Plasma Screening Effects Research Articles

Single-photon photoionization of highly charged ions under warm- and hot-dense plasmas using a unified description of screening

We present a detailed investigation of the spectral properties and photoionization of highly charged ions subjected to warm- and hot-dense plasma environments. A unified framework, based on the finite-temperature orbital-free density functional theory, is adopted to describe (warm- and hot-dense) plasma screening effects on the nucleus-electron interaction. Self-consistent solving the coupled radial Diarc equations for both bound and continuum wave functions is used through the model, EPPP, we developed, to account the relativistic and plasma shielding effects, which is based on the flexible atomic code. The key features of the proposed model are the capacities to systematically include gradient corrections and exchange-correlation effects. Additionally, numerical tests are conducted to validate the accuracy and stability of the model. The transition energies, radiative transition parameters, ionization potentials, and photoionization (radiation recombination) cross sections of an exemplary ion Al12+are studied under finite temperature and density conditions. The present work offers an insight into electron screening of ions and is expected to be beneficial for plasma modeling.

Analysis of circular polarization of the emitted photon in plasmas

In this paper, a new relativistic distorted wave approximation for cross section describing longitudinally-polarized electron impact excitation of ions in the presence of a strongly coupled plasma is proposed and implemented based on the flexible atomic code. The uniform electron gas model is used to incorporate the plasma effects, which includes the effect of static plasma screening on nuclear charge and the effect of confinement due to the neighbouring ions. For the bound and continuum wavefunctions, the Dirac equation with the ion-sphere potential is solved to account for relativistic effects. In order to check the consistency of the modifications, a self consistent theoretical attempt using the multiconfiguration Dirac-Fock method is also carried out to get the energy levels accounting for the plasma environment within the ion-sphere model. For the collision dynamics, as examples of applications, we investigate the total cross sections, the magnetic sublevels cross sections, and the degrees of circular polarizations of fluorescence radiation after 1s2s01→1s2ss03 and 1s2s01→1s2pp13,1 excitations of Helium-like Fe XXV ion by longitudinally-polarized electron impact with the ion-sphere potential. It is shown that the behavior of the cross sections for a pure Coulomb potential changes rapidly due to the plasma screening effects described by the ion-sphere potential in the process of calculating scattering matrix elements. A detailed, quantitative, comparison between the present results and other available theoretical values is presented for the plasma-free cases, showing good agreement. Our results contribute to a better understanding of the fundamentals of fluorescence polarization in strongly coupled plasmas. Results obtained in this work are beneficial for the diagnostic determination of laboratory plasmas.

Fluctuating temperature and baryon chemical potential in heavy-ion collisions and the position of the critical end point in the effective QCD phase diagram

We use the linear sigma model with quarks to locate the critical end point in the effective QCD phase diagram accounting for fluctuations in temperature and quark chemical potential. For this purpose, we use the non-equilibrium formalism provided by the superstatistics framework. We compute the effective potential in the high- and low-temperature approximations up to sixth order and include the contribution of ring diagrams to account for plasma screening effects. We fix the model parameters from relations between the thermal sigma and pion masses imposing a first order phase transition at zero temperature and a finite critical value for the baryon chemical potential that we take of order of the nucleon mass. We find that the CEP displacement due to fluctuations in temperature and/or quark chemical potential is almost negligible.

Plasma screening effects on the atomic structure of He-like ions embedded in strongly coupled plasma

The influence of plasma screening on the transition energies and radiative properties of He-like ions embedded in dense plasma environment has been analyzed. For this purpose, the multiconfiguration Dirac-Fock method and Flexible Atomic Code incorporating the analytical plasma screening potential of Li et al. (2019) [39] and uniform electron gas model potential have been implemented. Our calculated line shifts of 1s2S01→1s3pP1o1 He-β transition of Cl15+ are in excellent agreement with the recent measurements of Beiersdorfer et al. (2019) [11]. The plasma shielding effects on 1s2S01→1snpP1o3(n=2,3) and 1s2S01→1snpP1o1(n=2,3) transitions of Ar16+, Ti20+ and Fe24+ ions have also been studied. It is found that transition energies for these transitions are red shifted with respect to free electron densities. The present results should be advantageous in the modeling and diagnostics of laboratory and astrophysical plasmas.

