed in quantum plasma modeled by the MGECSC potential than that in Debye plasma due to the significant combined effects of screening parameters. Excellent convergence is obtained on comparing our results for plasma-free hydrogen atom with the currently available literature. This study is the first to examine the effects of shielding on Shannon entropy of hydrogen atoms in plasmas modeled by the MGECSC potential. These findings will be important for theoretical and experimental research in the disciplines of atomic physics and plasma diagnostics.

No abstract available

This paper proposes a novel plasma regulation method based on time-varying E × B fields to address communication blackout issues during hypersonic vehicle reentry. In conventional static E × B fields, the Debye shielding effect causes the current density j in plasma beyond the Debye radius to decay to zero (j = 0 A/m2), resulting in ineffective electron density reduction. To overcome this limitation, this paper introduces a time-varying electric field to enhance the current density in the plasma, thereby mitigating the Debye shielding effect. Through synchronized control of time-varying electric and magnetic fields (same frequency and phase), we maintain a consistent Lorentz force direction (f = J × B), effectively reinforcing electron repulsion. Experimental verification utilized low-pressure glow discharge (14 Pa) to generate uniform plasma (88% uniformity in the central region). A transverse 7 cm low-electron-density region was achieved with a maximum reduction of 70% at B = 0.05 T and U0 = 1000 V. This breakthrough not only validates the time-varying electric field’s capability to enhance conduction currents but also provides a new pathway for practical engineering applications of magnetic window techniques.

A laser pulse focused to relativistic intensity inside a magnetically confined fusion (MCF) plasma plows away all electrons in its path. The ensuing Coulomb explosion of the ions leaves behind a cavity of microscopic size, with gradients in the electric potential and plasma density orders of magnitude stronger than anything the plasma could generate spontaneously. When posing questions concerning the practical utility of such an exotic perturbation, the life time and structural evolution of the cavity are of interest. Our simulations in a simplified 1D + 2D setting and otherwise realistic parameters suggest that a sub-mm wide seed cavity (meant to resemble the laser wake channel) collapses or disintegrates within 10 ns. The dynamics are sensitive to the relative scales of the cavity, Debye shielding and gyration. We find evidence for the possibility that the collapsing seed cavity spawns solitary micro-cavities. It remains to be seen whether such structures form and survive long enough in a 3D setting to alter the local plasma conditions (e.g., as micro-cavity clusters) in ways that may be utilized for practical purposes such as plasma initiation, diagnostics or control.

Debye shielding in an electron-ion plasma with regularized kappa distribution is examined. An unmagnetized collisionless plasma sheath with regularized kappa distributed electrons is investigated and the modified Bohm criterion is derived. It is found that the variation of the electrostatic potential depends significantly on the superthermal index κ and cutoff parameter α. If κ < 3/2, a plasma sheath with a regularized kappa distribution exists. Our present work may be useful in understanding plasma processing and plasma sheaths in related plasma regions (i.e., Earth's inner magnetosphere).

No abstract available

We develop a model, called the "random-walk shielding-potential viscosity model" (RWSP-VM) that introduces the statistics of random-walk ions and the Debye shielding effect to describe the viscosities of warm dense metals. The viscosities of several metals with low to high atomic numbers (Be, Al, Fe, and U) are calculated using the analytical expression of RWSP-VM. Additionally, we simulate the viscosities of Fe and Be by employing the Langevin molecular dynamics (MD) and classical MD, while the MD data for Al and U are obtained from a previous work. The results of the RWSP-VM are in good agreement with the MD results, which validates the proposed model. Furthermore, we compare the RWSP-VM with the one-component plasma model and Yukawa viscosity model and show that the three models yield results in excellent agreement with each other in the regime where the RWSP-VM is applicable. These results indicate that the RWSP-VM is a universal, accurate, and highly efficient model for calculating the viscosity of metals in the warm dense state. The code of the proposed RWSP-VM is provided, and it is envisaged that it will have broad application prospects in numerous fields.

No abstract available

An interesting LIBS technique was used to investigate the optical emission spectral plasma of iron metal properties. To generate plasma from the surface Fe, Q-switched Nd-YAG laser with wavelength 532 nm and a focal length 10 cm was used with different energies (500-800) mJ. Then plasma parameters were calculated; electron density ne ranged between (0.92-1.4) × 1018 cm−3, the electron temperature Te was in the range of (2.19-2.59) eV. These calculations were done using Boltzmann’s plot and the Stark broadening respectively depending on the experimental spectrum, and followed up to estimate the others plasma parameters, Debye length (λD), frequency (fp ) and the Debye sphere (ND). Results indicate that plasma parameters are proportional to the energy of laser due to the increase in the intensity of spectral lines energy, and that plasma shielding of iron increases with laser energy in the range of (3.2-4.3).

We demonstrate and analyze the use of an ion chamber for measuring laser-induced ionization in cesium gas for the first time, which is of recent interest due to research in diode pumped alkali lasers (DPALs). In this report, the viability of an ion chamber diagnostic with high plasma density and ionization localized to a laser beam is investigated. A simulation of the laser-induced plasma in the ion chamber, based on the Thomson model with diffusion, is developed and will be shown to display similar qualitative behavior to measurements, and bound test results within model uncertainty. The analysis will show that complex processes occur: (1) space-charge limited ion drift, (2) Debye shielding preventing the electric field from penetrating a bulk plasma region, and (3) ambipolar diffusion across the bulk with possibly elevated electron temperature. However, these processes are well understood and do not limit the accuracy of an ion chamber diagnostic for laser-induced ionization rate measurement.

A potential scheme to enhance target ion flux extracted from decaying plasmas is proposed and verified by particle-in-cell simulations. By introducing light negative ions, the method significantly increases the collected target ion flux and shortens the total extraction time by a maximum factor of about 3 ∼ 4. Simulations show that the addition of light negative ions excites the ion–ion streaming instability, generating ion-acoustic waves that enhance the momentum transfer between ion species. This inter-species interaction accelerates the flow of target heavy ions towards the sheath, thereby enhancing the Bohm flux. The excitation of ion–ion streaming instability is also confirmed by comparing the calculated spectrum with the linear dispersion relation, supporting the mechanism of inter-species interaction. The proposed method provides a promising way to mitigate Debye shielding effect and control plasma decay, with potential applications involving decaying or afterglow plasmas, such as atomic vapor laser isotope separation.

No abstract available

If the electrons in a plasma are suddenly heated, the resulting change in Debye shielding causes the ion kinetic energy to quickly increase. For the first time, this correlation heating, which is much faster than collisional energy exchange, is rigorously derived for a moderately coupled, electron–ion plasma. The electron–ion mass ratio is taken to be the smallest parameter in the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, smaller even than the reciprocal of the plasma parameter. This ordering differs from conventional kinetic theory by making the electron collision rates faster than the ion plasma frequency, which allows stronger coupling and makes the ion heating a function only of the total energy supplied to the electrons. The calculation uses known formulae for correlations in a two-temperature plasma, for which a new, elementary derivation is presented. Suprathermal ions may be created more rapidly by this mechanism than by ion–electron Coulomb collisions. This means that the use of a femtosecond laser pulse could potentially help to achieve ignition in certain fast ignition approaches to inertial confinement fusion.

Experimental asymmetries in fusion implosions can lead to magnetic field generation in the hot plasma core. For typical parameters, previous studies found that the magnetization Hall parameter, given by the product of the electron gyro-frequency and Coulomb collision time, can exceed one. This will affect the hydrodynamics through inhibition and deflection of the electron heat flux. The magnetic field source is the collisionless Biermann term, which arises from the Debye shielding potential in electron pressure gradients. We show that there is an additional source term due to the Z dependence of the Coulomb collision operator. If there are ion composition gradients, such as jets of carbon ablator mix entering the hot-spot, this source term can rapidly exceed the Biermann fields. In addition, the Biermann fields are enhanced due to the increased temperature gradients from carbon radiative cooling. With even stronger self-generated fields, heat loss to the carbon regions will be reduced, potentially reducing the negative effect of carbon mix. This article is part of a discussion meeting issue ‘Prospects for high gain inertial fusion energy (part 1)’.

We point out that during the reionization epoch of the cosmic history, the plasma collective effect among the ordinary matter would suppress the large scale structure formation. The imperfect Debye shielding at finite temperature would induce an electrostatic pressure which, working together with the thermal pressure, would counter the gravitational collapse. As a result, the effective Jeans length, lambda[over ]_{J} is increased by a factor lambda[over ]_{J}/lambda_{J}=sqrt[8/5], relative to the conventional one. For scales smaller than the effective Jeans scale the plasma would oscillate at the ion-acoustic frequency. The modes that would be influenced by this effect lie roughly in the range 0.5h Mpc;{-1}<k, which corresponds to the Lyman-alpha forest from the intergalactic medium. We predict that in the linear regime of density-contrast growth, the plasma suppression of the matter power spectrum would approach 1-(Omega_{dm}/Omega_{m});{2} approximately 1-(5/6);{2} approximately 30%.

The Debye shielding of a charge immersed in a flowing plasma is an old classic problem. It has been given renewed attention in the last two decades in view of experiments with complex plasmas, where charged dust particles are often levitated in a region with strong ion flow. Efforts to describe the shielding of the dust particles in such conditions have been focused on the homogeneous plasma approximation, which ignores the substantial inhomogeneity of the levitation region. We address the role of the plasma inhomogeneity by rigorously calculating the point charge potential in the collisionless Bohm sheath. We demonstrate that the inhomogeneity can dramatically modify the wake, making it nonoscillatory and weaker.

We investigate the one- to two-dimensional zigzag transition in clusters consisting of a small number of particles interacting through a Yukawa (Debye) potential and confined in a two-dimensional biharmonic potential well. Dusty (complex) plasma clusters with n<or=19 monodisperse particles are characterized experimentally for two different confining wells. The well anisotropy is accurately measured, and the Debye shielding parameter is determined from the longitudinal breathing frequency. Debye shielding is shown to be important. A model for this system is used to predict equilibrium particle configurations. The experiment and model exhibit excellent agreement. The critical value of n for the zigzag transition is found to be less than that predicted for an unshielded Coulomb interaction. The zigzag transition is shown to behave as a continuous phase transition from a one-dimensional to a two-dimensional state, where the state variables are the number of particles, the well anisotropy and the Debye shielding parameter. A universal critical exponent for the zigzag transition is identified for transitions caused by varying the Debye shielding parameter.

