Local Thermodynamic Equilibrium Approximation Research Articles

Application of calibration-free high repetition rate laser-ablation spark-induced breakdown spectroscopy for the quantitative elemental analysis of a silver alloy.

In this work, we report the application of a calibration-free (CF) method combined with high repetition rate laser-ablation spark-induced breakdown spectroscopy (HRR LA-SIBS) to the analysis of a silver alloy. The sample was ablated by a fiber laser operated at a 30 kHz pulse repetition rate, and a spark discharge was applied to enhance plasma emission. Electron number density and plasma temperature were estimated using Stark broadening of spectral lines and the Saha-Boltzmann plot method, respectively. The fulfillment of the local thermodynamic equilibrium (LTE) approximation of the measurement was verified. Averaged electron density and plasma temperature were calculated as 1.11×1017cm-3 and 7355 K, respectively. The elemental composition of a silver alloy sample was determined, and the result was compared with that analyzed with inductively coupled plasma optical emission spectrometry (ICP-OES). The analytical error was within a 15% range. It was demonstrated that the CF HRR LA-SIBS technique could potentially provide elemental analysis for silver alloys without requiring a standard sample.

Questioning the spatial origin of complex organic molecules in young protostars with the CALYPSO survey

Context. Complex organic molecules (COMs) have been detected in a few Class 0 protostars but their origin is not well understood. While the usual picture of a hot corino explains their presence as resulting from the heating of the inner envelope by the nascent protostar, shocks in the outflow, disk wind, the presence of a flared disk, or the interaction region between envelope and disk at the centrifugal barrier have also been claimed to enhance the abundance of COMs. Aims. Going beyond studies of individual objects, we want to investigate the origin of COMs in young protostars on a statistical basis. Methods. We use the CALYPSO survey performed with the Plateau de Bure Interferometer of the Institut de Radioastronomie Millimétrique to search for COMs at high angular resolution in a sample of 26 solar-type protostars, including 22 Class 0 and four Class I objects. We derive the column densities of the detected molecules under the local thermodynamic equilibrium approximation and search for correlations between their abundances and with various source properties. Results. Methanol is detected in 12 sources and tentatively in one source, which represents half of the sample. Eight sources (30%) have detections of at least three COMs. We find a strong chemical differentiation in multiple systems with five systems having one component with at least three COMs detected but the other component devoid of COM emission. All sources with a luminosity higher than 4 L⊙ have at least one detected COM whereas no COM emission is detected in sources with internal luminosity lower than 2 L⊙, likely because of a lack of sensitivity. Internal luminosity is found to be the source parameter impacting the COM chemical composition of the sources the most, while there is no obvious correlation between the detection of COM emission and that of a disk-like structure. A canonical hot-corino origin may explain the COM emission in four sources, an accretion-shock origin in two or possibly three sources, and an outflow origin in three sources. The CALYPSO sources with COM detections can be classified into three groups on the basis of the abundances of oxygen-bearing molecules, cyanides, and CHO-bearing molecules. These chemical groups correlate neither with the COM origin scenarios, nor with the evolutionary status of the sources if we take the ratio of envelope mass to internal luminosity as an evolutionary tracer. We find strong correlations between molecules that are a priori not related chemically (for instance methanol and methyl cyanide), implying that the existence of a correlation does not imply a chemical link. Conclusions. The CALYPSO survey has revealed a chemical differentiation in multiple systems that is markedly different from the case of the prototypical binary IRAS 16293-2422. This raises the question of whether all low-mass protostars go through a phase showing COM emission. A larger sample of young protostars and a more accurate determination of their internal luminosity will be necessary to make further progress. Searching for correlations between the COM emission and the jet/outflow properties of the sources may also be promising.