Generalized potential for confined positronium atom immersed in plasmas

We suggest, for the first time, the more general exponential cosine screened Coulomb (MGECSC) potential to investigate the positronium (Ps) atom immersed in Debye and quantum plasmas. Ps atom immersed in Debye and quantum plasmas under spherical confinement is examined by solving the corresponding Schrödinger equation via the tridiagonal matrix method. The MGECSC potential has four different sets to model Debye and quantum plasmas. But, we consider only two sets as the screened Coulomb (SC) potential for Debye plasma and the MGECSC potential for quantum plasma. The results of the confinement and the plasma screening effects on the energies, radial matrix elements, dipole polarizabilities and oscillator strengths of Ps atom are obtained, discussing in detail. It is worthwhile to specify that the spectroscopic features of Ps atom located in only plasma environment enable detailed information about plasma environment. The MGECSC potential is proposed to model various interactions of Ps atom immersed in plasma environment. In this study, the necessity and details of the MGECSC potential is discussed.

Influence of plasma screening on the energies and transition properties of the Al9+ ion using Debye and ion-sphere models

Investigations on the energies and radiative properties of a highly charged ion embedded in plasma in the weak- and strong-coupling regimes are made, taking the Al9+ ion as an example. The Debye and ion-sphere (IS) potentials are adopted to describe the plasma screening effects, respectively. The multiconfiguration Dirac-Fock (MCDF) method is employed to describe the relativistic and electronic correlation effects in the above atomic system. The screening effects on the ionization potential (IP), transition energies, and radiative rates are estimated. Results obtained are compared with the available results in the literature. Comparisons between the Debye and IS models results are also carried out considering similar plasma conditions. The present data are useful for diagnostics of astrophysical and laboratory plasmas.

Electron capture, excitation and ionization processes in He2+–H collisions in dense quantum plasmas

Electron capture, excitation and ionization processes in He2+–H collisions taking place in quantum plasmas are studied by employing the two-center atomic orbital close coupling (TC-AOCC) method. The Debye-Huckel-cosine (DHC) potential is used to describe the plasma screening effects on the Coulomb interaction between charged particles. The properties of eigenenergies of hydrogen-like atom with DHC potential are investigated as function of the screening length of the potential. It is found that the binding energies of nl states decrease with decreasing the screening length of the potential. The dynamics of excitation, electron capture and ionization processes in He2+–H collision system is investigated when the screening length of the potential varies for a wide collision energy range. The TC-AOCC cross sections are compared with those for the pure Coulomb potential and, for the total electron capture, with the results of classical trajectory Monte Carlo method.

Dipole and generalized oscillator strength derived electronic properties of an endohedral hydrogen atom embedded in a Debye-Hückel plasma

We report electronic properties of a hydrogen atom encaged by an endohedral cavity under the influence of a weak plasma interaction. We implement a finite-difference approach to solve the Schrödinger equation for a hydrogen atom embedded in an endohedral cavity modeled by the Woods-Saxon potential with well depth V0, inner radius R0, thickness Δ, and smooth parameter γ. The plasma interaction is described by a Debye-Hückel screening potential that characterizes the plasma in terms of a Debye screening length λD. The electronic properties of the endohedral hydrogen atom are reported for selected endohedral cavity well depths, V0, and screening lengths, λD, that emulate different confinement and plasma conditions. We find that for low screening lengths, the endohedral cavity potential dominates over the plasma interaction by confining the electron within the cavity. For large screening lengths, a competition between both interactions is observed. We assess and report the photo-ionization cross section, dipole polarizability, mean excitation energy, and electronic stopping cross section as function of λD and V0. We find a decrease of the Generalized Oscillator Strength (GOS) when the final excitation is to an s state as the plasma screening length decreases. For a final excitation into a p state, we find an increase in the GOS as the endohedral cavity well-depth increases. For the case of the electronic stopping cross section, we find that the plasma screening and endohedral cavity effects are larger in the low-to-intermediate projectile energies for all potential well depths considered. Our results agree well to available theoretical and experimental data and are a first step towards the understanding of dipole and generalized oscillator strength dependent properties of an atom in extreme conditions encaged by an endohedral cavity immersed in a plasma medium.