Photoelectron spectra (PES) of the atom are investigated in a Debye plasma environment using an intense, linearly polarized femtosecond (fs) pulsed laser. In the strong field approximation, for a single active electron, the three-dimensional nonrelativistic time-dependent Schrödinger equation is solved numerically by the Crank–Nicolson method. PES is investigated for different Debye lengths (5[Formula: see text]a.u.,10[Formula: see text]a.u. and 15[Formula: see text]a.u.) using the infinite surface flux method, and a shift in the peak positions is observed. PES in the plasma environment for various laser pulse cycles ([Formula: see text], 20 and 30) is also analyzed. Momentum-resolved PES shows the increase in the radius of the above-threshold ionization (ATI) rings due to the plasma screening effect.

Abstract Two-photon transition amplitudes for endohedrally confined plasma-embedded hydrogen are calculated for various values of the incident photon frequencies. Calculations are performed for the plasma-embedded H@C60. Resonance enhancements characteristic of two-photon transitions are observed, and the frequencies for the resonant enhancement of the transitions are noted. The two-photon process for such systems has not been explored earlier. For H@C60 the variation of the transition amplitudes on the frequency of photons and the Debye screening parameter, µ, are shown graphically.

This paper investigates the dynamics of crystalline clusters observed in Molecular Dynamics (MD) studies conducted earlier [Yadav, M., et al. Physical Review E, 107(5), 055214(2023)] for ultra-cold neutral plasmas. An external oscillatory forcing is applied for this purpose and the evolution is tracked with the help of MD simulations using the open source LAMMPS software. Interesting observations relating to cluster dynamics are presented. The formation of a pentagonal arrangement of particles is also reported.

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Energy-energy correlators (EECs) are promising observables for probing the dynamics of jet evolution in the quark-gluon plasma (QGP). By studying jet propagation in a uniform QGP medium, we isolate and examine the individual effects of jet energy loss, jet-induced medium response, and medium-induced gluon radiation on the EECs. We find that the enhancement of EECs at large angles arises predominantly from medium response via elastic scatterings, rather than from medium-induced gluon radiation. In contrast, EECs are suppressed at small angles due to energy loss and transverse momentum broadening of the jet shower partons. We further present the first complete calculation of EECs in high-energy heavy-ion collisions using realistic simulations. These medium-induced modifications are shown to be sensitive to the angular scale of in-medium interactions, as characterized by the Debye screening mass. Experimental measurements of such modifications can thus provide insight into this scale and reveal the short-distance structure of the QGP.

The space-charge field of a relativistic charged bunch propagating in plasma is screened due to the presence of mobile charge carriers. We experimentally investigate such screening by measuring the effect of dielectric wakefields driven by the bunch in a uncoated dielectric capillary where the plasma is confined. We show that the plasma screens the space-charge field and therefore suppresses the dielectric wakefields when the distance between the bunch and the dielectric surface is much larger than the plasma skin depth. Before full screening is reached, the effects of dielectric and plasma wakefields are present simultaneously.

Energy-energy correlators (EECs) are promising observables to study the dynamics of jet evolution in the quark-gluon plasma (QGP) through its imprint on angular scales in the energy flux of final-state particles. We carry out the first complete calculation of EECs using realistic simulations of high-energy heavy-ion collisions and dissect the different dynamics underlying the final distribution through analyses of jet propagation in a uniform medium. The EECs of γ-jets in heavy-ion collisions are found to be enhanced by the medium response from elastic scatterings instead of induced gluon radiation at large angles. In the meantime, EECs are suppressed at small angles due to energy loss and transverse momentum broadening of jet shower partons. These modifications are further shown to be sensitive to the angular scale of the in-medium interaction, as characterized by the Debye screening mass. Experimental verification and measurement of such modifications will shed light on this scale and the short-distance structure of the QGP in heavy-ion collisions.

When an external electric field appears in a homogeneous plasma, ions move into regions where their electrostatic energy is lower. Simultaneously, forces arise that counteract this effect, causing the plasma to reach equilibrium when the field disappears completely. In collisional plasma, the resulting charge inhomogeneities decrease both Coulomb energy and entropy. Randomly induced diffusion flows tend to hinder their growth, minimizing free energy at any point. Accordingly, in the Debye–Hückel theory, the external field strength decreases exponentially with distance within the plasma. In a collisionless plasma, an antiscreening mechanism operates differently. Each ion moves in a self-consistent field along distinct trajectories, following classical dynamics laws. An external field bends these trajectories, bringing ions into regions where their Coulomb energy is lower. The antiscreening mechanism occurs when ions accelerate into potential wells, increasing the distances between them along their trajectories and decreasing their number densities along these paths. The law of energy conservation for any single ion governs this principally nonlocal process, and the dependence of field strength on distance is not necessarily exponential. This paper demonstrates that the Debye–Hückel theory should not be used to describe the charge density distribution within an unrestricted stream of collisionless plasma, such as the solar wind. It also analyzes non-exponential solutions of the Poisson equation for plasma sheaths above flat surfaces, from which such a flow takes off and on which it falls, obtained in quadratures.

This paper considers hydrogen, non-ideal plasma. The structural properties of such plasma were investigated. To study properties of plasma, effective potentials describing the interaction between particles were used. These potentials take into account various effects: screening and quantum-mechanical (diffraction and symmetry). The Pauli exclusion principle prohibits the simultaneous presence of two identical particles with a half-integer spin (in this case, electrons) in the same state. Pair correlation functions were calculated in hyper-netted chain approximation for the integral equation of the Ornstein-Zernike on the basis of the interaction potentials. The symmetry effect is more pronounced at short distances and for higher values of density. The antiparallel direction of the electron spins increases the probability of finding electrons at distance R from each other, the parallel direction decreases this probability due to the prohibition of the presence of two electrons with the same spins in the same state.

The plasmon pole approximation used for the stopping function in a dense electron plasma is given a temperature‐dependent cutoff wavenumber via the ion projectile thermal wavelength. Excepted for projectile inter‐ion distance smaller than the target electron screening length and small ion fragment velocities, featuring a attosecond interaction time with a maximum correlated ion stopping (CIS) in inertial confinement fusion and warm dense matter (WDM), the given procedure is shown to yield back accurately the CIS estimated within the standard random phase approximation framework at any temperature, provided the ion fragment distribution is taken Gaussian.

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A simple minimally perturbative method is introduced which provides the ability to experimentally measure both the radial confining potential and the interaction potential between two individual dust particles, levitated in the sheath of a radio-frequency (RF) argon discharge. In this technique, a single dust particle is dropped into the plasma sheath to interact with a second individual dust particle already situated at the system's equilibrium point, without introducing any external perturbation. The resulting data are analyzed using a method employing a polynomial fit to the particle displacement(s), X(t) , to reduce uncertainty in calculation. Employing this technique, the horizontal confinement is shown to be parabolic over a wide range of pressures and displacements from the equilibrium point. The interaction potential is also measured and shown to be well described by a screened Coulomb potential and to decrease with increasing pressure. Finally, the charge on the particle and the effective dust screening distance are calculated. It is shown for the first time experimentally that the charge on a particle in the sheath of an RF plasma decreases with increasing pressure, in agreement with theoretical predictions. The screening distance also decreases with increasing pressure as expected. This technique can be used for rapid determination of particle parameters in dusty plasma.

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A plasma is a set of charged particles consisting of electrons and ionized atoms whose quantity is sufficiently large to behave collectively through the long-distance electromagnetic fields they produce. It is thought that more than 99.9% of visible matter in the universe is in the plasma state. In a collisionless plasma consisting in an ionized gas composed of electrons moving inbetween much heavier ions, any electrostatic field is rapidly screened by the plasma electrons over the Debye screening distance (Debye & Hückel, 1923). When the number of electrons in these Debye spheres can be assumed to be infinite, the plasma electron population is correctly described by the Vlasov equation (Vlasov, 1938) that neglects all correlations between particles such as the binary Coulomb collisions between them. In addition to being simple, the resulting Vlasov-Maxwell set of equations is extremely rich in physics and has many applications ranging from astrophysics and theoretical plasma physics to intense laser-matter interaction experiments. ESVM (ElectroStatic Vlasov-Maxwell) is a Vlasov-Maxwell Fortran 95 standardcompliant code, parallelized with OpenMP and using Python 3 for post-processing, that allows for the study of these collisionless plasmas. Many finite volume advection schemes (Godunov, 1959) are implemented in order to discretize the Vlasov equation, namely:

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Dense plasma environment affects the electronic structure of ions via variations of the microscopic electrical fields, also known as plasma screening. This effect can be either estimated by simplified analytical models, or by computationally expensive and to date unverified numerical calculations. We have experimentally quantified plasma screening from the energy shifts of the bound-bound transitions in matter driven by the x-ray free electron laser (XFEL). This was enabled by identification of detailed electronic configurations of the observed Kα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upalpha$$\end{document}, Kβ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upbeta$$\end{document} and Kγ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upgamma$$\end{document} lines. This work paves the way for improving plasma screening models including connected effects like ionization potential depression and continuum lowering, which will advance the understanding of atomic physics in the Warm Dense Matter regime.

We study a plasma screening effect in a warm solid-density iron plasma. All the calculations are done using the average atom model in the muffin-tin approximation using the density functional theory in local density approximation at finite temperature in local thermodynamic equilibrium. Between temperatures equal to 15 and 20 eV, the system undergoes a huge change due to the 3d orbital becoming bound. In clear, four electrons become bound. Various average ionizations are defined to see this effect. At temperature equal to 20 eV, all the average ionizations agree to predict a Fermi energy and a plasma frequency that are close to the temperature of the medium. The density of states show a prominent resonance due to d orbital just below temperature equal to 15 eV. We show that the spectral opacity is drastically modified near the L shell threshold due to the appearance of a 2p→3d absorption line.

We provide analytic expressions for the effective Coulomb logarithm for inverse bremsstrahlung absorption which predict significant corrections to the Langdon effect and overall absorption rate compared to previous estimates. The calculation of the collisional absorption rate of laser energy in a plasma by the inverse bremsstrahlung mechanism usually makes the approximation of a constant Coulomb logarithm. We dispense with this approximation and instead take into account the velocity dependence of the Coulomb logarithm, leading to a more accurate expression for the absorption rate valid in both classical and quantum conditions. In contrast to previous work, the laser intensity enters into the Coulomb logarithm. In most laser-plasma interactions the electron distribution function is super-Gaussian [Langdon, Phys. Rev. Lett. 44, 575 (1980)0031-900710.1103/PhysRevLett.44.575], and we find the absorption rate under these conditions is increased by as much as ≈30% compared to previous estimates at low density. In many cases of interest the correction to Langdon's predicted reduction in absorption is large; for example at Z=6 and T_{e}=400eV the Langdon prediction for the absorption is in error by a factor of ≈2. However, we also account for the additional effect of plasma screening, which predicts a reduction in absorption by a similar amount (up to ≈30%). These two effects compete to determine the overall absorption, which may be increased or decreased, depending on the conditions. The corrections can be incorporated into radiation-hydrodynamics simulation codes by replacing the familiar Coulomb logarithm with an analytic expression which depends on the super-Gaussian order "M" and the screening length.

