Ionization Potential Depression Research Articles

Nonideal effects on ionization potential depression and ionization balance in dense Al and Au plasmas.

For low-density plasmas, the ionization balance can be properly described by the normal Saha equationin the chemical picture. For dense plasmas, however, nonideal effects due to the interactions between the electrons and ions and among the electrons themselves affect the ionization potential depression and the ionization balance. With the increasing of plasma density, the pressure ionization starts to play a more obvious role and competes with the thermal ionization. Based on a local-density temperature-dependent ion-sphere model, we develop a unified and self-consistent theoretical formalism to simultaneously investigate the ionization potential depression, the ionization balance, and the charge states distributions of the dense plasmas. In this work, we choose Al and Au plasmas as examples as Al is a prototype light element and Au is an important heavy element in many research fields such as in the inertial confinement fusion. The nonideal effect of the free electrons in the plasmas is considered by the single-electron effective potential contributed by both the bound electrons of different charge states and the free electrons in the plasmas. For the Al plasmas, we can reconcile the results of two experiments on measuring the ionization potential depression, in which one experiment can be better explained by the Stewart-Pyatt model while the other fits better with the Ecker-Kröll model. For dense Au plasmas, the results show that the double peak structure of the charge state distribution appears to be a common phenomenon. In particular, the calculated ionization balance shows that the two- and three-peak structures can appear simultaneously for denser Au plasmas above ∼30g/cm^{3}.

Dielectronic satellite emission from a solid-density Mg plasma: Relationship to models of ionization potential depression.

We report on experiments where solid-density Mg plasmas are created by heating with the focused output of the Linac Coherent Light Source x-ray free-electron laser. We study the K-shell emission from the helium- and lithium-like ions using Bragg crystal spectroscopy. Observation of the dielectronic satellites in lithium-like ions confirms that the M-shell electrons appear bound for these high charge states. An analysis of the intensity of these satellites indicates that when modeled with an atomic-kinetics code, the ionization potential depression model employed needs to produce depressions for these ions which lie between those predicted by the well known Stewart-Pyatt and Ecker-Kroll models. These results are largely consistent with recent density functional theory calculations.

Toward constraint of ionization-potential depression models in a convergent geometry

We demonstrate the value of inner-shell X-ray absorption spectroscopy for dense-plasma atomic physics and explore the coupling between constraint of the thermodynamic state and constraint of ionization-potential depression models. Synthetic K-shell absorption spectra are generated along a radius from a point-like core and analyzed using different ionization-potential depression models. Within this synthetic analysis framework, we identify plasma conditions (Te=400 eV, ρ=40 g/cm3) accessible by spherical implosions where K-shell absorption spectra discriminate between models if the material temperature is measured to a precision of 20%. The analysis is extensible to a finite-sized core and can be used to guide future studies of ionization-potential depression, informing material and radiative properties of matter in fusion plasmas and stellar interiors.

Plasma density effects on electron impact ionization.

We present new results on ionization by electron impacts in a dense plasma. We are interested in the density effect known as ionization potential depression and its role in atomic structure. Rather than using the well-known Stewart-Pyatt or Ecker-Kröll formulas for the ionization potential depression, we consider a distribution function of the ionization energy, which involves the plasma fluctuations due to ion dynamics. This distribution is calculated within classical molecular dynamics. The removal of the noise yields a new distribution which is composed of a small set of Gaussian peaks among which one peak is selected by considering the signal-to-noise ratio. This approach provides an ionization potential depression in good agreement with experimental results obtained at the Linac Coherent Light Source facility. Our results are also compared with other calculations. In a second part, we investigate the effects of the ionization potential depression and the fluctuations on ionization by electron impacts. We propose an expression of the cross sectionthat is based on an average over the ionization energy distribution. This cross sectioncan be calculated analytically. The main strength of our work is to account for the fluctuations due to ion dynamics.

