Local field correction to ionization potential depression of ions in warm or hot dense matter (original) (raw)
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Ionization-potential depression and dynamical structure factor in dense plasmas
Physical Review E, 2017
The properties of a bound electron system immersed in a plasma environment are strongly modified by the surrounding plasma. The modification of an essential quantity, the ionization energy, is described by the electronic and ionic self-energies including dynamical screening within the framework of the quantum statistical theory. Introducing the ionic dynamical structure factor as the indicator for the ionic microfield, we demonstrate that ionic correlations and fluctuations play a critical role in determining the ionization potential depression. This is in particular true for mixtures of different ions with large mass and charge asymmetry. The ionization potential depression is calculated for dense aluminum plasmas as well as for a CH plasma and compared to the experimental data and more phenomenological approaches used so far.
Effective field theory for highly ionized plasmas
Physics Reports, 2001
We examine the equilibrium properties of hot, non-relativistic plasmas. The partition function and density correlation functions of a plasma with several species are expressed in terms of a functional integral over electrostatic potential distributions. This is a convenient formulation for performing a perturbative expansion. The theory is made well-defined at every stage by employing dimensional regularization which, among other virtues, automatically removes the unphysical (infinite) Coulomb self-energy contributions. The leading order, field-theoretic tree approximation automatically includes the effects of Debye screening. No further partial resummations are needed for this effect. Subleading, one-loop corrections are easily evaluated. The two-loop corrections, however, have ultraviolet divergences. These correspond to the short-distance, logarithmic divergence which is encountered in the spatial integral of the Boltzmann exponential when it is expanded to third order in the Coulomb potential. Such divergences do not appear in the underlying quantum theory-they are rendered finite by quantum fluctuations. We show how such divergences may be removed and the correct finite theory obtained by introducing additional local interactions in the manner of modern effective quantum field theories. We compute the two-loop induced coupling by exploiting a non-compact su(1, 1) symmetry of the hydrogen atom. This enables us to obtain explicit results for density-density correlation functions through two-loop order and thermodynamic quantities through three-loop order. The induced couplings are shown to obey renormalization group equations, and these equations are used to characterize all leading logarithmic contributions in the theory. A linear combination of pressure plus energy and number densities is shown to be described by a field-theoretic anomaly. The effective Lagrangian method that we employ yields a simple demonstration that, at long distance, correlation functions have an algebraic fall off (because of quantum effects) rather than the exponential damping of classical Debye screening. We use the effective theory to compute, easily and explicitly, this leading long-distance behavior of density correlation functions. The presentation is pedagogical and self-contained. The results for thermodynamic quantities at three-loop [or O(n 5/2)] order, and for the leading long-distance forms of correlation functions, agree with previous results in the literature, but they are obtained in a novel and simple fashion using the effective field theory. In C.
Path-Integral Monte Carlo Simulation of the Warm Dense Homogeneous Electron Gas
Physical Review Letters, 2013
We perform calculations of the 3D finite-temperature homogeneous electron gas (HEG) in the warm-dense regime (rs ≡ (3/4πn) 1/3 a −1 B = 1.0−40.0 and Θ ≡ T /TF = 0.0625−8.0) using restricted path integral Monte Carlo (RPIMC). Precise energies, pair correlation functions, and structure factors are obtained. For all densities, we find a significant discrepancy between the ground state parameterized local density approximation (LDA) and our results around TF . These results can be used as a benchmark for improved functionals, as well as input for orbital-free DFT formulations.
Physical Review E, 2012
We study the problem of electron-ion temperature equilibration in plasmas. We consider pure H at various densities and temperatures and Ar-doped H at temperatures high enough so that the Ar is fully ionized. Two theoretical approaches are used: classical molecular dynamics (MD) with statistical two-body potentials and a generalized Lenard-Balescu (GLB) theory capable of treating multicomponent weakly coupled plasmas. The GLB is used in two modes: (1) with the quantum dielectric response in the random-phase approximation (RPA) together with the pure Coulomb interaction and (2) with the classical (h −→ 0) dielectric response (both with and without local-field corrections) together with the statistical potentials. We find that the MD results are described very well by classical GLB including the statistical potentials and without local-field corrections (RPA only); worse agreement is found when static local-field effects are included, in contradiction to the classical pure-Coulomb case with like charges. The results of the various approaches are all in excellent agreement with pure-Coulomb quantum GLB when the temperature is high enough. In addition, we show that classical calculations with statistical potentials derived from the exact quantum two-body density matrix produce results in far better agreement with pure-Coulomb quantum GLB than classical calculations performed with older existing statistical potentials.