In the classical treatment the screening phenomenon of electric fields in a plasma is solely caused by charged particles, i.e. electrons and ions. In contrast, the present consideration focuses on the role of neutrals in a situation when the correlations between the charged and neutral components of the plasma medium turn rather significant. The consideration is entirely based on the renormalization procedure for interparticle interactions, which takes into account collective events in the generalized Poisson–Boltzmann equation relating the true microscopic potentials with their effective macroscopic counterparts. A meaningful approach is proposed to analytically derive the screening length from an appropriate assumption on the asymptotic behaviour of the macroscopic potential at large interparticle separations. It is clearly demonstrated that the neutral component really affects the screening length when the plasma reaches states corresponding to warm dense matter conditions. It is also shown that, at certain critical values of the plasma parameters, the character of the screening changes from exponential to oscillatory decay.

We characterize in detail the very dense $e^- e^+ \gamma$ plasma present during the Big-Bang Nucleosynthesis (BBN) and explore how it is perturbed electromagnetically by \lq\lq impurities, {\it i.e.\/}, spatially dispersed protons and light nuclei undergoing thermal motion. The internuclear electromagnetic screened potential is obtained (analytically) using the linear response approach, allowing for the dynamic motion of the electromagnetic field sources and the damping effects due to plasma component scattering. We discuss the limits of the linear response method and suggest additional work needed to improve BBN reaction rates in the primordial Universe. Our theoretical methods to describe the potential between charged dust particles align with previous studies on planetary and space dusty plasma and could have significant impact on interpretation of standard cosmological model results.

Self-consistent strong plasma screening around light nuclei is implemented in the Big Bang nucleosynthesis (BBN) epoch to determine the short-range screening potential, e ϕ(r)/T ≥ 1, relevant for thermonuclear reactions. We numerically solve the nonlinear Poisson–Boltzmann equation incorporating Fermi–Dirac statistics, adopting a generalized screening mass to find the electric potential in the cosmic BBN electron–positron plasma for finite-sized α particles (4He++) as an example. Although the plasma follows Boltzmann statistics at large distances, Fermi–Dirac statistics is necessary when work performed by ions on electrons is comparable to their rest-mass energy. While self-consistent strong screening effects are generally minor owing to the high BBN temperatures, they can enhance the fusion rates of high-Z (Z > 2) elements while leaving fusion rates of lower-Z (Z ≤ 2) elements relatively unaffected. Our results also reveal a pronounced spatial dependence of the self-consistent strong screening potential near the nuclear surface. These findings about the electron–positron plasma’s role refine BBN theory predictions and offer broader applications for studying weakly coupled plasmas in diverse cosmic and laboratory settings.

An analysis of lattice wave spectra in a three-dimensional dusty plasma structure formed in a direct current gas discharge with alternating polarity under microgravity conditions is reported. The spectra are determined using the Fourier transform of microparticle velocities, measured by tracking microparticles with subpixel resolution. Both longitudinal and transverse modes are detected and analyzed. The absence of a "k-gap" in the long-wavelength domain of the transverse mode strongly suggests that the microparticles form a solid structure. Therefore, the experimental spectra are compared with the spectra obtained from molecular dynamics simulations for different lattice structures and their orientation. This comparison yields important dusty plasma parameters, such as the particle charge and the plasma screening length. The measured longitudinal and transverse sound velocities allow us to estimate the elastic moduli of the particle component. These are rather small in the absolute magnitude, but when normalized by the number density and the interaction energy of the particles resemble those in conventional matter.

The impact of dense plasma environment on the K-shell photoionization (PI) cross sections of ground and excited states of the plasma-embedded Li-like Fe XXIV ion is analyzed using the relativistic distorted wave method by incorporating analytical plasma screening potential. Excited state energies of target ion Fe XXV and transition probabilities for 1s2 1S0 → 1s3p 1,3P1o transitions of target ion Fe XXV are investigated at various plasma conditions. Plasma screening effects on K-threshold, auger widths, auger energy, and ionization potential depression of the Li-like Fe XXIV have also been investigated. Further, plasma screening effects on the continuum wave function of the orbitals 1s1/2, 2s1/2, and 2p3/2 of Fe XXIV have been shown. Furthermore, plasma screening effects on PI cross sections for the states 1s22s 2S1/2 and 1s22p 2P1/2,3/2o and photorecombination for the states 1s22s 2S1/2 and 1s22p 2P1/2o of Li-like Fe XXIV ion are studied. These findings will be useful in the modeling of astrophysical and laboratory plasmas.

In this paper, the process of electron capture in nonideal plasma has been investigated. For this goal the Bohr-Lindhard method has been applied to obtain the electron capture cross section. All calculations have been done in the framework of the trajectories of incident electron near hydrogen ion (proton) obtained by the numerical simulation of the equations of motion. The effective interaction potential, which takes into account the static or dynamic screening effects at large distances and quantum diffraction effects at short distances, was used. The results of numerical calculations of the electron capture radius, differential and total cross section for different values of the density parameter and velocity are presented. It is shown that dynamic charge screening increases the capture cross sections in comparison with static screening.

In this work, we present an improved model for ionization potential depression (IPD) in dense plasmas that builds upon the approach introduced by Lin et al., which utilizes a dynamical structure factor (SF) to account for ionic microfield fluctuations. The main refinements include the following: (1) replacing the Wigner–Seitz radius with an ion-sphere radius, thereby treating individual ionization events as dynamically independent; (2) incorporating electron degeneracy through a tailored interpolation between Debye–Hückel and Thomas–Fermi screening lengths. Additionally, we solve the Saha equation iteratively, ensuring self-consistent determination of the ionization balance and IPD corrections. These modifications yield significantly improved agreement with recent high-density and high-temperature experimental data on warm dense aluminum, especially in regimes where strong coupling and partial degeneracy are crucial. The model remains robust over a broad parameter space, spanning temperatures from 1 eV up to 1 keV and pressures beyond the Mbar range, thus making it suitable for applications in high-energy-density physics, inertial confinement fusion, and astrophysical plasma research. Our findings underscore the importance of accurately capturing ion microfield fluctuations and electron quantum effects to properly describe ionization processes in extreme environments.

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This paper offers a clear methodology for the characterization of cold atmospheric plasmas and their development. The optical emission spectra of an Ar/O2 plasma jet produced in a plasma jet system at constant flow rates and for various potential discharges between 14 kV and 18 kV revealed that variations in voltage caused a significant difference in the intensity of the Ar/O2 emission. The plasma characteristics of electron temperature (Te), electron density (ne), plasma frequency (fp), Debye length (λD), and the number of particles in the Debye sphere (ND), were estimated using the technique of optical emission spectroscopy (OES). The obtained data are subject to further analysis and discussion. It was determined that potential discharges increased, and an electron temperature increased from 1.34 eV to 1.54 eV. With rising potential discharges, the Debye length decreases while the electron density, plasma frequency, and number of particles in the Debye sphere increase.  

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In the present paper, we introduced two approximation methods to investigate the spherically compressed lithium atom under the influence of Debye plasma. Specifically, the diffusion and the variational Monte Carlo methods are used for the first time to study this case. We incorporated an exponential screening into the nuclear Coulomb potential to account for the plasma influence. We focused our investigation on analyzing the combined effect of compression and plasma environment on the behavior of the lithium atom in its ground state. The resulting outcomes exhibited consistent pattern across various confinement radii and Debye plasma lengths . Many of the results are novel contributions, as they have yet to be explored. Moreover, the findings from this study demonstrated reasonable agreement with the limited existing theoretical results.

Complex multi-body interactions between ions and surrounding charged particles exist in hot and dense plasmas. It will screen the Coulomb potential between the nucleus and electrons, and significantly change the atomic structures and dynamic properties. This will further affect macroscopic plasma properties such as radiation opacity and the equation of state. Based on the atomic-state-dependent (ASD) screening model, we investigate the photoionization dynamic of Fe25+ ion in hot and dense plasmas. The photoionization cross section for all transition channels and total cross sections of n ≤ 2 states for Fe25+ are studied in detail, as well as the low-energy characteristics induced by plasma screening. Compared to the classical Debye Hückel model, the ASD model incorporated the degeneracy effects by inelastic collision processes, resulting in higher plasma density requirements for bound electrons to merge into the continuum. Near the threshold, the photoionization cross section obeys the Wigner threshold law after considering the screening effect. As the energy increases, the cross sections show low-energy characteristics such as shape resonance, Cooper minimum, low-energy enhancement, and Combet-Farnoux minimum, etc., which can significantly increase or decrease the cross section of the corresponding energy region. For example, the low-energy enhancement in the 2p→εs1/2 channel increases the cross section by several orders of magnitude, drastically changing the properties of the photoelectron spectrum. It is significant to study the low-energy characteristics for understanding the physical properties of the photoionization cross section. Fe is an important element in astrophysics. The cross section results in the middle and high energy region calculated by the ASD model in this paper can provide theoretical and data support for the investigation of hot and dense plasmas in Astrophysics and laboratory situations.

We study external forcing-driven dynamical structure formation in a binary dusty plasma mixture. Using two-dimensional driven-dissipative molecular dynamics simulations, we demonstrate phase segregation into bands and lanes beyond a critical forcing threshold. The particles interact via the Debye–Hückel potential, with interaction strength serving as a control parameter for determining the critical forcing. During early evolution, the results exhibit features of two-stream instability. A steady-state phase-space diagram indicates that bands and lanes emerge beyond a critical forcing and coupling strength. Lanes predominantly form under high external forcing. Multiple independent diagnostics, including the order parameter, drift velocity, diffusion coefficients, domain size, and the final-to-initial coupling strength ratio, provide insight into phase segregation and help determine the critical forcing amplitude. Furthermore, we show that the time evolution of band and lane widths follows an exponent of 1/3 for both critical and off-critical mixtures. These findings contrast with the previously reported scaling of 1/2 for equilibrium phase separation in critical mixtures. These results help bridge the gap between dusty plasmas and colloidal systems and facilitate controlled dusty plasma experiments in this direction.