Relativistic effects on the energy levels and radiative properties of He-like ions immersed in Debye plasmas

Systematic investigations are performed for the energy levels and radiative properties for selected He-like C4+, Ne8+, Ar16+, and Kr34+ ions embedded in weakly coupled plasmas. For the conditions in which the Coulomb coupling parameter is small, the standard Debye model is adopted to describe the plasma screening effects. Within the relativistic framework, the modified version of the Flexible Atomic Code computations is carried out by considering a Debye-Hückel potential, in which the plasma screening is taken into account for both the electron-nucleus and electron-electron (e-e) interactions. An independent calculation for various Debye lengths is also presented using the multiconfiguration Dirac-Fock method for comparison purposes. For the nonrelativistic treatment, the analytical solution of the Schrödinger equation with the Debye screened potential is proposed. The variation method is developed with Slater wave function as a trial wave function that contains the variational parameters. An exact analytical expression of relativistic corrections such as the mass-velocity correction, the one/two-body Darwin correction, the spin-spin contact interaction correction, and the orbit-orbit interaction correction is derived. Differences among our three kinds of calculated energy levels and transition properties are analyzed in terms of the nuclear charge and/or the Debye length. Systematic trend is observed for all the properties under study with respect to increased screening. The influence of relativistic effects is also investigated in detail and found to play an important role in these systems. Our results are compared with available results from other theoretical calculations and the experimental values in the literature, and a good agreement is achieved. This work should be useful for astrophysical applications where such plasma environments exist.

Relativistic calculations of fine-structure energy levels of He-like Ar in dense plasmas**Project supported by the National Natural Science Foundation of China (Grant No. 11474208) and the Doctoral Science Foundation of Longdong University, China (Grant No. XYBY1704).

The fine-structure energy levels of 1s2s and 1s2p atomic states for the He-like Ar ion immersed in dense plasmas are calculated. The ion sphere model is used to describe the plasma screening effect on the tested ion. The influences of the hard sphere confinement and plasma screening on the fine-structure energy levels are investigated respectively. The calculated results show that the confined effect of the hard sphere on the fine-structure energy levels increases with decreasing hard sphere radius, and the plasma screening effect on the fine-structure energy levels increases with the increase of free electron density. In dense plasmas, the confined effect of the hard sphere on the fine-structure energy levels can be neglected generally, compared with the contribution from free electron screening. An interesting phenomenon about the energy level crossing is found among 1s2s (1S0) and 1s2p (3P0,1) atomic states. The results reported at the present work are useful for plasma diagnostics.

Plasma Response to Resonant Perturbations at Tokamak Edge

In certain circumstances, plasma response suppresses magnetic islands expected at perturbed resonant magnetic surfaces. We investigate the plasma response to the resonant magnetic perturbations in a large aspect ratio tokamak perturbed by external resonant helical windings, considering polar toroidal coordinates for which analytical toroidal equilibrium solutions and perturbing fields are available. We apply an empirical approach to mimic the plasma screening effects by introducing presumed plasma current sheets on the resonance surfaces to cancel the RMP effects. Numerical examples show the effect of plasma response reducing magnetic islands at the plasma edge and also regularizing field lines around the resonant surface. The distribution of connection lengths along the plasma cross section indicates that the plasma response increases the connection lengths since more toroidal turns are performed until a field line reaches the tokamak wall.