The Role of Stepwise Photoionization in Measurements of the Ionization Potentials in Dense Plasma

The interaction of high-contrast high-intensity laser radiation with solids allows us to create hot or warm plasma of solid or even over-solid density, such as in the case of inertial fusion particularly. The multicharged ions contained in it can no longer be considered isolated. As a result, this leads to a decrease in the ionization potentials and to the disappearance of a number of bound ionic states. To describe the ionization potential depression, two major approaches are now used predominantly, where the key parameter is either average interelectronic or interionic distance. Since neither of the approaches can be substantiated purely theoretically, their applicability can only be established by comparison with experimental results. In recent experiments with X-ray free-electron lasers, it was concluded that the ionization potential depression rather depends on the interelectronic distance. However, when measuring ionization potentials, it was assumed that the main role in ionization processes is played by the direct photoionization of the ion ground state. In the present paper, we show that stepwise photoionization processes should play a significant role in dense plasma, disrupting a straight correspondence between the threshold in direct photoionization by X-ray laser photons and the actual ionization potential of multicharged ions. It means that the measurement results mentioned above are not correct, and the main conclusion about the importance of the interelectronic distance for depression of the ionization potential is not correct.

Generalized chemical model for plasmas with application to the ionization potential depression

On the basis of the generalized Poisson–Boltzmann equation derived from the Bogolyubov chain of equations for the equilibrium distribution functions in the pair correlation approximation, a general expression is proposed for the Helmholtz free energy of a system that contains any number of components and whose particles interact via arbitrary potentials. This opens up an extraordinary opportunity to simultaneously treat a whole range of physical effects including partial ionization, quantum effects of diffraction and electron degeneracy, short- and long-range interactions of charged particles with neutrals, finite size effects, etc. It is shown that all medium constituents are tied together in a single screening matrix, whose determinant and trace determine the excess contribution to the free energy. The approach developed is then applied to the problem of the ionization potential depression (IPD) leading to quite simple analytical expressions, which turn out to be useful for various practical purposes. In particular, for a single ionization from the neutral state the IPD is shown to significantly depend on the ionization degree such that it consists of the difference of charged and neutral contributions for a fully ionized plasma and turns non-zero for an almost neutral medium. On the other hand, for a multiple ionization process finite size effects of atoms and ions are demonstrated to be of great importance and accounted for in order to achieve good agreement with experimental data on the IPD under warm dense matter conditions.

The colliding planar shocks platform to study warm dense matter at the National Ignition Facility

We have developed an experimental platform at the National Ignition Facility that employs colliding planar shocks to produce warm dense matter with uniform conditions and enable high-precision equation of state measurements. The platform uses simultaneous x-ray Thomson scattering and x-ray radiography to measure the density, electron temperature, and ionization state in warm dense matter. The experimental platform is designed to create a large volume of uniform plasma (approximately 700×700×150μm3) at pressures approaching 100 Mbar and minimize the distribution of plasma conditions in the x-ray scattering volume, significantly improving the precision of the measurements. Here, we present the experimental design of the platform and compare hydrodynamic simulations to x-ray radiography data from initial experiments studying hydrocarbons, producing uniform densities within ±25% of the average probed condition. We show that the platform creates a homogeneous plasma that can be characterized using x-ray Thomson scattering. Thus, the new platform enables accurate measurements of plasma conditions necessary to test models for the equation of state and ionization potential depression in the warm dense matter regime.

Transitional Strength Under Plasma: Precise Estimations of Astrophysically Relevant Electromagnetic Transitions of Ar7, Kr7, Xe7, and Rn7 Under Plasma Atmosphere++++

The growing interest in atomic structures of moderately stripped alkali-like ions in the diagnostic study and modeling of astrophysical and laboratory plasma makes an accurate many-body study of atomic properties inevitable. This work presents transition line parameters in the absence or presence of plasma atmosphere for astrophysically important candidates Ar7+, Kr7+, Xe7+, and Rn7+. We employ relativistic coupled-cluster (RCC) theory, a well-known correlation exhaustive method. In the case of a plasma environment, we use the Debye Model. Our calculations agree with experiments available in the literature for ionization potentials, transition strengths of allowed and forbidden selections, and lifetimes of several low-lying states. The unit ratios of length and velocity forms of transition matrix elements are the critical estimation of the accuracy of the transition data presented here, especially for a few presented for the first time in the literature. We do compare our findings with the available recent theoretical results. Our reported data can be helpful to the astronomer in estimating the density of the plasma environment around the astronomical objects or in the discovery of observational spectra corrected by that environment. The present results should be advantageous in the modeling and diagnostics laboratory plasma, whereas the calculated ionization potential depression parameters reveal important characteristics of atomic structure.