In this paper, the energy eigenvalues of the helium atom and the helium-like ions up to Z=5 in dense plasma are investigated with screened interaction potentials using Debye-Hückel model and exponential cosine screened Coulomb potential using variational Monte Carlo method. The calculations which are carried out in this paper are based on using trial wave functions with different asymptotic behaviors, classified as polynomial correlation, exponential decreasing, and exponential increasing functions. Furthermore, the low-lying excited states of the helium atom were investigated under the same model potentials using trial wave functions for the lowest four excited states, corresponding to the configurations 1s2s and 1s2p. Interesting results are obtained in comparison with results obtained by using other trial wave functions.

We investigate the empirical relationship between the spacecraft potential (Vs) measured by the Electric Field Double Probes, and the electron density (Ne) measured by the Fast Plasma Instrument on the MMS spacecraft. We derive their relationship during fast‐mode intervals when the Active Spacecraft Potential Control Devices are off. Then we apply this relationship to slow‐mode intervals during the perigee passes where Vs can be less than +2 V and Ne can exceed 1,000 cm−3. Because such a parameter range is never observed by MMS during fast‐mode intervals, we define this part of the relationship using simultaneous observations from the Van Allen mission where Ne is measured up to 3,000 cm−3 while Vs is less than +2 V. We compare the empirical relationship to the predictions by an orbital motion limited theory. This suggests how to model the photoelectron current above +5 V and the collection of ambient electrons for moderate Debye lengths. We apply the empirical relationship (i.e., theoretical curves are not used here) to several consecutive plasmapause crossings by MMS during two magnetic storms. The erosion rates of the plasmasphere were ∼60 cm−3/day at 7 MLT and ∼30 cm−3/day at 14 MLT. In the duskside, the erosion rate decreases with L due to increasing flux tube volumes, being about 10–20 cm−3/day at L ∼ 7. The refilling rates are similar to the erosion rates, but in the dawnside, the refilling is delayed due to a slow expansion of the plasmapause to higher L.

Ion saturation current and floating potential were calculated for non-emissive and emissive probes using a kinetic approach. A wide range of plasma pressures was considered: from almost collisionless R/l ≪ 1 up to almost continuous (R/l ≫ 1) cases, where R is the probe radius and l is the ion free path. Calculations were performed for cold ions (ion temperature Ti = 0) and for warm ions (the ratio of the ion temperature to the electron temperature Ti/Te not exceeding approximately 0.3). The Debye radius was assumed to be much narrower than all of the characteristic lengths. Simple approximation formulas are suggested for the ion current and the floating potential for both (non-emissive and emissive) types of probes. Calculations showed that the ion velocity at the sheath-presheath boundary corresponds to the Bohm criterion for all the considered cases.

The dust kinetic Alfvén wave is examined in a plasma made up of negatively charged dust grains, superthermal electrons, and ions. The Korteweg–de Vries (KdV) equation is derived for nonlinear dust kinetic Alfvén waves (DKAWs) in a low-β framework using the reductive perturbation technique (RPM). The normalization approach described in Hasegawa and Mima [Phys. Rev. Lett. 37, 690 (1976)] is utilized to derive the KdV equation. The KdV equation is then turned into the Sagdeev potential energy integral equation. Kinetic Alfvén waves (KAWs) and the formation of possible solitons with both KdV and Sagdeev potential approach are illustrated with suitable plasma parameters of Saturn's F-ring. The investigation on how obliqueness of propagation (θ), superthermal indices κi (for ions) and κe (for electrons), and dust concentration (f) affect the shape and size of DKASWs, is carried. Only negative potential (rarefactive) structures are seen here. It is concluded that any plasma parameter that is going to modify its effective Debye length will always modify the structure profile of both Sagdeev potential curves and the corresponding profile of solitons. This investigation could help us comprehend the creation of nonlinear structures in space plasma especially Saturn's F-ring.

Research in the field of hot dense matter and inertial confinement of nuclear fusion is gaining increasing importance in modern science. It also allows for a deeper understanding of the internal dynamics of giant planets, accretion of matter near stars, the influence of radiation pressure, including convection and diffusion processes in their internal structure, and spectral evolution. Metallic hydrogen plays a key role in studying heat transfer and diffusion processes in dense environments. It has significant practical applications, potentially being used as a superconductor in science and technology. This work investigates diffusion processes in dense hydrogen plasma. Using the Debye potential model, diffusion coefficients were calculated for different values of the plasma non-ideality parameter using the Chapman-Enskog method. Special attention was given to the interaction of plasma with materials based on silicon and graphite. The results obtained using the Debye potential show good agreement with molecular dynamics models and AA-TCP (average-atom two-component plasma) models in the regime of weak interactions, where Γ < 1. This confirms the reliability of the method and its applicability for analyzing weakly bound systems.

We consider a quantum multicomponent plasma made with S species of point charged particles interacting via the Coulomb potential. We derive the screened activity series for the pressure in the grand-canonical ensemble within the Feynman-Kac path integral representation of the system in terms of a classical gas of loops. This series is useful for computing equations of state for it is nonperturbative with respect to the strength of the interaction and it involves relatively few diagrams at a given order. The known screened activity series for the particle densities can be recovered by differentiation. The particle densities satisfy local charge neutrality because of a Debye-dressing mechanism of the diagrams in these series. We introduce a new general neutralization prescription, based on this mechanism, for deriving approximate equations of state where consistency with electroneutrality is automatically ensured. This prescription is compared to other ones, including a neutralization scheme inspired by the Lieb-Lebowitz theorem and based on the introduction of (S-1) suitable independent combinations of the activities. Eventually, we briefly argue how the activity series for the pressure, combined with the Debye-dressing prescription, can be used for deriving approximate equations of state at moderate densities, which include the contributions of recombined entities made with three or more particles.

It is shown that the dust density regimes in the dusty plasma are characterized by two complementary screening processes: (i) the low dust density regime where the Debye screening is the dominant process and (ii) the high dust density regime where the “Coulomb screening” is the dominant process. The Debye regime is characterized by a state where all dust particles carry an equal and constant charge. The high dust density regime or the “Coulomb plasma” regime is characterized by (a) “Coulomb screening” where the dust charge depends on the spatial location and is screened by other dust particles in the vicinity by charge reduction, (b) “asymptotic freedom” where dust particles, which on an average carry minimal electric charge, are asymptotically free in the high dust density limit, (c) uniform dust charge density and plasma potential, (d) dust charge neutralization by a uniform background of hot ions, and (e) dust is weakly coupled due to strong Coulomb screening. Thus, the dusty plasma is essentially a weakly coupled, one-component plasma with screening in the high dust density limit. Molecular dynamics (MD) simulations verify these properties. The MD simulations are performed, using a recently proposed Hamiltonian formalism to study the dynamics of Yukawa particles carrying variable electric charge. A hydrodynamic model for describing the collective properties of Coulomb plasma and its characteristic acoustic mode called the “Coulomb acoustic mode” arising due to imperfect Coulomb screening is given.

We investigated the two-dimensional binary phase separation process of plasma species using classical molecular dynamics in the strongly coupled regime. Both the plasma species interact via a pairwise screened Coulomb (Debye–Hückel) potential; however, the screening parameter κ is different for like- and unlike-species and is the cause for phase separation. We characterize the separation process by measuring the domain growth of equilibrium phases as a function of time—generally, the more significant the inhomogeneity in pairwise interaction, the faster the domain growth. Typically, the domain growth follows a power law in time with an exponent β characterizing the underlying coarsening mechanism. We demonstrate that the growth law exponent is β=1/2 for equal-number-density mixtures and 1/3 otherwise. Further, by comparing these with the corresponding growth laws in binary mixtures of viscous fluids, we show that the viscoelastic nature of plasma fluid modifies the coarsening dynamics, which in turn leads to the observed growth law exponents, notably in the unequal-number-density case.

In the quantized field formalism, using Kramers–Henneberger unitary transformation as the semi-classical counterpart of Block–Nordsieck transformation, the dynamics of entanglement during the low energy scattering processes in bi-partite systems at the presence of a laser beam fields are studied. The stationary-state Schrodinger equation for the quantum scattering process is obtained for such systems. Then, using partial wave analysis, we introduce a new form of entanglement fidelity considering the effect of high-intensity laser beam fields. The effective potential of hot quantum plasma including plasmon and quantum screening effects is used to obtain the entanglement fidelity ratio as a function of the laser amplitude, and plasmon and Debye length parameters for the elastic electron-ion collisions. It is shown that the plasma free electrons oscillations under interaction with laser beam fields improve the correlations between charged particles and consequently lead to the increase in the system entanglement.

In order to describe a dense plasma the approach of cut-off Coulomb potential was used. After testing of model the step further was made. Inclusion of more complex models has been conducted with the help of Hartree-Fock generated potentials. Although the potentials were a good way to describe a complex emitters in a plasma the step forward in describing a collective phenomena of plasma was needed. The simple, but still a nice model introduced coming in focus was considering a plasma as a composition of dense packed ions, and as such a model of dense sphere packing came in place. Here a model that includes inter-ionic distances based on plasma density as well as simplest Debye screening model, rough for dense plasma has been used to generate more applicable model potential of emitter in dense plasma than earlier considered simple cut-off one. The complex model potentials are generated and solved for several temperatures and densities of considered plasma. The work on inclusion of more complex plasma interactions is going on.

The composition, thermodynamic properties and transport coefficients of Ar–H2–Si and N2–H2–Si plasma within a temperature range of 300–30 000 K and pressure range of 0.1–10 atm are calculated under the assumptions of local thermal equilibrium (LTE) and local chemical equilibrium (LCE). Taking Debye–Hückel corrections into account, the chemical equilibrium composition and thermodynamic properties of these two plasma systems are derived using the mass action law and classical statistical thermodynamics respectively. The transport coefficients, including viscosity, conductivity, and thermal conductivity, are calculated using the Chapman–Enskog (C–E) method extended to a third-order approximation (second-order for viscosity and heavy particle translational thermal conductivity). Some of the results have been compared with those of other researchers, and there is a good level of agreement. The slight difference arises from the selection of interaction potential. The final calculation reveals that the introduction of silicon vapor significantly alters the thermodynamic properties and transport coefficients of Ar/N2–H2–Si plasma, even at a small concentration of silicon vapor (1%), the effect on the electrical conductivity cannot be ignored. Furthermore, our calculation results provide the fundamental data for numerical simulations of magnetohydrodynamics (MHD) for the synthesis of silicon nanoparticles and silicon composites.