Study of the ionizing gas flow in the channel of plasma accelerator with different ways of gas inflow at the inlet

Numerical studies of the ionization process are presented for various ways of the gas supplying at the inlet of the coaxial channel of the quasi-stationary plasma accelerator. Simulation of two-dimensional axisymmetric flows of ionizing gas was carried out on the basis of the equations of radiation magnetic gas dynamics taking into account radiation transport. The approximation of local thermodynamic equilibrium in three-component medium consisting of atoms, ions, and electrons was used in the MHD model. It was determined that non-uniform gas inflow at the channel inlet leads to even greater instability of the pulsating unsteady flows of the ionizing gas in the plasma accelerator. The method of long characteristics was used in the 3D model of radiation transport, including the basic mechanisms of emission and absorption for different portions of the spectrum. The radiation field in the ionizing gas flow was determined, including the integral radiation characteristics and the spectral radiation intensities in the narrow ranges of frequencies or photon energies.

Readdressing the UV solar variability with SATIRE-S: non-LTE effects

Context. Solar spectral irradiance (SSI) variability is one of the key inputs to models of the Earth’s climate. Understanding solar irradiance fluctuations also helps to place the Sun among other stars in terms of their brightness variability patterns and to set detectability limits for terrestrial exoplanets. Aims. One of the most successful and widely used models of solar irradiance variability is Spectral And Total Irradiance REconstruction model (SATIRE-S). It uses spectra of the magnetic features and surrounding quiet Sun that are computed with the ATLAS9 spectral synthesis code under the assumption of local thermodynamic equilibrium (LTE). SATIRE-S has been at the forefront of solar variability modelling, but due to the limitations of the LTE approximation its output SSI has to be empirically corrected below 300 nm, which reduces the physical consistency of its results. This shortcoming is addressed in the present paper. Methods. We replaced the ATLAS9 spectra of all atmospheric components in SATIRE-S with spectra that were calculated using the Non-LTE Spectral SYnthesis (NESSY) code. To compute the spectrum of the quiet Sun and faculae, we used the temperature and density stratification models of the FAL set. Results. We computed non-LTE contrasts of spots and faculae and combined them with the corresponding fractional disc coverages, or filling factors, to calculate the total and spectral irradiance variability during solar cycle 24. The filling factors have been derived from solar full-disc magnetograms and continuum images recorded by the Helioseismic and Magnetic Imager on Solar Dynamics Observatory (SDO/HMI). Conclusions. The non-LTE contrasts yield total and spectral solar irradiance variations that are in good agreement with empirically corrected LTE irradiance calculations. This shows that the empirical correction applied to the SATIRE-S total and spectral solar irradiance is consistent with results from non-LTE computations.

Re-exploring Molecular Complexity with ALMA (ReMoCA): interstellar detection of urea

Context. Urea, NH2C(O)NH2, is a molecule of great importance in organic chemistry and biology. Two searches for urea in the interstellar medium have been reported in the past, but neither were conclusive. Aims. We want to take advantage of the increased sensitivity and angular resolution provided by the Atacama Large Millimeter/submillimeter Array (ALMA) to search for urea toward the hot molecular cores embedded in the high-mass-star-forming region Sgr B2(N). Methods. We used the new spectral line survey named ReMoCA (Re-exploring Molecular Complexity with ALMA) that was performed toward Sgr B2(N) with ALMA in its observing cycle 4 between 84 and 114 GHz. The spectra were analyzed under the local thermodynamic equilibrium approximation. We constructed a full synthetic spectrum that includes all the molecules identified so far. We used new spectroscopic predictions for urea in its vibrational ground state and first vibrationally excited state to search for this complex organic molecule in the ReMoCA data set. We employed the gas-grain chemical kinetics model MAGICKAL to interpret the astronomical observations. Results. We report the secure detection of urea toward the hot core Sgr B2(N1) at a position called N1S slightly offset from the continuum peak, which avoids obscuration by the dust. The identification of urea relies on nine clearly detected transitions. We derive a column density of 2.7 × 1016 cm−2 for urea, two orders of magnitude lower than the column density of formamide, and one order of magnitude below that of methyl isocyanate, acetamide, and N-methylformamide. The latter molecule is reliably identified toward N1S with 60 clearly detected lines, confirming an earlier claim of its tentative interstellar detection. We report the first interstellar detections of NH2CH18O and 15NH2CHO. We also report the nondetection of urea toward the secondary hot core Sgr B2(N2) with an abundance relative to the other four species at least one order of magnitude lower than toward the main hot core. Our chemical model roughly reproduces the relative abundances of formamide, methyl isocyanate, acetamide, and N-methylformamide, but it overproduces urea by at least one order of magnitude. Conclusions. Urea is clearly detected in one of the hot cores. Comparing the full chemical composition of Sgr B2(N1S) and Sgr B2(N2) may help understand why urea is at least one order of magnitude less abundant in the latter source.