Nonideal effect of free electrons on ionization equilibrium and radiative property in dense plasmas.

The thermodynamic as well as optical properties of strongly coupled plasmas depend crucially on the average degree of ionization and the ionic state composition, which, however, cannot be determined by using the normal Saha equationusually used for the ideal plasmas. Hence, an adequate treatment of the ionization balance and the charge state distribution of strongly coupled plasmas is still a challenge for theory due to the interactions between the electrons and ions and among the electrons themselves. Based on a local density temperature-dependent ion-sphere model, the Saha equationapproach is extended to the regime of strongly coupled plasmas by taking into account the free-electron-ion interaction, the free-free-electron interaction, the nonuniform free-electron space distribution, and the free-electron quantum partial degeneracy. All the quantities, including the bound orbitals with ionization potential depression, free-electron distribution, and bound and free-electron partition function contributions, are calculated self-consistently in the theoretical formalism. This study shows that the ionization equilibrium is evidently modified by considering the above nonideal characteristics of the free electrons. Our theoretical formalism is validated by the explanation of a recent experimental measurement of the opacity of dense hydrocarbon.

Multi-Configuration Calculation of Ionization Potential Depression

The modelling of ionization potential depression in warm and hot dense plasmas constitutes a real theoretical challenge due to ionic coupling and electron degeneracy effects. In this work, we present a quantum statistical model based on a multi-configuration description of the electronic structure in the framework of Density Functional Theory. We discuss different conceptual issues inherent to the definition of ionization potential depression and compare our results with the famous and widely-used Ecker-Kröll and Stewart-Pyatt models.

Homogeneous, Micron-Scale High-Energy-Density Matter Generated by Relativistic Laser-Solid Interactions.

Short-pulse, laser-solid interactions provide a unique platform for studying complex high-energy-density matter. We present the first demonstration of solid-density, micron-scale keV plasmas uniformly heated by a high-contrast, 400nm wavelength laser at intensities up to 2×10^{21} W/cm^{2}. High-resolution spectral analysis of x-ray emission reveals uniform heating up to 3.0keV over 1 μm depths. Particle-in-cell simulations indicate the production of a uniformly heated keV plasma to depths of 2 μm. The significant bulk heating and presence of highly ionized ions deep within the target are attributed to the few MeV hot electrons that become trapped and undergo refluxing within the target sheath fields. These conditions enabled the differentiation of atomic physics models of ionization potential depression in high-energy-density environments.

Plasma environmental effects in the atomic structure for simulating x-ray free-electron-laser-heated solid-density matter.

High energy density (HED) matter exists extensively in the Universe, and it can be created with extreme conditions in laboratory facilities such as x-ray free-electron lasers (XFEL). In HED matter, the electronic structure of individual atomic ions is influenced by a dense plasma environment, and one of the most significant phenomena is the ionization potential depression (IPD). Incorporation of the IPD effects is of great importance in accurate modeling of dense plasmas. All theoretical treatments of IPD so far have been based on the assumption of local thermodynamic equilibrium, but its validity is questionable in ultrafast formation dynamics of dense plasmas, particularly when interacting with intense XFEL pulses. A treatment of transient IPD, based on an electronic-structure calculation of an atom in the presence of a plasma environment described by classical particles, has recently been proposed [Phys. Rev. E 103, 023203 (2021)2470-004510.1103/PhysRevE.103.023203], but its application to and impact on plasma dynamics simulations have not been investigated yet. In this work, we extend XMDYN, a hybrid quantum-classical approach combining Monte Carlo and molecular dynamics, by incorporating the proposed IPD treatment into plasma dynamics simulations. We demonstrate the importance of the IPD effects in theoretical modeling of aluminum dense plasmas by comparing two XMDYN simulations: one with electronic-structure calculations of isolated atoms (without IPD) and the other with those of atoms embedded in a plasma (with IPD). At equilibrium, the mean charge obtained in the plasma simulation with IPD is in good agreement with the full quantum-mechanical average-atom model. The present approach promises to be a reliable tool to simulate the creation and nonequilibrium evolution of dense plasmas induced by ultraintense and ultrashort XFEL pulses.