Lunar polar region has become the focus of future explorations due to the possible ice reservoir in the permanently shadowed craters. However, the space environment near the polar crater is quite complicated, and a plasma mini‐wake can be caused by the topographic obstruction. So far, three‐dimensional (3D) numerical simulations of the mini‐wake around a crater far larger than the Debye length are still limited. Here we present a 3D electrostatic hybrid particle‐in‐cell model to study the plasma mini‐wake of a polar crater on scale of about 1 km. It is found that the mini‐wake can begin upstream from the crater with a cone angle of about 8.8°. There is a plasma void with extra electrons near the leeward crater wall, where the electric potential can be as low as −60 V. A part of solar wind ions can be diverted into the crater, and the ratio of the diverted flux is about 4% on the crater bottom and about 18% on the windward crater wall, which provide an important source for the surface sputtering. Further studies show that the mini‐wake can change with the solar wind parameters and the crater shapes. Our results are helpful to assess the space environment and the water loss rate of a polar crater, and have general implications in studying the plasma mini‐wake caused by a crater on the other airless bodies.

In the presence of ion streaming, the potential around dust particles immersed in plasma becomes anisotropic. In this scenario, the repulsive Debye–Hückel potential is superimposed with an attractive wake potential. This work presents an analytical study of the complex behavior of such a wake potential in the presence of a magnetic field (oriented transversely to the ion flow) and ion-neutral collisions using linear response formalism, both in subsonic and supersonic regimes. The amplitude and periodicity of this potential are found to be controlled by the interplay among ion streaming velocity, ion cyclotron frequency, and ion-neutral collision frequency. Due to the tunable nature of this potential, it is possible to control the crystal formation, phase transitions, and transport properties of dusty plasma by adjusting the external magnetic field. The study also reveals that the wake potential almost disappears in a collision-dominant regime.

The formation of electrostatic potential in an expanding magnetic field divertor is numerically simulated using a kinetic model. As theoretically expected, the electrostatic potential is formed in the expanding magnetic field, which, in combination with the Debye potential near target walls, repels electrons back and balances electron and ion currents. Going beyond the existing theoretical description of the pre-sheath potential formation limited to the asymptotically low electron flow (ue≪vTe), we demonstrate the limit of applicability of asymptotic theory and study pre-sheath potential in practically important range of electron flow [0<Ie<2Isat, where Isat=en(Te+Ti)/mi is the ion saturation current]. Results of the asymptotic theory are fully reproduced at the low side of this range (Ie≪Isat), whereas at high electron current range Ie∼Isat, the pre-sheath potential substantially decreases. The formation of the pre-sheath potential minimizes the interaction of plasma electrons with the material walls and reduces the Debye sheath potential. Reducing the Debye potential forms favorable conditions for eliminating arcing and cold electron emission from the walls. In these favorable conditions, electron thermal losses at the wall could be reduced to minimal theoretical limit of ∼5−8Te per lost ion.

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We present a state-of-the-art determination of the complex valued static quark-antiquark potential at phenomenologically relevant temperatures around the deconfinement phase transition. Its values are obtained from nonperturbative lattice QCD simulations using spectral functions extracted via a novel Bayesian inference prescription. We find that the real part, both in a gluonic medium, as well as in realistic QCD with light u, d, and s quarks, lies close to the color singlet free energies in Coulomb gauge and shows Debye screening above the (pseudo)critical temperature T_{c}. The imaginary part is estimated in the gluonic medium, where we find that it is of the same order of magnitude as in hard-thermal loop resummed perturbation theory in the deconfined phase.

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The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory astrophysical plasmas, can be described by the self-consistent Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a perturbative (linear and second-order) analysis of the Boltzmann-Poisson equations and obtain exact analytic solutions which resolve some longstanding controversies regarding the impact of weak collisions on the continuous spectra, the discrete Landau eigenmodes, and the decay of plasma echoes. We retain both damping and diffusion terms in the collision operator throughout our treatment. We find that the linear response is a temporal convolution of two types of contribution: a continuum that depends on the continuous velocities of particles (crucial for the plasma echo), and another, consisting of discrete modes that are coherent modes of oscillation of the entire system. The discrete modes are exponentially damped over time due to collective effects or wave-particle interactions (Landau damping), as well as collisional dissipation. The continuum is also damped by collisions but somewhat differently than the discrete modes. Up to a collision time, which is the inverse of the collision frequency ν_{c}, the continuum decay is driven by the diffusion of particle velocities and is cubic exponential, occurring over a timescale ∼ν_{c}^{-1/3}. After a collision time, however, the continuum decay is driven by the collisional damping of particle velocities and diffusion of their positions and occurs exponentially over a timescale ∼ν_{c}. This slow exponential decay causes perturbations to damp the most on scales comparable to the mean free path but very slowly on larger scales. This establishes the local thermal equilibrium, which is the essence of the fluid limit. The long-term decay of the linear response is driven by the discrete modes on scales smaller than the mean free path but, on larger scales, is governed by a combination of the slowly decaying continuum and the least damped discrete mode. This slow exponential decay implies that the echo, which results from the interference of the continuum response to two subsequent pulses, is detectable even on scales comparable to the mean free path, as long as the second pulse is introduced within a few phase-mixing timescales after the first.

A recent publication by Köhn et al (2023 Plasma Sources Sci. Technol. 32 055012) studied the quasi-equilibria of high power magnetron discharges through thermodynamic principles. A generalized, magnetic-field aware Poisson–Boltzmann relation for the electric potential and the electron density was established using a non-standard (multi-objective) variational principle. This addendum demonstrates that, assuming slow or quasistatic evolution, the same result can be realized via a standard (single-objective) variational principle, thereby streamlining the theoretical framework while preserving the robustness of the finding.

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In this paper, we study an asymptotic preserving (AP), energy stable and positivity preserving semi-implicit finite volume scheme for the Euler-Poisson-Boltzmann (EPB) system in the quasineutral limit. The key to energy stability is the addition of appropriate stabilisation terms into the convective fluxes of mass and momenta, and the source term. The space-time fully-discrete scheme admits the positivity of the mass density, and is consistent with the weak formulation of the EPB system upon mesh refinement. In the quasineutral limit, the numerical scheme yields a consistent, semi-implicit discretisation of the isothermal compressible Euler system, thus leading to the AP property. Several benchmark numerical case studies are performed to confirm the robustness and efficacy of the proposed scheme in the dispersive as well as the quasineutral regimes. The numerical results also corroborates scheme's ability to very well resolve plasma sheaths and the related dynamics, which indicates its potential to applications involving low-temperature plasma problems.

We consider a two‐component asymmetric complex plasma of finite‐size macroions with charges Z$$ Z $$ ( Z≫1$$ Z\gg 1 $$ ) and point oppositely charged microions with unit charges. System pressure is calculated within the framework of the Poisson–Boltzmann plus hole approximation by obtaining the Coulomb nonideal parts of interaction energy and Helmholtz free energy. It is shown that both the pressure and plasma isothermal compressibility are positive over the entire range of macroion concentrations. We compared pressure and isothermal compressibility in linearized approximations and in the Poisson–Boltzmann plus hole approximation where the nonlinear screening effect is taken into account and showed a significant difference for some macroions concentrations.

The Poisson–Boltzmann (PB) equation is a nonlinear partial differential equation that describes the equilibria of conducting fluids. Using a thermodynamic variational principle based on the balances of particle number, entropy, and electromagnetic enthalpy, it can also be justified for a wide class of unmagnetized technological plasmas (Köhn et al 2021 Plasma Sources Sci. Technol. 30 105014). This study extends the variational principle and the resulting PB equation to high power magnetron discharges as used in planar high power pulsed magnetron sputtering. The example in focus is that of a circular high power magnetron. The discharge chamber and the magnetic field are assumed to be axisymmetric. The plasma dynamics need not share the symmetry. The domain is split into the ionization region close to the cathode where electrons are confined, i.e. can escape from their magnetic field lines only by slow processes such as drift and diffusion, and the outer region , where the electrons are largely free and the plasma is cold. With regard to the dynamics of the electrons and the electric field, a distinction is made between a fast thermodynamic and a slow dissipative temporal regime. The variational principle established for the thermodynamic regime is similar to its counterpart for unmagnetized plasmas but takes magnetic confinement explicitly into account by treating the infinitesimal flux tubes of as individual thermodynamic units. The obtained solutions satisfy a generalized PB relation and represent thermodynamic equilibria in the fast regime. However, in the slow regime, they must be interpreted as dissipative structures. The theoretical characterization of the dynamics is corroborated by experimental results on high power magnetrons published in the literature. These results are briefly discussed to provide additional support.

We study the geometric particle-in-cell methods for an electrostatic hybrid plasma model. In this model, ions are described by the fully kinetic equations, electron density is determined by the Boltzmann relation and space-charge effects are incorporated through the Poisson equation. By discretizing the action integral or the Poisson bracket of the hybrid model, we obtain a finite dimensional Hamiltonian system, for which the Hamiltonian splitting methods or the discrete gradient methods can be used to preserve the geometric structure or energy. The global neutrality condition is conserved under suitable boundary conditions. Moreover, the results are further developed for an electromagnetic hybrid model proposed by Vu (J. Comput. Phys., vol. 124, issue 2, 1996, pp. 417–430). Numerical experiments of finite grid instability, Landau damping and resonantly excited nonlinear ion waves illustrate the behaviour of the numerical methods constructed.

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We introduce a fluid computational model for the numerical simulation of atmospheric pressure dielectric barrier discharge plasmas. Ion and neutral species are treated with an explicit drift diffusion approach. The Boltzmann relation is used to compute the spatial distribution of electrons as a function of the electrostatic potential and the ionic charge density. This technique, widely used to speed up particle and fluid models for low-pressure conditions, poses several numerical challenges for high-pressure conditions and large electric field values typical of applications involving atmospheric-pressure plasmas. We develop a robust algorithm to solve the non-linear electrostatic Poisson problem arising from the Boltzmann electron approach under AC electric fields based on a charge-conserving iterative computation of the reference electric potential and electron density. We simulate a volumetric reactor in dry air, comparing the results yielded by the proposed method with those obtained when the drift diffusion approach is used for all charged species, including electrons. We show that the proposed methodology retains most of the physical information provided by the reference modeling approach while granting a substantial advantage in terms of computation time.

