Non-local Thermodynamic Equilibrium Plasmas Research Articles

Monte Carlo method for investigating population kinetics in non-local thermodynamic equilibrium plasmas

We propose a new method to solve the collisional-radiative (CR) model with the Monte Carlo method for investigating population kinetics of non-local thermodynamic equilibrium plasmas. The CR model is solved using massive sample particles accounting detailed energy levels. Whether an atom/ion undergoes an ionization/excitation/decay process is determined by probabilities calculated from ionization cross-sections, excitation and decay rates. By continuously iterating this process for massive atoms/ions, the ionization population distribution is obtained. The numerical convergence can be achieved for a mid-Z element using 103 particles in the Monte Carlo simulation. The results of the Monte Carlo simulations are compared with other methods and experimental results. The self emission spectra of silicon plasma is obtained and the ionization population distribution of silicon and iron plasmas are calculated. The proposed method can be used to interpret high energy density experiments and astrophysical phenomena where non-local thermodynamic equilibrium effects play vital roles.

Decreasing ultrafast x-ray pulse durations with saturable absorption and resonant transitions.

Saturable absorption is a nonlinear effect where a material's ability to absorb light is frustrated due to a high influx of photons and the creation of electron vacancies. Experimentally induced saturable absorption in copper revealed a reduction in the temporal duration of transmitted x-ray laser pulses, but a detailed account of changes in opacity and emergence of resonances is still missing. In this computational work, we employ nonlocal thermodynamic equilibrium plasma simulations to study the interaction of femtosecond x rays and copper. Following the onset of frustrated absorption, we find that a K-M resonant transition occurring at highly charged states turns copper opaque again. The changes in absorption generate a transient transparent window responsible for the shortened transmission signal. We also propose using fluorescence induced by the incident beam as an alternative source to achieve shorter x-ray pulses. Intense femtosecond x rays are valuable to probe the structure and dynamics of biological samples or to reach extreme states of matter. Shortened pulses could be relevant for emerging imaging techniques.

Ionization balance of non-LTE plasmas from an average-atom collisional-radiative model

We present a simplified version of an average-atom collisional-radiative model employing both local-thermodynamic-equilibrium average-atom and isolated-ion atomic data. The simplifications introduced do not lead to any substantial errors, and they significantly speed up calculations compared with the basic average-atom model involving direct solution of the self-consistent-field equations. Average ion charges, charge state distributions, and emission spectra of non-local-thermodynamic-equilibrium (NLTE) gold plasmas calculated using various modifications of the average-atom collisional-radiative model are compared with those obtained using the THERMOS model with the detailed configuration accounting approach. We also propose an efficient method to calculate thermodynamic functions of NLTE plasmas in the context of the simplified average-atom collisional-radiative model.

Measurement of L-shell emission from mid-Z targets under non-LTE conditions using Transmission Grating Spectrometer and DANTE power diagnostics.

In this work, we present the measurement of L-band emission from buried Sc/V targets in experiments performed at the OMEGA laser facility. The goal of these experiments was to study non-local thermodynamic equilibrium plasmas and benchmark atomic physics codes. The L-band emission was measured simultaneously by the time resolved DANTE power diagnostic and the recently fielded time integrated Soreq-Transmission Grating Spectrometer (TGS) diagnostic. The TGS measurement was used to support the spectral reconstruction process needed for the unfolding of the DANTE data. The Soreq-TGS diagnostic allows for broadband spectral measurement in the 120 eV-2000 eV spectral band, covering L- and M-shell emission of mid- and high-Z elements, with spectral resolution λ/Δλ = 8-30 and accuracy better than 25%. The Soreq-TGS diagnostic is compatible with ten-inch-manipulator platforms and can be used for a wide variety of high energy density physics, laboratory astrophysics, and inertial confinement fusion experiments.