Ionization potential depression in dense iron plasmas near solid density

In a dense hot plasma, the energy levels of an embedded ion are lowered by the induced screening potential, which is termed as the ionization potential depressions (IPDs) for the continuum levels. Recent experiments on the precision measurements of the IPDs in solid-density plasmas made it feasible to validate the widely used models. Yet, to date, most of the renewed experimental and theoretical verifications were focused on the low Z dense plasmas. In this work, the IPDs of heavier Fe plasmas were studied near solid density using a recently developed self-consistent temperature dependent ion-sphere model. The present results show reasonable agreement with the b4-potential method at some densities and temperatures, yet there exist large discrepancies between our predicted IPDs and those by the widely used simple closed analytical models. Namely, for Fe plasmas in a density range of 1–16 g cm−3 and a temperature range of 100–1000 eV, a simplified modification of Ecker–Kröll model predicts a much higher IPD than our model, whereas the Stewart–Pyatt, the ion-sphere, and the Debye–Hückel models predict much lower IPDs, which indicates the need of further study on the plasma screening potential. The results obtained in this work should be helpful for the astrophysical and inertial-fusion applications where the IPDs are vital parameters in determining the ionization balance.

Ionization by electron impacts and ionization potential depression

We calculate the cross-section of ionization by free-electron impacts in high or moderate density plasmas. We show that the so-called ionization potential depression (IPD) strongly affects the magnitude of the cross-section in the high-density domain. We use the well-known IPD formulas of Stewart–Pyatt and Ecker–Kröll. A more recent approach based on classical molecular dynamics simulation is also investigated. The latter provides an alternative way to calculate IPD values. At near-solid densities the effects of the free-electron degeneracy should be investigated. The rates are then calculated within the Fermi–Dirac statistics. We first use the semi-empirical formula of Lotz for ionization cross-section. The results may differ significantly from measured cross-sections or calculations with reliable atomic codes. Then, in a second step, we propose a new formula that combines the Lotz formula and a polynomial expansion in terms of the ratio of the energy of the incident electron and the ionization energy. The coefficients of the polynomial expansion are adjusted to fit the cross-section provided by robust atomic codes. A great advantage of the new formula is that it allows a fully analytical calculation of the ionization rate. Our results are compared to experiments measuring IPDs, cross-sections and rate coefficients on aluminum at high and moderate densities and on Be-like CNO ions.

Numerical study of radiating xenon plasma

In this paper numerical simulation of the spectral properties of xenon plasma is carried out for various parameters (temperature, density, pressure) within the framework of the Saha-Boltzmann approximation. For calculations, pre-prepared atomic databases with varying degrees of detail of ion states were used. The effect of ionization potential depression was taken into account. The spectral absorption coefficients and emissivity, as well as the spectral radiation energy flux for a homogeneous plasma in a spherically symmetric geometry, were obtained. The identification of strong spectral lines in the wavelength ranges of interest has been carried out.

Cтолкновительно-излучательная модель неравновесной плазмы с произвольным полем излучения

The collisional-radiative model for calculating the radiative and thermodynamic properties of a plasma with an arbitrary radiation field is considered. The basic equations of the model, formulas for calculating the rates of elementary processes, the absorption coefficient and emissivity, as well as the equation of state of matter are given. Methods for describing ionization potential depression in dense plasma are presented. A method is proposed for taking into account hot electrons with a temperature much higher than the plasma temperature.

Local field correction to ionization potential depression of ions in warm or hot dense matter.

An analytical self-consistent approach was recently established to predict the ionization potential depression (IPD) in multicomponent dense plasmas, which is achieved by considering the self-energy of ions and electrons within the quantum statistical theory. In order to explicitly account for the exchange-correlation effect of electrons, we incorporate the effective static approximation of local field correction (LFC) within our IPD framework through the connection of dynamical structure factor. The effective static approximation poses an accurate description for the asymptotic large wave number behavior with the recently developed machine learning representation of static LFC induced from the path-integral Monte Carlo data. Our calculation shows that the introduction of static LFC through dynamical structure factor brings a nontrivial influence on IPD at warm/hot dense matter conditions. The correlation effect within static LFC could provide up to 20% correction to free-electron contribution of IPD in the strong coupling and degeneracy regime. Furthermore, a new screening factor is obtained from the density distribution of free electrons calculated within the average-atom model, with which excellent agreements are observed with other methods and experiments at warm/hot dense matter conditions.