Space and astrophysical plasmas or gases can reach various states of thermal or nonthermal quasi-equilibrium, depending on the collisional age of the observed system. Widely observed in space plasmas, the Kappa (or κ —power-law) velocity distribution (KVD) is eloquent evidence of nonthermal states. M. P. Leubner has developed KVD models for luminous gases and cold dark matter (DM) with empirical density profiles described by κ > 0 and κ < 0, respectively. The predicted temperature profiles, however, are not in qualitative agreement with the nonmonotonic features expected in some gas and DM models. This study adopts the more consistent regularized Kappa distribution (RKD) to derive the equilibrium profiles of self-gravitating gas and DM halos within a Boltzmann–Poisson theoretical approach. The new RKD models can replicate better than the KVD models the Navarro–Frenk–White density profile of the DM near the basic halos and can also produce nonmonotonic temperature profiles. The same RKD formalism is also applied to non-self-gravitating astrophysical systems, which shows that for highly nonthermal cases ( κ~1 < 3/2), the temperature of the surrounding gases decreases initially in a narrow region. The temperature then increases sharply and reaches a high saturated value, resembling the overheated solar atmosphere, while the density profile near the surface may depart from the observations. Compared to the KVD models, the new RKD models can provide improved descriptions of gravitational equilibrium systems, especially for highly nonthermal cases and temperature profiles.

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This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB) model of plasma physics. This model consists of the pressureless gas dynamics equations coupled with the Poisson equation and where the Boltzmann relation relates the potential to the electron density. If the quasi-neutral assumption is made, the Poisson equation is replaced by the constraint of zero local charge and the model reduces to the Isothermal Compressible Euler (ICE) model. We compare a numerical strategy based on the EPB model to a strategy using a reformulation (called REPB formulation). The REPB scheme captures the quasi-neutral limit more accurately.

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We study the large-time asymptotic behavior of solutions to the one-dimensional damped pressureless Euler-Poisson system with variable background states, subject to a neutrality condition. In the case where the background density converges asymptotically to a positive constant, we establish the convergence of global classical solutions toward the corresponding equilibrium state. The proof combines phase plane analysis with hypocoercivity-type estimates. As an application, we analyze the damped pressureless Euler--Poisson system arising in cold plasma ion dynamics, where the electron density is modeled by a Maxwell-Boltzmann relation. We show that solutions converge exponentially to the steady state under suitable a priori bounds on the density and velocity fields. Our results provide a rigorous characterization of asymptotic stability for damped Euler-Poisson systems with nontrivial background structures.

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A set of evolutionary equations is proposed for a self-consistent description of Langmuir wave dynamics in an inhomogeneous plasma. In contrast to the traditionally used set of equations consisting of the kinetic Boltzmann–Vlasov equation for the distribution function and the Poisson equation for the scalar potential of the wave electric field, we describe the latter with the help of a vector potential. This makes the set of equations an evolutionary type of system, which allows solving the initial problem for the distribution function and the wave field. The inclusion of non-resonant particles into consideration with the help of permittivity makes it possible to solve the kinetic equation only for resonant particles. This radically reduces the amount of numerical calculations and allows solving the problem on a personal computer, while the traditional approach in which the kinetic equation is solved for all particles requires much more computational resources. The results obtained include various cases of homogeneous and inhomogeneous plasma as well as the cases of a single wave and a wide spectrum.

Dusty plasma, composed of charged dust grains, electrons and ions, plays a fundamental role in both space and laboratory environments. Understanding nonlinear wave propagation in such plasma is essential for studying complex plasma behaviour. In this paper, we consider the excitation of three-dimensional dust-acoustic waves in a five-component dusty plasma system consisting of positively charged dust grains, solar wind-driven electrons and ions and Maxwell–Boltzmann-distributed species. Using the reductive perturbation technique, we reduced the governing hydrodynamic and Poisson equations to the KP equation. We derived analytical KP equation solutions using direct integration, factorization and bilinear methods. The results revealed novel wave structures, including solitary and explosive pulses, shock-like waves, and lump waves, in dusty plasma. This study highlights the importance of analytical techniques for solving nonlinear partial differential equations (PDEs) in plasma physics, notably contributing to understanding the behaviour of dust-acoustic waves, with implications for planetary magnetospheres such as Jupiter.

Abstract The Poisson–Vlasov formalism, pertaining to the well-known kinetic description model of plasmas, is employed to investigate the shear-modified ion-acoustic instability in nonthermal, anisotropic, Cairns-distributed ionospheric magnetoplasma characterized by parallel flow shear. The kinetic dielectric response function of the shear-modified ion-acoustic instability is calculated. The real (oscillatory) frequency and growth rate (imaginary frequency) of the plasma mode under consideration are explored through an exact numerical solution of the kinetic dispersion relation. In particular, the role of parallel flow shear in the excitation of the instability associated with the ion-acoustic mode is thoroughly examined. It is observed that the instability growth rate is significantly influenced by variations in the magnitudes of the relevant dimensionless parameters, including velocity shear S i , nonthermality parameter α, ion temperature anisotropy ratio σ i , and ion-to-electron temperature ratio Λi,e. The present investigation is relevant for understanding plasma dynamics in space environments comprising nonthermal particle populations, e.g., the upper ionosphere.

In this paper, we present the nonmodal kinetic theory of the macroscale two-dimensional compressed-sheared non-diffusive convective flows of a magnetized plasma generated by the inhomogeneous microturbulence. This theory is based on the two-scale approach to the solution of the Vlasov–Poisson system of equations for magnetized plasma, in which the self-consistent evolution of the plasma and of the electrostatic field on the microscales, commensurable with the wavelength of the microscale instabilities and of the ion gyroradius, as well as on the macroscales of a bulk of plasma, is accounted for. It includes the theory of the formation of the macroscale spatially inhomogeneous compressed-sheared convective flows by the inhomogeneous microturbulence, the theory of the back reaction of the macroscale convected flows on the microturbulence, and the slow macroscale response of a bulk of plasma on the development of the compressed-sheared convective flows.

Kinetic simulations of collisionless plasmas are computationally challenging due to phase-space mixing and filamentation, resulting in fine-scale velocity structures. This study compares three methods developed to reduce artifacts related to limited velocity resolution in Hermite-based Vlasov–Poisson simulations: artificial collisions, filtering, and nonlocal closure approaches. We evaluate each method's performance in approximating the linear kinetic response function and suppressing recurrence in linear and nonlinear regimes. Numerical simulations of Landau damping demonstrate that artificial collisions, particularly higher orders of the Lenard-Bernstein collisional operator, most effectively recover the correct damping rate across a range of wavenumbers. Moreover, Hou-Li filtering and nonlocal closures underdamp high wavenumber modes in linear simulations, and the Lenard-Bernstein collisional operator overdamps low wavenumber modes in both linear and nonlinear simulations. This study demonstrates that hypercollisions offer a robust approach to kinetic simulations, accurately capturing collisionless dynamics with limited velocity resolution.

After finding an exact solution to the Vlasov–Boltzmann kinetic equation (i.e., finding distribution functions for plasma particles), we consider the description of Landau damping using Poisson's equation, since with the complete distribution function, there is no need to split the kinetic equation into equilibrium and perturbed parts for the subsequent implementation of the pole bypass in the integrand expression. The found distribution function depends, in addition to velocity, on the coordinates and can be used to analytically consider different cases and configurations of the spatial confinement of the plasma. General distribution function for electrons is discussed. We consider the behavior of Langmuir waves, also at the nonlinear stage.

The description dust plasma behavior via a multi-fluid model, Where it represents that Boltzmann distributed electrons and ions, the dust momentum and Poisson's equations, in addition to the continuity equation that has a source term for the dust grains. The Runge-Kutta technique of fourth order was then used to numerically solve the equation. The solution shows a variety of behaviors under wide range of parameters changes. In particular, the solution of the equation shows a chaotic behavior  at  α= 1.0. In this study, the chaotic behavior in the plasma complex is graphically studied and discussed for some certain parameters. The aim of this study can be helped the researchers to investigate several nonlinear oscillations in different plasma and fluid mechanics models.  

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We present a comprehensive theoretical and numerical investigation of dust-acoustic waves (DAWs) in a collisionless, unmagnetized dusty plasma comprising electrons, ions, and negatively charged dust grains. Using both fluid theory and Vlasov–Poisson simulations, we explore the effects of drift velocities in different plasma species on the stability and nonlinear evolution of DAWs. In the absence of drift, the plasma remains stable, exhibiting no wave growth or nonlinear phase-space structures. The introduction of drift in dust particles leads to fluid instabilities at certain threshold value, while ion drift proves to be a more efficient driver of instability, inducing both kinetic and fluid responses at comparatively lower drift speeds. Electron drift, due to the electrons' smaller mass and higher thermal velocity, requires significantly higher drift values to destabilize the system. The simulations reveal key nonlinear features, including wave amplification, energy transfer from drifting species to dust grains, the formation of phase-space holes, and the eventual saturation of wave energy. A transition from kinetic to fluid instability regimes is also observed with increasing drift velocity, particularly in ion-driven cases. These results offer valuable insights into the mechanisms of wave–particle interactions, energy transport, and instability formation in both laboratory and space dusty plasma environments.

The ionosphere’s plasma characteristics, including Debye length of electron (λDe), Plasma frequency of electron (flpe), Number of particles in a Debye sphere (ND) and plasma coupling parameter of electron (Γ) over Iraqi capital “Baghdad” (44.30E, 33.30 N) within the F-layer for various seasons (Winter, Spring, Summer and Autumn) during the year (2017) for solar cycle 24 have been calculated. Solar activity as indicated in terms of sunspots number (SSN) and solar flux (F10.7 cm), which are used to compute electron temperature and density using the international reference ionosphere (IRI-2016) model for different heights (150-500) km with 50 km increment. Depending on changes in temperature (Te) and electron density (ne), the ionosphere’s plasma characteristics vary from height to height throughout the year. It is observed that when electron density rises as a result of plasma frequency, the plasma’s coupling parameter also rises. It has been shown that a rise in electron temperature also causes an increase in electron velocity, Debye length, and Debye sphere.