Super Transition Arrays: A Tool for Studying Spectral Properties of Hot Plasmas

For the theoretical study of X and extreme-UV spectra of ions in plasmas, quantum mechanics brings more detailed results than statistical physics. However, it is impossible to handle individually the billions of levels that must be taken into account in order to properly describe hot plasmas. Such levels can be gathered into electronic configurations or superconfigurations (groups of configurations) and the corresponding calculations rely on appropriate statistical methods, for local or non-local thermodynamic equilibrium plasmas. In this article we present the basic principles of the Super-Transition-Array approach as well as its practical implementation. During the last decades, calculations performed with the SCO code (Superconfiguration Code for Opacity) have been compared to opacity measurements. The code includes static screening of ions by plasma and is well suited for studying plasma density effects (for example pressure ionization) on opacity and equation of state. The recently developed SCO-RCG code (Superconfiguration Code for Opacity combined with Robert Cowan’s “G” subroutine) combines statistical methods from SCO and fine-structure (detailed-level-accounting) calculations using subroutine RCG from Cowan’s code. SCO-RCG enables us to obtain very detailed spectra and to significantly improve the interpretation of experimental spectra. The Super-Transition-Array formalism is still the cornerstone of several opacity codes, and new ideas are emerging, such as the Configurationally Resolved-Super-Transition-Array approach or the extension of the Partially Resolved-Transition-Array concept to the superconfiguration method.

A hybrid method for investigating the detailed emission spectra of mid-Z plasmas in non-local thermodynamic equilibrium: Ge as an example

The detailed radiative properties of plasmas in non-local thermodynamic equilibrium (NLTE) are important for determining experimental plasma states. However, a complete detailed-level-accounting approach calculation is impractical for mid- and high-Z elements. Herein, we propose a hybrid method for obtaining the detailed radiative properties of mid-Z NLTE plasmas. First, a large-scale rate equation within the framework of a detailed-configuration-accounting method is established using atomic data in a configuration–configuration formalism. Second, we assume that the population distributions in fine-structure levels belonging to a particular configuration are in equilibrium. Thus, the populations at fine-structure levels are obtained through the populations in the corresponding configurations. Finally, detailed radiative properties are calculated using the populations in fine-structure levels and radiative data in level–level formalism. Such a method can balance computation costs and accuracy. Examples utilizing Ge plasmas demonstrate that the proposed method can better predict detailed structures in emission spectra than the detailed-configuration-accounting method.

Atomic kinetics calculations of complex highly-charged ions in plasmas in non-local thermodynamic equilibrium by using a Monte-Carlo approach

A new calculation of atomic kinetics of multiple-charged tungsten ions in a high temperature plasma in the non-local thermodynamic equilibrium (nLTE) based on the Markov chain Monte-Carlo (MCMC) method is presented. It is shown that the fractional ion abundance and the resulting mean charge of the plasma can be calculated with much lower computational time compared to conventional methods. The present method can be easily parallelized and is applicable to larger problems, such as modeling coupled atomic processes and radiation hydrodynamics.

Versatile code DLAYZ for investigating population kinetics and radiative properties of plasmas in non-local thermodynamic equilibrium

A versatile code DLAYZ based on collisional-radiative model is developed for investigating the population kinetics and radiative properties of plasmas in non-local thermodynamic equilibrium. DLAYZ is implemented on the detailed level accounting (DLA) approach and can be extended to detailed configuration accounting (DCA) and hybrid DLA/DCA approaches. The code can treat both steady state and time-dependent problems. The implementation of the main modules of DLAYZ is discussed in detail including atomic data, rates, population distributions and radiative properties modules. The complete set of basic atomic data is obtained using relativistic quantum mechanics. For dense plasmas, the basic atomic data with plasma screening effects can be obtained. The populations are obtained by solving the coupled rate equations, which are used to calculate the radiative properties. A parallelized version is implemented in the code to treat the large-scale rate equations. Two illustrative examples of a steady state case for carbon plasmas and a time-dependent case for the relaxation of a K-shell excited argon are employed to show the main features of the present code.