QCD phase diagram from chiral symmetry restoration: analytic approach at high and low temperature using the Linear Sigma Model with Quarks

We use the linear sigma model with quarks to study the QCD phase diagram from the point of view of chiral symmetry restoration. We compute the leading order effective potential for high and low temperatures and finite quark chemical potential, up to the contribution of the ring diagrams to account for the plasma screening effects. We fix the values of the model couplings using physical values for the input parameters such as the vacuum pion and sigma masses, the critical temperature at vanishing quark chemical potential and the conjectured end point value of the baryon chemical potential of the transition line at vanishing temperature. We find that the critical end point (CEP) is located at low temperatures and high quark chemical potentials $(\mu^{\text{CEP}}>320\ {\mbox{MeV}},T^{\text{CEP}}<40\ {\mbox{MeV}})$.

Angular Distribution and Linear Polarization of X-ray Radiation Resulting from Electron Impact Excitation of Highly Charged Ions in Debye Plasmas

Plasma-screening effects on the $$1s _{1/2} \rightarrow 2l \; (l = s , p )$$ and $$1s _{1/2} \rightarrow 3d _{3/2}$$ electron-impact excitation of highly charged ions are investigated, together with their subsequent radiative decay. The analysis is performed based on the multi-configuration Dirac–Fock method and the fully relativistic distorted-wave method incorporating the Debye–Huckel potential. To explore the nature of the effects, calculations are carried out based on detailed analyses of the integrated total and magnetic sublevel cross sections, the alignment parameters, the linear polarizations, and the angular distribution of the X-ray photoemission, as well as on corresponding data calculated in various Debye lengths/environments, taking the $$2p _{3/2}\rightarrow 1s _{1/2}$$ and $$3d _{3/2}\rightarrow 1s _{1/2}$$ characteristic lines of H-like $$\hbox {Fe}^{25+}$$ ion as an example. The present results are compared with experimental data and other theoretical predictions where available.

Information-theoretic measures of hydrogen-like ions in weakly coupled Debye plasmas

Recent development of information theory provides researchers an alternative and useful tool to quantitatively investigate the variation of the electronic structure when atoms interact with the external environment. In this work, we make systematic studies on the information-theoretic measures for hydrogen-like ions immersed in weakly coupled plasmas modeled by Debye-Hückel potential. Shannon entropy, Fisher information, and Fisher-Shannon complexity in both position and momentum spaces are quantified in high accuracy for the hydrogen atom in a large number of stationary states. The plasma screening effect on embedded atoms can significantly affect the electronic density distributions, in both conjugate spaces, and it is quantified by the variation of information quantities. It is shown that the composite quantities (the Shannon entropy sum and the Fisher information product in combined spaces and Fisher-Shannon complexity in individual space) give a more comprehensive description of the atomic structure information than single ones. The nodes of wave functions play a significant role in the changes of composite information quantities caused by plasmas. With the continuously increasing screening strength, all composite quantities in circular states increase monotonously, while in higher-lying excited states where nodal structures exist, they first decrease to a minimum and then increase rapidly before the bound state approaches the continuum limit. The minimum represents the most reduction of uncertainty properties of the atom in plasmas. The lower bounds for the uncertainty product of the system based on composite information quantities are discussed. Our research presents a comprehensive survey in the investigation of information-theoretic measures for simple atoms embedded in Debye model plasmas.

Spectra of confined positronium

Positronium is studied under the effect of spherically confined plasma environment. Exponentially Cosine Screened Coulomb potential (ECSC) has been used to include the dense plasma screening effect on positronium. Time independent Schrodinger equation is solved numerically. Various physical parameters such as energy eigenvalues, radial matrix elements, oscillator strengths, and polarizability are well explored as a function of confinement parameters. Oscillator strength gets drastically modified under confinement. We have also obtained the results for Ps confined under spherically confined Debye potential and compared with results of ECSC potential. Also incidental degeneracy for different values of confinement parameters has been reported for the first time for positronium.

Plasma-screening effects on positronium formation**Project supported by the National Natural Science Foundation of China (Grant Nos. 11404223, 11447158, and 11604223) and the Doctoral Program Foundation of Shenyang Aerospace University, China (Grant No. 13YB26).