Evolution of space open electric arc burning in the external axial magnetic field

The calculation was made for open DC electric arc burning in an external uniform axial magnetic field. It was performed within the framework of a nonstationary three-dimensional mathematical model in approximation of partial local thermodynamic equilibrium of plasma. A “schematic” analog of electron temperature fluctuations was proposed for numerical realization of the open electric arc column of a helical shape. According to calculations, it was established that the column of the open electric arc takes a helical space shape. Plasma rotates around a longitudinal axis of the arc, at that the directions of plasma rotation near the cathode and the anode are opposite. In the arc cross-sections, the velocity of plasma rotation is unequal and the deviation value of the same part of the arc from the central axis varies in time. A helical shape of the open arc is not stable and varies in time. Apparently, the open arc cannot remain stable and invariable in the time helical shape in the external axial magnetic field.

Quantitative analysis of Ge/Si alloys using double-pulse calibration-free laser-induced breakdown spectroscopy

In this work, we report the first application of the double-pulse Calibration-Free Laser-Induced Breakdown Spectroscopy (DP-CF-LIBS) to the analysis of Ge-Cu/Si and Ge-Ba/Si alloys. The plasma was produced using two collinear Nd:YAG lasers, operating at 1064 nm. The experimental parameters such as inter-pulse delay, gate delay and energy ratio between the two laser pulses were optimized to maximize the signal to background and signal to noise ratio in the resulting LIBS spectra. The fulfillment of the Local Thermodynamic Equilibrium (LTE) approximation in the time window of the measurement was verified using the McWhirter criterion and considering the relaxation time and diffusion length of the atoms in the plasma. The effect of self-absorption on the lines used in the CF-LIBS analysis was considered and found negligible. The DP-CF-LIBS analysis allowed the determination of the stoichiometric ratio of the elements in the two alloys, an important parameter for industrial quality control and fundamental studies on germanium/silicon alloys.

Albedo of an irradiated plane-parallel atmosphere with finite optical depth

Abstract We analytically derive albedo for a plane-parallel atmosphere with finite optical depth, irradiated by an external source, under the local thermodynamic equilibrium approximation. Albedo is expressed as a function of the photon destruction probability ε and optical depth τ, with several parameters such as dilution factors of the external source. In the particular case of the infinite optical depth, albedo A is expressed as $A=[1 + (1-W_J/W_H)\sqrt{3\varepsilon }/3]/(1+\sqrt{3\varepsilon })$, where WJ and WH are the dilution factors for the mean intensity and Eddington flux, respectively. An example of a model atmosphere is also presented under a gray approximation.

Transition Probabilities of Co ii Weak Lines to the Ground and Low Metastable Levels.