Effects of plasma screening on radiative transition and photoionization of Si[formula omitted]–Si[formula omitted] in a dense plasma environment

The screening induced by a dense plasma environment is crucially important for determining radiative atomic data including bound–bound radiative decay rates and photoionization cross sections, which are vital for obtaining accurate opacity. Previous experimental investigations of ionization potential depression have shown that the widely used analytical models of screening struggle to capture the essential physics in the solid-density plasma. In the present work, we investigate how plasma screening affects the radiative atomic data of Si10+–Si13+ embedded in a dense plasma environment using a self-consistent field finite temperature ion sphere model. The single-electron effective potential of an embedded atom has a short-range feature that determines the available number of bound states. Plasma screening is effective in modifying the matrix elements of the radiative dipole transitions, thereby generally increasing the photoionization cross section near the ionization threshold and decreasing the bound–bound radiative decay rates. The enhancement of the photoionization processes stems from lowering the ionization threshold and the shape and virtual-state resonances, where the upper bound levels become delocalized after a certain critical screening strength. With increasing plasma density, the Rydberg series for the bound–bound radiative transitions disappear successively.

Transient ionization potential depression in nonthermal dense plasmas at high x-ray intensity.

The advent of x-ray free-electron lasers (XFELs), which provide intense ultrashort x-ray pulses, has brought a new way of creating and analyzing hot and warm dense plasmas in the laboratory. Because of the ultrashort pulse duration, the XFEL-produced plasma will be out of equilibrium at the beginning, and even the electronic subsystem may not reach thermal equilibrium while interacting with a femtosecond timescale pulse. In the dense plasma, the ionization potential depression (IPD) induced by the plasma environment plays a crucial role for understanding and modeling microscopic dynamical processes. However, all theoretical approaches for IPD have been based on local thermal equilibrium (LTE), and it has been controversial to use LTE IPD models for the nonthermal situation. In this work, we propose a non-LTE (NLTE) approach to calculate the IPD effect by combining a quantum-mechanical electronic-structure calculation and a classical molecular dynamics simulation. This hybrid approach enables us to investigate the time evolution of ionization potentials and IPDs during and after the interaction with XFEL pulses, without the limitation of the LTE assumption. In our NLTE approach, the transient IPD values are presented as distributions evolving with time, which cannot be captured by conventional LTE-based models. The time-integrated ionization potential values are in good agreement with benchmark experimental data on solid-density aluminum plasma and other theoretical predictions based on LTE. The present work is promising to provide critical insights into nonequilibrium dynamics of dense plasma formation and thermalization induced by XFEL pulses.

Ionization potential depression and ionization balance in dense carbon plasma under solar and stellar interior conditions

Recent quantitative experiments on the ionization potential depression (IPD) in dense plasma show that the observational results are difficult to explain with the widely used analytical models for plasma screening. Here, we investigate the effect of plasma screening on the IPD and ionization balance of dense carbon plasma under solar and stellar interior conditions using our developed consistent nonanalytical model. The screening potential can be primarily attributed to the free electrons in the plasma and is determined by the microspace distribution of these free electrons. The ionization balance is determined by solving the Saha equation, including the effect of IPD. The predicted IPD and average ionization degree are larger than those obtained using the Stewart–Pyatt model for mass densities that are greater than 3.0 g cm−3. Under solar interior conditions, our results are in better agreement with the Ecker–Kröll model at electron temperatures and densities lower than 250 eV and 2.1 × 1023 cm−3 and in the best agreement with the ion-sphere model at 303 eV and 4.3 × 1023 cm−3. Finally, our results are compared with those obtained via a recent experiment on a CH-mixture plasma that has been compressed six times. The predicted average ionization degree of C in a CH mixture agrees better with the experiment than the Stewart–Pyatt and Thomas–Fermi models when the screening from free electrons contributed by hydrogen atoms is included. Our results provide useful information concerning the ionization balance and can be applied to investigate the opacity and equations of state for dense plasma under the solar and stellar interior conditions.