Plasma-screening effects on positronium (Ps) formation for positron–hydrogen collisions in a Debye plasma environment is further investigated using the screening approximation model with the inclusion of the modified structure of Ps. More accurate Ps formation cross sections (n = 1, 2) are obtained for various Debye lengths from the Ps formation thresholds to 50 eV. The influence of considering modified bound-state wave functions and eigenenergies for the Ps is found to result in the reduction of the Ps formation cross sections at low energies, whereas it cannot counteract the enhancement of the Ps formation by the Debye screening.

Characteristics of Polarisation in the Ramsauer–Townsend Minima in Strongly Coupled Semiclassic Plasmas

Abstract The influence of quantum shielding on the Ramsauer–Townsend phenomena for the total electron–atom polarisation collision cross-section is investigated in partially ionised strongly coupled semiclassic plasmas. The result shows that the quantum shielding effect changes the position of the Ramsauer energy in partially ionised strongly coupled plasmas. It is also found that the quantum shielding effect enhances the total electron–atom collision cross-section when the collision energy is greater than the Ramsauer energy; however, it suppresses the collision cross-section when the collision energy is smaller than the Ramsauer energy. In addition, it is shown that the plasma screening effect significantly changes the position of the Ramsauer energy and the influence of plasma screening on the magnitude of the collision cross-section is more significant near the Ramsauer energy domain. The variations of the Ramsauer energy and the collision cross-section due to the quantum shielding effect are also discussed.

Influence of plasma environment on K-line emission in highly ionized iron atoms evaluated using a Debye–Hückel model

The influence of plasma environment on the atomic parameters associated with the K-vacancy states has been investigated theoretically for several iron ions. To do this, a time-averaged Debye–Hückel potential for both the electron–nucleus and electron–electron interactions has been considered in the framework of relativistic multiconfiguration Dirac–Fock computations. More particularly, the plasma screening effects on ionization potentials, K-thresholds, transition energies, and radiative rates have been estimated in the astrophysical context of accretion disks around black holes. In the present paper, we describe the behaviour of those atomic parameters for Ne-, Na-, Ar-, and K-like iron ions.

Electrostatic interaction of macroparticles in a plasma in the strong screening regime

We have studied the electrostatic interaction of spherical particles in an equilibrium plasma or an electrolyte in the moderate and strong screening regimes when the macroparticle size is comparable with or much larger than the Debye screening radius. We have developed an approximate theory of the electrostatic interaction of macroparticles in the case of constant potentials of their surfaces in the weak or moderate screening regimes. In this theory, the charges of macroparticles with a fixed spacing between them are determined using vacuum capacitive coefficients, which are corrected taking into account the plasma screening effects. The force of interaction with the resultant charges is calculated based on the solution of the problem of interaction in a homogeneous dielectric (vacuum) and is multiplied by the plasma factor. We have also obtained an approximate solution to the problem in the strong screening regime. Comparison with the exact solution has demonstrated high accuracy of the proposed methods of calculation.

Photoionization of hydrogen-like ions in dense quantum plasmas

The photoionization of hydrogen-like ions in n≤3 bound states, embedded in cold, dense quantum plasmas, is investigated in detail. The electron energies and wave functions for the bound and continuum states are determined by numerically solving the scaled Schrödinger equation by the fourth-order symplectic integration scheme. The monotonic behavior of the photoionization cross section for a pure Coulomb potential is dramatically changed due to the plasma screening effects described by the cosine-Debye-Hückel potential. In the region of low photoelectron energies, the photoionization cross section, besides the usual Wigner-law threshold behavior, exhibits a rich structure of shape and virtual-state resonances when the plasma screening parameter takes values around the critical screening parameter for which a bound state enters the continuum. It is observed that a shape resonance is followed by a Cooper minimum in the photoionization cross section when the principal quantum number of continuum quasi-bound state is equal to the one of the initial bound states.