Microwave-Induced Plasma Desorption/Ionization Source for Ambient Mass Spectrometry

A new ionization source based on microwave induced plasma was developed for ambient desorption/ionization. The microwave-induced plasma desorption/ionization source (MIPDI) was composed of a copper Surfatron microwave cavity where a fused-silica tube was centered axially. Stable nonlocal thermodynamic equilibrium plasma was generated in the quartz discharge tube when a microwave at a frequency of 2450 MHz was coupled to the microwave cavity. Analytes deposited on the surface of poly(tetrafluoroethylene) (PTFE) or quartz slide after hydrofluoric acid (HF) etching were desorbed and ionized by the plasma. The performance of the MIPDI technique was validated by the analysis of a variety of chemical substances, polymer compounds, and pharmaceutical drugs using argon or helium as the discharge gas. Protonated [M + H](+) or deprotonated [M - H](-) ions were observed in the positive or negative mode. MIPDI was also used for the analysis of compounds in a complex matrix without any sample preparation. MIPDI was also capable of analyzing liquid samples. The signal-to-noise ratio was 463 in the analysis of 9.2 ng of phenylalanine, and the limit of detection was 60 pg for phenylalanine. MIPDI could desorb and ionize analytes with a molecular weight of up to 1200, which was demonstrated by the analysis of polyethylene glycol 800 (PEG800). MIPDI has advantages of simple instrumentation, relatively high temperature, stability, and reproducibility.

Population kinetics and M band emission spectra of gold plasmas in non-local thermodynamic equilibrium by using a detailed relativistic configuration approach

A collisional-radiative model based on the approach of detailed relativistic configurations is developed, where the complete set of atomic data including photo-excitation, photoionization, electron impact excitation, electron impact ionization and autoionization is calculated, and the data of the inverse processes are obtained by detailed balance. The population distribution is obtained by solving the rate equation under the steady-state condition. The present model is applied to calculate the charge state distribution and M band emission spectra of gold plasmas in non-local thermodynamic equilibrium under a variety of plasma conditions. Comparisons between the present work and experimental results were made and good agreement is found. For the strong transition lines, the intensities predicted by the present model agree with those of experimental spectra within 50%. The present work is useful in analyzing and interpreting experiments as well as in diagnosing the electron temperature in experiments.

Study of Gas Heating by a Microwave Plasma Torch

Among the different types of microwave plasma torches, the axial injection torch (TIA) has been used for several years to create chemically active species, in applications such as gas analysis, surface processing and gaseous waste treatments. The TIA allows the coupling of microwave energy (2.45 GHz) to a gas injected axially at the nozzle’s exit. The TIA produces non-local thermodynamic equilibrium plasmas with a high luminosity and a maximum density of charged particles at the nozzle’s exit. The present work is dedicated to study the plasma created by a TIA, running at atmospheric pressure. The study involves both experiment and modeling of this torch, in order to maximize the coupling between the microwave power and the plasma and to define the optimum plasma and flow operating conditions for plasma-to-gas heat transfer.

Gold charge state distributions in highly ionized, low-density beam plasmas

We present a systematic study of Au charge state distributions (CSDs) from low density, nonlocal thermodynamic equilibrium plasmas created in the Livermore electron beam ion traps (EBIT-I and EBIT-II). X-ray emission from Ni-like to Kr-like Au ions has been recorded from monoenergetic electron beam plasmas having E(beam)=2.66, 2.92, 3.53, and 4.54 keV, and the CSDs of the beam plasmas have been inferred by fitting the collisionally excited line transitions and radiative recombination emission features with synthetic spectra. We have modeled the beam plasmas using a collisional-radiative code with various treatments of the atomic structure for the complex M- and N-shell ions and find that only models with extensive doubly excited states can properly account for the dielectronic recombination (DR) channels that control the CSDs. This finding would be unremarkable for plasmas with thermal electron distributions, where many such states are sampled, and the importance of DR is well established. But in an EBIT source, the beam is resonant with only a subset of such states having spectator electrons in orbitals with high principal quantum number n (8≤n≤20). The inclusion of such states in the model was also necessary to obtain agreement with observed stabilizing transitions in the x-ray spectra.