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The plasma-induced charge of non-spherical microparticles is a crucial parameter in complex plasma physics, aerosol science and astrophysics. Yet, the literature describes this charge by two competing models, neither of which has been experimentally verified or refuted. Here we offer experimental proof that the charge on a two-particle cluster (doublet) in the spatial afterglow of a low-pressure plasma equals the charge that would be obtained by the smallest enclosing sphere and that it should therefore not be based on its geometrical capacitance but rather on the capacitance of its smallest enclosing sphere. To support this conclusion, the size, mass and charge of single particles (singlets) and doublets are measured with high precision. The measured ratio between the plasma-afterglow-induced charges on doublets and singlets is compared to both models and shows perfect agreement with the predicted ratio using the capacitance of the smallest enclosing sphere, while being significantly dissimilar to the predicted ratio based on the particle’s geometrical capacitance. Here the authors report measurements of the charge ratio and mass of two-particle clusters and single microparticles in the spatial plasma afterglow. The insights contribute to the general understanding of non-spherical particle charging in ionized gasses.

The evolution of the properties of short‐scale electrostatic waves across collisionless shocks remains an open question. We use a method based on the interferometry of the electric field measured aboard the magnetospheric multiscale spacecraft to analyze the evolution of the properties of electrostatic waves across four quasi‐perpendicular shocks, with 1.4≤MA≤4.2 $1.4\le {M}_{A}\le 4.2$ and 66°≤θBn≤87° $66{}^{\circ}\le {\theta }_{Bn}\le 87{}^{\circ}$ . Most of the analyzed wave bursts across all four shocks have a frequency in the plasma frame fpl ${f}_{pl}$ lower than the ion plasma frequency fpi ${f}_{pi}$ and a wavelength on the order of 20 Debye lengths λD ${\lambda }_{D}$ . Their direction of propagation is predominantly field‐aligned upstream and downstream of the bow shock, while it is highly oblique within the shock transition region, which might indicate a shift in their generation mechanism. The similarity in wave properties between the analyzed shocks, despite their different shock parameters, indicates the fundamental nature of electrostatic waves for the dynamics of collisionless shocks.

In the last experiment with the PK-3 Plus laboratory onboard the International Space Station, interactions of millimeter-size metallic spheres with a complex plasma were studied [M. Schwabe et al., New J. Phys. 19, 103019 (2017)10.1088/1367-2630/aa868c]. Among the phenomena observed was the formation of cavities (regions free of microparticles forming a complex plasma) surrounding the spheres. The size of the cavity is governed by the balance of forces experienced by the microparticles at the cavity edge. In this article we develop a detailed theoretical model describing the cavity size and demonstrate that it agrees well with sizes measured experimentally. The model is based on a simple practical expression for the ion drag force, which is constructed to take into account simultaneously the effects of nonlinear ion-particle coupling and ion-neutral collisions. The developed model can be useful for describing interactions between a massive body and surrounding complex plasma in a rather wide parameter regime.

Prompt redeposition is a process in which a neutral atom sputtered from a divertor target or the first wall of a tokamak returns on the surface right after ionization, before experiencing any collisions with the background plasma. This paper presents analytical solutions of kinetic equations for sputtered neutrals and resulting ions. Using obtained distribution functions, the redeposition coefficient and average impact angle are derived under assumptions of thin Debye sheath. Our expression for the prompt redeposition coefficient explicitly depends on the angular and energy distributions of sputtered atoms and, therefore, is more universal than often used Fussmann equation valid only for cosine distribution. The effect of the angular distributions of sputtered particles on the prompt redeposition efficiency and parameters of redeposited ions is analyzed.

Positronium formation processes in positron-helium collisions with Debye potentials are studied using the screening approximation model in incident energy range from the threshold to 100 eV for screening parameters μ=0.00-0.25.

Experimental investigations into the plasma’s response to a pulsed ion acoustic wave excited via a grid have been carried out in a quiescent, multi-dipole confined hot cathode discharge. A frequency limit at ∼1/140 of the ion plasma frequency fpi has been found in the plasma’s ion acoustic response to the excitation wave. This limiting response frequency is much lower than a plasma’s expected ion acoustic resonance frequency, which previous computational and experimental investigations revealed to be >fpi/10. The corresponding wavelength at ∼860 times the Debye length λDebye also mismatches both the plasma resonance wavelengths, the device dimensions and the grid dimensions. It was found that multi-cycle pulses do not drastically change the frequency but only increase the response amplitude, which closely reflects the increase in transmitted total pulse energy. These findings show that the preferred plasma response to an excitation pulse might not reflect its wave resonance characteristics and other plasma parameter related effects might be at play. Experiments also show an inverse relationship between plasma density and excited wave amplitude with identical excitation parameters, and a strong inverse correlation between the amplitude of the excited wave and the expected sheath thickness near the launch grid, suggesting that the fundamental process of exciting ion acoustic waves mirrors that of capacitively coupled plasma heating, i.e. via sheath fluctuations. The change of the ion acoustic wave damping length is also found to reflect the change of neutral pressure but only up a certain limit, which could be either due to a cone expansion of the launched waves and/or an additional damping mechanism other than ion-neutral collisions. The implications of these findings for other wave-related plasmas, i.e. pulsed rf-plasmas, are discussed.

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Quasi‐thermal noise (QTN) spectroscopy is a plasma diagnostic technique that enables precise measurements of moments for the local electron velocity distribution function. Previous studies on the QTN technique applied to weakly ionized collisional plasma were limited by the assumptions of unmagnetized and Maxwellian distributions. In this paper, we extend prior research by considering collisional and a secondary hot Maxwellian distribution. Further analysis indicates that as the collision frequency increases, the peak power spectral density at the electronplasmafrequencyfp $\text{electron}\,\text{plasma}\,\text{frequency}\ {f}_{p}$ decreases. In addition, we find that the influence of collisions on low‐frequency cyclotron harmonic signals in a magnetized plasma is mainly related to the plasma‐to‐electron cyclotron frequency ratio ωpe/Ωce ${\omega }_{\text{pe}}/{{\Omega }}_{\text{ce}}$ , but also has non‐trivial dependencies on the plasma Debye Length LD ${L}_{D}$ . Finally, we observed that in eight representative cases, the plasma harmonic disappearance frequency ratio is generally ∼0.25. Our research provides valuable theoretical guidance for the future application of QTN techniques in detecting plasma parameters, especially for collision frequencies typical of Earth's ionosphere.

No abstract available

e n waves (KAWs) within the 0 – 10 R Sun range, has been a subject of great interest for many decades. This study investigates and explores the acceleration and heating of charged particles and the role of KAWs in the solar corona. We investigate how KAWs transport energy and accelerate and heat the charged particles, focusing on the behavior of perturbed electromagnetic (EM) fields, the Poynting flux vectors, net power transfer through the solar flux loop tubes, resonant particles' speed, group speed, and the damping length of KAWs. The study examines how these elements are influenced by suprathermal particles $( and the electron-to-ion temperature ratios ($ T_e/T_i e n waves travel in the kinetic limits; that is, $m_e/m_i 1$. Furthermore, the plasma incorporates suprathermal high-energy particles, necessitating an appropriate distribution function to accurately describe the system. We adopted the Kappa distribution function as the most suitable choice for our analysis. The results show that the perturbed EM fields are significantly influenced by kappa and the effect of $ T_e/T_i $. We evaluate both the parallel and perpendicular Poynting fluxes and find that the parallel Poynting flux ($ S_z $) dissipates gradually for lower kappa values. In contrast, the perpendicular flux ($ S_x $) dissipates quickly over shorter distances. Power deposition in solar flux tubes is significantly influenced by kappa and $ T_e/T_i $. We find that particles can heat the solar corona over long distances (R Sun ) in the parallel direction and short distances in the perpendicular direction. The group velocity of KAWs increases for lower kappa values, and the damping length, $ L_G $, is enhanced under lower kappa , suggesting longer energy transport distances (R Sun ). These findings offer a comprehensive understanding of particle-wave interactions in the solar corona and wind, with potential applications for missions such as the Parker Solar Probe, (PSP), and can also apply to other environments where non-Maxwellian particle distributions are frequently observed.

For some class of studies, the space charge is treated as frozen, allowing to capture the dynamics of incoherent phenomena. We explore the possibility that a beam may exhibit non-resonant coherent behavior by developing and studying a one-dimensional model.

In quantum electrodynamics, static electric fields are screened at nonzero temperatures by charges in the plasma. The inverse screening length, or Debye mass, may be analyzed in perturbation theory and is of order {ital eT} at relativistic temperatures. An analogous situation occurs when non-Abelian gauge theories are studied perturbatively, but the perturbative analysis breaks down when corrections of order {ital e}{sup 2}{ital T} are considered. At this order, the Debye mass depends on the nonperturbative physics of confinement, and a perturbative ``definition`` of the Debye mass as the pole of a gluon propagator does not even make sense. In this work, we show how the Debye mass can be defined nonperturbatively in a manifestly gauge-invariant manner (in vectorlike gauge theories with zero chemical potential). In addition, we show how the {ital O}({ital e}{sup 2}{ital T}) correction could be determined by a fairly simple, three-dimensional, numerical lattice calculation of the perimeter-law behavior of large, adjoint-charge Wilson loops. {copyright} 1995 The American Physical Society.

No abstract available

The purpose of this paper is to investigate the Tonks‐Langmuir model by assuming that the electrons obey the q‐ non‐extensive distribution. The plasma equation is analytically solved. It is revealed that the quasi‐neutrality length of the glow discharge exceeds with the decrement of the non‐extensive parameter q. In the extensive limiting case ( q→1$$ q\to 1 $$ i.e., Maxwellian case) the previously well‐known results are recovered. Moreover, by evaluating the mean inverse kinetic energy of ions, it is illustrated that the kinetic Bohm criterion does not represent an inherent property of the collision‐ and ionization‐free one‐dimensional space‐charge sheaths in the case of non‐extensive electron distribution, contrary to the Maxwellian one. Finally, the plasma‐sheath equation is numerically solved in the case of non‐extensive electron distribution. It is found that the decrement of q gives rise to the increment of the wall potential value and sheath thickness for super‐thermal electron distribution q < 1. On the other hand, it is observed that the wall potential value and the sheath thickness decrease as q increases for sub‐thermal electron distribution q > 1. On this basis, it is concluded that the characteristics of the space‐charge sheath in the low‐pressure plane symmetric discharge depend on the electron non‐extensive parameter q. This is in agreement with the prior practical measurements on the ion sheath formed around a non‐extensive single electric probe in plasma.