New branching fraction (BF) measurements based primarily on data from a cross-dispersed echelle spectrometer are reported for 84 lines of Co ii. The BFs for 82 lines are converted to absolute atomic transition probabilities using radiative lifetimes from laser-induced fluorescence (LIF) measurements on 19 upper levels of the lines. A lifetime of 3.3(2) ns for the z5D0 level is used based on LIF measurements for lifetimes of the four other levels in the z5D term. Twelve of the eighty-four lines are weak transitions connecting to the ground and low metastable levels of Co+. Another 46 lines are strong transitions connecting to the ground and low metastable levels of Co+. For these lines, log(gf) values were measured in earlier studies and, with a few exceptions, are confirmed in this study. Such lines, if unblended in stellar spectra, have the potential to yield Co abundance values unaffected by any breakdown of the local thermodynamic equilibrium approximation in stellar photospheres because the ground and low metastable levels of Co+ are the primary population reservoirs of Co in the photospheres of interest. Weak lines, if unblended, are useful in photospheres with high Co abundance, and strong lines are useful in metal-poor photospheres. New hyperfine structure A constants for 28 levels of ionized Co from least-squares fits to Fourier transform spectra line profiles are reported. These laboratory data are applied to re-determine the Co abundance in the metal-poor halo star HD 84937. BFs and transition probabilities for 19 lines are reported for the first time.

Atomic structure data based on average-atom model for opacity calculations in astrophysical plasmas

Influence of the plasmas parameters on the electron structure of ions in astrophysical plasmas is studied on the basis of the average-atom model in the local thermodynamic equilibrium approximation. The relativistic Dirac–Slater method is used for the electron density estimation. The emphasis is on the investigation of an impact of the plasmas temperature and density on the ionization stages required for calculations of the plasmas opacities. The level population distributions and level energy spectra are calculated and analyzed for all ions with 6 ≤ Z ≤ 32 occurring in astrophysical plasmas. The plasma temperature range 2−200 eV and the density range 2−100 mg/cm3 are considered. The validity of the method used is supported by good agreement between our values of ionization stages for a number of ions, from oxygen up to uranium, and results obtained earlier by various methods among which are more complicated procedures.

Numerical modelling of high-pressure arc discharges: matching the LTE arc core with the electrodes

A widely used approach to simulation of high-pressure arc discharges is based on the system of magneto-hydrodynamic equations written in the approximation of local thermodynamic equilibrium (LTE). In this work, boundary conditions on the surface of the electrodes are formulated with the use of equations of balance of energy in the non-equilibrium near-electrode layers that separate the LTE bulk plasma and the electrodes. As an example, numerical simulations of a free-burning arc in atmospheric-pressure argon plasma in the current range from 20 to 200 A are reported. Simulation results are in reasonably good agreement with those given by more sophisticated models and with the experiment. Simulations performed for cathodes of slightly different geometries have predicted a strong effect produced by details of the cathode geometry over the distribution of the current density along the cathode surface and therefore over the plasma temperature, an interesting and potentially important result that is worth further numerical investigation and experimental verification.

Wall ablation of heated compound-materials into non-equilibrium discharge plasmas

The discharge properties of the plasma bulk flow near the surface of heated compound-materials strongly affects the kinetic layer parameters modeled and manifested in the Knudsen layer. This paper extends the widely used two-layer kinetic ablation model to the ablation controlled non-equilibrium discharge due to the fact that the local thermodynamic equilibrium (LTE) approximation is often violated as a result of the interaction between the plasma and solid walls. Modifications to the governing set of equations, to account for this effect, are derived and presented by assuming that the temperature of the electrons deviates from that of the heavy particles. The ablation characteristics of one typical material, polytetrafluoroethylene (PTFE) are calculated with this improved model. The internal degrees of freedom as well as the average particle mass and specific heat ratio of the polyatomic vapor, which strongly depends on the temperature, pressure and plasma non-equilibrium degree and plays a crucial role in the accurate determination of the ablation behavior by this model, are also taken into account. Our assessment showed the significance of including such modifications related to the non-equilibrium effect in the study of vaporization of heated compound materials in ablation controlled arcs. Additionally, a two-temperature magneto-hydrodynamic (MHD) model accounting for the thermal non-equilibrium occurring near the wall surface is developed and applied into an ablation-dominated discharge for an electro-thermal chemical launch device. Special attention is paid to the interaction between the non-equilibrium plasma and the solid propellant surface. Both the mass exchange process caused by the wall ablation and plasma species deposition as well as the associated momentum and energy exchange processes are taken into account. A detailed comparison of the results of the non-equilibrium model with those of an equilibrium model is presented. The non-equilibrium results show a non-equilibrium region near the plasma–wall interaction region and this indicates the need for the consideration of the influence of the possible departure from LTE in the plasma bulk on the determination of ablation rate.