Higher-order contributions to transport coefficients in two-temperature hydrogen thermal plasma

Within the framework of Chapman-Enskog method, electron transport properties and their higher-order contributions have been studied in temperature range 5000–40 000 K at different pressures for hydrogen thermal plasma in local thermodynamic equilibrium (LTE) and non-local thermodynamic equilibrium (NLTE) regimes. Two cases of thermal plasma have been considered: (i) Ground state (GS) plasma in which all atomic hydrogen has been assumed to be in ground state and (ii) the excited state (ES) plasma in which hydrogen atoms are distributed in various possible electronically excited states (EES). The plasma composition is calculated by modified Saha equation of van de Sanden et al. The influence of non-equilibrium parameter θ (=Te/Th) on these properties has been examined in both the cases. It has been observed that both EES and θ modify the plasma composition and consequently affect the electron transport properties (viz., electron thermal conductivity, electrical conductivity, thermal diffusion and thermal diffusion ratio). It is shown that non-equilibrium parameter θ has meager effect on the higher-order convergence in comparison to EES. The unique behaviour observed for third-order contribution to these transport properties in GS plasma for small values of θ could be explained only when EES are taken into account. It is noted that EES show their influence on higher-orders to a considerable extent even when e-H(n) cross-sections are replaced by the ground state ones. Thus electron transport coefficients and their higher-order contributions are affected significantly due to inclusion of EES in LTE and NLTE plasmas.

Modeling the population kinetics of NLTE plasmas based on approximations of nonrelativistic configurations

For the rapid calculation of population kinetics of high-Z nonlocal thermodynamic equilibrium (NLTE) plasmas, a collisonal–radiative model based on the nonrelativistic configurations approach was developed. The required atomic data about the collisonal and radiative processes such as photoexcitation, electron-impact excitation, photoionization, electron-impact ionization and autoionzation were obtained by using a set of analytical formulae. The population kinetics were determined by solving the rate equation in the steady-state approach. As illustrative results, experimental measurements of the average ionization degree and population distribution of Xe and Au plasmas were reproduced, and overall good agreement was found. The present model provides a useful tool for modeling the population kinetics of NLTE plasmas.

Density-induced continuum resonances and quasi-bound states in the collisional-radiative equilibrium of dense plasmas

The aim of this work is to improve the treatment of density effects in non-local thermodynamic equilibrium plasmas. The density effect on atomic structure (wavefunctions and energy levels) is modelled by an ion-sphere potential. The modification of the atomic potential, continuum lowering and appearance of resonances are presented. In particular, we show that the continuum resonances are linked to the electrons in the subshells passed into the continuum. Their presence determines the existence of partially bound configurations, which must be taken into account in the collisional-radiative model. We introduce in the set of rate equations a supplementary ionization process due to the plasma environment. This process (and its inverse) enters into the balance of all the other processes. It is equivalent to tunnelling ionization where an outer electron located above the ionization threshold (and trapped by the potential barrier) crosses the barrier. As an application, we studied the influence of temperature and density on the average ionization and the ionic populations of a carbon plasma. We compared these calculations with the traditional method based on the chemical picture with continuum lowering.