The influence of the non‐ideality (NI) of the classical plasmas on the doubly excited singlet S states of the helium atom (He) embedded in the plasma has been investigated theoretically. A pseudopotential containing the Debye length and the non‐ideality parameter (NIP) as its characteristics is used to represent the screened interaction potentials in the plasma. Using a large wavefunction within the framework of the stabilization method, it has been possible to recognize six doubly excited singlet S states (five lying below the He+(2S) excitation threshold and one lying below the He+(3S) excitation threshold) for the plasma‐free case. The energies and the autoionization life‐times of those states are computed by fitting the density of states to the Lorentzian form. Convergence of the computed results is corroborated by increasing the number of terms in the employed wavefunction. For the plasma‐free case, these results are in excellent agreement with the established results in the literature. A comprehensive analysis has been made on changes induced on those doubly excited states by varying NI over a wide range. It has been observed that the energies of the states gradually approach the corresponding threshold energies with the increasing NI of the plasma, whereas the change in the life‐times (alternatively the widths of the states) of the states shows distinctive features depending on the angular momentum of an individual electron.

No abstract available

The effects of the non-ideality (NI) of the classical plasmas on the 1Se resonance states of the negative ion of hydrogen (H−) have been investigated theoretically by using the stabilization method. The organized effect of the plasma charged particles is represented by a pseudopotential, which depends on the Debye length D and the non-ideality parameter γ. Densities of the resonance states as a function of D and γ are calculated by employing a highly correlated and extensive basis set. Convergence of the resonance parameters (energy and width) is ensured by increasing the number of terms in the basis. Three 1Se resonance states are found to emerge below the H(4S) excitation threshold. Our present results for lowest lying resonance for plasma-free cases as well as in weakly coupled plasmas are in excellent agreement with the established results in the literature. An extensive study is carried out to explore the changes in the resonance parameters of the three states due to the effects of plasma NI. It is found that, for a given Debye length, the resonance energy increases, and the resonance width decreases with increasing plasma non-ideality.

An elegant calculation is carried out to investigate the effects of the non‐ideality of classical plasma on the energy levels of the hydrogenic atoms held in a spherical cage. Organized effect of the non‐ideal classical plasma is described by an analytical pseudopotential which contains the Debye length and non‐ideality parameter as parameters. Convergent results for the bound states are obtained variationally by utilizing a large trail function containing cosine term which automatically takes care of the requisite boundary conditions. For the plasma‐free case, our results are in excellent agreement with the most accurate results available in the literature. An inclusive study is made to explore the changes emerging in the energy levels due to the variation of the plasma parameters and cage size. Special emphasis is made on the determination of critical cage size precisely. The present study specifically reveals that the increasing plasma non‐ideality leads to the elongation of the critical cage size. Moreover, it is empirically found that the critical cage size for a given hydrogenic atom can be obtained from a scaling law.

This paper discusses thermal equilibrium states of single-species plasmas, such as pure electron plasmas and pure positron plasmas, that are confined in a dipole trap. Thermal equilibrium states for such plasmas are routinely realized in the homogeneous magnetic field of Penning–Malmberg traps. We generalize the theory of these states to include inhomogeneous magnetic dipole fields. The approach to thermal equilibrium takes place in two stages with well separated time scales. On the collision time scale, thermal equilibrium is established along each magnetic field line. On the much longer transport time scale, heat conduction and viscosity bring the plasmas on different flux contours into thermal equilibrium, we call this a state of global thermal equilibrium. We present numerical results for local and global thermal equilibria. These results agree with the analytic predictions for charge collections that are large compared with the Debye length. There is, in principle, no limit to the confinement time of a single-species plasma in a global thermal equilibrium state. Experiments with hot electron–ion plasmas performed in the LDX and RT1 devices give us confidence that, in contrast to a Penning–Malmberg trap, a magnetic dipole field can also confine cold quasi-neutral electron–positron pair plasmas on the time scale of the phenomena of interest. Such pair plasmas are assumed to form in the magnetosphere of neutron stars but have so far not been realized in a laboratory. The creation of an electron–positron pair plasma is the main goal of the APEX collaboration.

No abstract available

In this paper, we study the global in time quasi-neutral limit for a two-fluid non-isentropic Euler–Poisson system in one space dimension. We prove that the system converges to the non-isentropic Euler equations as the Debye length tends to zero. This problem is studied for smooth solutions near the constant equilibrium state. To prove this result, we establish uniform energy estimates and various dissipation estimates with respect to the Debye length and the time. These estimates allow to pass to the limit to obtain the limit system by compactness arguments. In addition, the global convergence rate is obtained by use of stream function technique.

An advanced computational approach to determination of the electron-collisional strengths and cross-sections for atomic ions in the Debye plasmas is presented and used to calculate effective collision strengths of the Kr26+ Ne-like ion excitation states for temperature T=5×106K and density ne==1014cm−3 . The obtained results are compared with the R-matrix data by Griffin et al and other theoretical estimates. The approach is based on the generalized relativistic energy formalism and relativistic many-body perturbation theory with the Debye shielding model Hamiltonian for electron-nuclear and electron-electron systems. The optimized one-electron representation in the perturbation theory zeroth approximation is constructed by means of the correct treating the gauge dependent multielectron contribution of the lowest perturbation theory corrections to the radiation widths of atomic levels.

This work investigates the formation and dynamics of electrostatic freak waves in pair-ion (PI) and pair-ion--electron (PIE) plasmas. The analysis begins with the derivation of the Korteweg--de Vries (KdV) equations for both plasma configurations, from which the corresponding nonlinear and dispersive coefficients are obtained. By employing the wave superposition principle, the KdV equations are systematically reduced to the nonlinear Schrödinger equation (NLSE), enabling the exploration of modulation instability and rogue wave generation. Analytical solutions of the NLSE are utilized to construct parametric plots that elucidate the evolution of freak waves in PI and PIE plasmas. Comparative analysis reveals pronounced differences in the amplitude, localization, and structural properties of the freak waves in the two plasma environments, highlighting the critical role of electron contributions in shaping nonlinear wave phenomena.

This investigation analyzes the propagation of nonlinear ion-acoustic waves (IAWs) in an unmagnetized, collisionless plasma composed of inertial positive ions and inertialess Maxwellian positrons as well as the inertialess non-Maxwellian electrons that obey (r, q)-distribution. To observe the impact of particle trapping on the nonlinear IAWs in an electron–positron–ion plasma, the Korteweg–De Vries (KdV) and modified KdV (mKdV) equations are derived using a reductive perturbation method. In the distribution function, the spectral parameters (r, q) put up their contribution to the flatness and high-energy tails, respectively. An important aspect of this investigation is the determination of well-known quasi-periodic solutions, multi-soliton solutions, breathers, and shocks under the variation of different physical parameters, especially spectral indices (r, q). Finally, the interaction of solitons is also presented for discussion of the complete profile. In addition, a detailed comparison, especially in a periodic wave, is made between the generalized (r, q)-distribution and the limiting cases of Kappa and Maxwellian distributions. The results presented in this study contribute to a better understanding of the characteristics of both high- and low-energy parts of the electron distribution function as well as the formation of periodic, soliton, multi-soliton, breathers, and shocks in space and astrophysical plasmas.

This manuscript introduces a relativistic method to determine the electronic structure and electron collision ionization process of atoms placed in a semiclassical plasma. The method uses the effective interaction pseudo‐potential derived for general two interacting charged particles taking into account the quantum mechanical and screening effects to model the plasma environment. The Dirac equation with the aforementioned pseudo‐potential is solved numerically to obtain the bound state and continuous state wave functions. The method starts from the Dirac equation and thus includes the relativistic effects on the one‐electron level. The effects coming from the Breit interaction and quantum electrodynamics corrections are included. As a representative example, we investigate the plasma electron screening effect and the plasma ion screening effect, separated and combined, on the level delocalization and electron collision ionization process of hydrogen atoms placed in a strongly coupled semiclassical plasma environment. Properties of the spectra such as energies, oscillator strengths, and relativistic energy shifts corresponding to bound states are determined. The relativistic distorted wave method is used to provide a consistent and elaborate description of the ionization cross sections of the electron collisions involved. Our results reveal that the plasma electron shielding effect contributes to a reduced ionization potential and oscillator strength, while increasing the electron impact ionization cross section, when compared with the results of an isolated scenario. When the plasma ion shielding effect is included, these observed alterations are further enhanced, highlighting the considerable role of the plasma ion shielding effect in this process. Our results are in agreement with other theoretical data. The present study not only extends the relativistic distorted wave approach to the analysis of collision processes in semiclassical plasmas and evaluates the impact of the plasma ion screening effect but also has practical implications for radiation physics, inertial confinement devices, and the interiors of stars.

We present an improved model for the study of edge biasing in a tokamak plasma that incorporates electron and ion mobility contributions. The non-ambipolar nature of the drifts due to the electron/ion mobility terms influences the space charge separation due to edge biasing and affects plasma dynamics in the edge and SOL regions in a significant manner. In contrast to earlier studies, the present model enables simulation studies at higher biasing voltages. The inclusion of mobility enhances/decreases the effect of negative/positive biasing. The radial profiles of plasma density, electron temperature, radial electric field, and its shear for positive as well as negative biasing are investigated as a function of mobility.

It is pointed out that the role of electrons in the dynamics of pair ion and negative positive ion plasmas cannot be neglected even at extremely low density of electrons, i.e., ne0n+0≪mem+ (where nj0 is the background density of jth species and mj is the mass of the particles of the j-species while j = e, +, −) because electron thermal velocity is almost always larger than thermal velocities of ions, i.e., vT± ≪ vTe. An analysis of electrostatic waves in unmagnetized negative positive ion electron (NPIE) and pair ion electron (PIE) plasmas is presented for the case ωpe ≪ ωp+ (where ωpj=(4πnj0e2mj)1/2 is the plasma oscillation frequency corresponding to j-species). The electron dynamics contribute to electrostatic perturbations at ion plasma oscillation time scale at longer wavelengths for λDe2k2<1 where λDe=(Te4πne0)1/2 is the electron Debye length. On the other hand, the electron plasma wave turns into thermal wave when the conditions ωpe ≪ ωp± and 1≪λDe2k2 hold simultaneously and ion acoustic wave approaches the sum of ion plasma oscillation frequencies of positive and negative ions. The only electrostatic normal mode of such a plasma is the ion plasma wave corresponding to longer wavelengths, which also includes the contribution of electrons. The electron thermal wave is separated from plasma oscillations and electron time scale disappears with respect to electrostatic perturbations. Similar situation also occurs in plasmas having negatively charged dust particles. To elaborate these points, the analytical results are applied to the two experiments with NPIE and PIE plasmas.