Self-consistent average-atom scheme for electronic structure of hot and dense plasmas of mixture
Physical review. E, Statistical, nonlinear, and soft matter physics, 2002
An average-atom model is proposed to treat the electronic structures of hot and dense plasmas of mixture. It is assumed that the electron density consists of two parts. The first one is a uniform distribution with a constant value, which is equal to the electron density at the boundaries between the atoms. The second one is the total electron density minus the first constant distribution. The volume of each kind of atom is proportional to the sum of the charges of the second electron part and of the nucleus within each atomic sphere. By this way, one can make sure that electrical neutrality is satisfied within each atomic sphere. Because the integration of the electron charge within each atom needs the size of that atom in advance, the calculation is carried out in a usual self-consistent way. The occupation numbers of electron on the orbitals of each kind of atom are determined by the Fermi-Dirac distribution with the same chemical potential for all kinds of atoms. The wave functio...
Characterization of electron states in dense plasmas and its use in atomic kinetics modeling
Journal of Quantitative Spectroscopy and Radiative Transfer, 2003
We describe a self-consistent statistical approach to account for plasma density e ects in collisional-radiative kinetics. The approach is based on the characterization of three distinct types of electron states, namely, bound, collectivized, and free, and on the formalism of the e ective statistical weights (ESW) of the bound states. The present approach accounts for individual and collective e ects of the surrounding electrons and ions on atomic (ionic) electron states. High-accuracy expressions for the ESWs of bound states have been derived. The notions of ionization stage population, free electron density, and rate coe cient are redeÿned in accordance with the present characterization scheme. The modiÿed expressions for the probabilities of electron-impact induced transitions as well as spontaneous and induced radiative transitions are then obtained. The in uence of collectivized states on a dense plasma ionization composition is demonstrated to be strong. Examples of calculated ESWs and populations of ionic quantum states for steady state and transient plasmas are given. ?
First Principle Thermodynamic and Dynamic Simulations for Dense Quantum Plasmas
Contributions to Plasma Physics, 2005
We present a detailed analysis of temperature-dependent effective quantum pair potentials. These potentials are derived from first-principle path integral Monte Carlo simulations and are accurate even at strong coupling and partial ionization. They can be efficiently used in molecular-dynamics (MD) simulations to obtain accurate thermodynamic and dynamic properties of strongly coupled hydrogen down to the temperatures of about 60 000 K. Furthermore, using spin-dependent pair potentials, dynamic structure factors and spin-density correlation functions were calculated for different values of coupling and degeneracy.
Ionization by electron impacts and ionization potential depression
Journal of Physics B: Atomic, Molecular and Optical Physics
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 t...
Ionization potential depression and Pauli blocking in degenerate plasmas at extreme densities
Physical Review E, 2019
New facilities explore warm dense matter (WDM) at conditions with extreme densities (exceeding ten times condensed matter densities) so that electrons are degenerate even at temperatures of 10 − 100 eV. Whereas in the non-degenerate region correlation effects such as Debye screening are relevant for the ionization potential depression (IPD), new effects have to be considered in degenerate plasmas. In addition to the Fock shift of the self-energies, the bound-state Pauli blocking becomes important with increasing density. Standard approaches to IPD such as Stewart-Pyatt and widely used opacity tables (e.g., OPAL) do not contain Pauli blocking effects for bound states. The consideration of degeneracy effects leads to a reduction of the ionization potential and to a higher degree of ionization. As an example, we present calculations for the ionization degree of carbon plasmas at T = 100 eV and extreme densities up to 40 g/cm 3 , which are relevant to experiments that are currently scheduled at the National Ignition Facility.
Journal of Physics: Conference Series, 2017
The radiative properties of an emitter surrounded by a plasma, are modified through various mechanisms. For instance the line shapes emitted by bound-bound transitions are broadened and carry useful information for plasma diagnostics. Depending on plasma conditions the electrons occupying the upper quantum levels of radiators no longer exist as they belong to the plasma free electron population. All the charges present in the radiator environment contribute to the lowering of the energy required to free an electron in the fundamental state. This mechanism is known as ionization potential depression (IPD). The knowledge of IPD is useful as it affects both the radiative properties of the various ionic states and their populations. Its evaluation deals with highly complex n-body coupled systems, involving particles with different dynamics and attractive ion-electron forces. A classical molecular dynamics (MD) code, the BinGo-TCP code, has been recently developed to simulate neutral multi-component (various charge state ions and electrons) plasma accounting for all the charge correlations. In the present work, results on IPD and other dense plasma statistical properties obtained using the BinGo-TCP code are presented. The study focuses on aluminum plasmas for different densities and several temperatures in order to explore different plasma coupling conditions.