Collisional-radiative Calculations of Optically Thin and Thick Plasmas Using the Computational Package ABAKO/RAPCAL

Non-local thermodynamic equilibrium (NLTE) conditions are universal in laboratory and astrophysical plasmas and, for this reason, the theory of NLTE plasmas is nowadays a very active subject. The populations of atomic levels and radiative properties are essential magnitudes in the study of these plasmas and the calculation of those properties relies on the so-called collisional-radiative (CR) models. However, the complexity of these models has led to the development of numerous collisionalradiative codes and this is a current research topic in plasmas. In this work is presented a versatile computational package, named ABAKO/RAPCAL, to calculate the populations of atomic levels and radiative properties of optically thin and thick, lowto-high Z, NLTE plasmas. ABAKO/RAPCAL combines a set of analytical approximations which yield substantial savings in computing running time, still comparing well with more elaborated codes and experimental data. In order to show the capabilities of the code and the accuracy of its results, calculations of several relevant plasma magnitudes for various plasma situations are shown and compared. PACS: 52.25Dg, 52.25Os

Calculations of nuclear excitation by electron capture (NEET) in nonlocal thermodynamic equilibrium plasmas

The nuclear excitation by electron capture (NEET) process may occur when the energy differences between two nuclear levels and between two electronic states are nearly equal, provided the quantum selection rules are fulfilled. These resonant conditions drastically limit the number of possible candidates, even though thermodynamic conditions encountered in hot dense plasmas do modify the orbital electronic binding energy and the resonance conditions. $^{201}\mathrm{Hg}$, with a low-lying isomeric state located at $1.565$ keV, can be excited by NEET process in a laser-created plasma. However, its correct calculation requires nonlocal thermodynamic equilibrium (non-LTE) atomic physics treatment because current laser-created plasmas do not reach high-enough temperature in the area at LTE. In this article, we describe the calculation leading to an estimated excitation rate and discuss the influence of LTE$/$non-LTE physics with an average-atom model and the use of a Gaussian variance calculation to estimate the broadening around the mean energy mismatch.

Theoretical calculations of X-ray spectra of Au plasma

By using a detailed configuration accounting method in the collisional radiative equilibrium model, and Cowans relativistic atomic structure code with respect to ionic averaged configurations and Hartree-Fock-Slater potential, we solve the rate equations for populations of all ionic and level populations of all excited states, in which main consider main atomic dynamic processes in a non-local thermodynamic equilibrium plasma can be considered, thereby obtaining the ionic populations and energy level populations and the ionic charge stage distribution and the average charge for Au. We also simulate and calculate the X-ray emission spectra of Au 5f—3d transition arrays. The calculated results are in good agreement with the experimental data for a well-characterized highly ionized Au plasma.

Opacity calculations for high-Z plasma in non-local thermodynamic equilibrium

Opacity of high-Z element plasma in non-local thermodynamic equilibrium (NLTE) is calculated. In the calculation, a collisional radiative model in detailed-configuration-accounting (DCA) is applied to population calculations for NLTE plasmas. Configuration-averaged rate coefficients that needed in the rate equations are obtained based on the first order perturbation theory. The Hatree–Fock–Slater self-consistent-field method is used to calculate the electron wave functions. The spin–orbit splitting is included in the spectrum calculations. The unresolved transition array method is used in the opacity calculations. The calculated frequency-dependent opacity of high-Z plasma Lu is presented. The comparison shows that the present spectrum agrees with another theoretical result well except that the present one shifts a little to the lower energy due to its lower mean ionization stage. The effects of highly doubly excited states on ionization balance and on the opacity are investigated. The mean ionization stage increases more than three stages when doubly excited states 5 l6 l′ and 5 l5 l′ are not included in the population calculations and the absorption spectrum also shifts to the higher energy.

Effective temperatures in hot dense plasmas

In medium- and high- Z hot dense non-local thermodynamic equilibrium plasmas a standard level-by-level collisional-radiative model cannot be used because of the excessive number of levels involved. Gathering the levels into large ensembles is a convenient way for reducing the complexity of the calculations. A review is given of these approaches, whereby effective temperatures have been evidenced, and calculated ab initio. Numerical examples are presented in germanium and gold plasmas. The physical origin of these temperatures is discussed.