Thermodynamics of adaptive molecular resolution.

A relatively general thermodynamic formalism for adaptive molecular resolution (AMR) is presented. The description is based on the approximation of local thermodynamic equilibrium and considers the alchemic parameter λ as the conjugate variable of the potential energy difference between the atomistic and coarse-grained model Φ=U(1)-U(0) The thermodynamic formalism recovers the relations obtained from statistical mechanics of H-AdResS (Español et al, J. Chem. Phys. 142, 064115, 2015 (doi:10.1063/1.4907006)) and provides relations between the free energy compensation and thermodynamic potentials. Inspired by this thermodynamic analogy, several generalizations of AMR are proposed, such as the exploration of new Maxwell relations and how to treat λ and Φ as 'real' thermodynamic variablesThis article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Numerical simulation of a helical shape electric arc in the external axial magnetic field

Within the frameworks of non-stationary three-dimensional mathematical model, in approximation of a partial local thermodynamic equilibrium, a numerical calculation was made of characteristics of DC electric arc burning in a cylindrical channel in the uniform external axial magnetic field. The method of numerical simulation of the arc of helical shape in a uniform external axial magnetic field was proposed. This method consists in that that in the computational algorithm, a “scheme” analog of fluctuations for electrons temperature is supplemented. The “scheme” analogue of fluctuations increases a weak numerical asymmetry of electrons temperature distribution, which occurs randomly in the course of computing. This asymmetry can be “picked up” by the external magnetic field that continues to increase up to a certain value, which is sufficient for the formation of helical structure of the arc column. In the absence of fluctuations in the computational algorithm, the arc column in the external axial magnetic field maintains cylindrical axial symmetry, and a helical form of the arc is not observed.

Multifrequency studies of massive cores with complex spatial and kinematic structures

Five regions of massive star formation have been observed in various molecular lines in the frequency range $\sim 85-89$ GHz. The studied regions possess dense cores, which host young stellar objects. The physical parameters of the cores are estimated, including kinetic temperatures ($\sim 20-40$ K), sizes of the emitting regions ($\sim 0.1-0.6$ pc), and virial masses ($\sim 40-500 M_{\odot}$). Column densities and abundances of various molecules are calculated in the local thermodynamical equilibrium approximation. The core in 99.982+4.17, associated with the weakest IRAS source, is characterized by reduced molecular abundances. Molecular line widths decrease with increasing distance from the core centers ($b$). For $b\ga 0.1$~pc, the dependences $\Delta V(b)$ are close to power laws ($\propto b^{-p}$), where $p$ varies from $\sim 0.2$ to $\sim 0.5$, depending on the object. In four cores, the asymmetries of the optically thick HCN(1--0) and HCO$^+$(1--0) lines indicate systematic motions along the line of sight: collapse in two cores and expansion in two others. Approximate estimates of the accretion rates in the collapsing cores indicate that the forming stars have masses exceeding the solar mass.

Thermodynamic stability of sulfide electrolyte/oxide electrode interface in solid-state lithium batteries

Thermodynamic analyses were made on the sulfide electrolyte–oxide electrode interfaces in all solid-state lithium batteries using chemical potential diagrams, constructed under the local thermodynamic equilibrium approximation. The chemical potential diagrams were first made for the Li–S–O system and the Li–Co–O system, to show that the stable region for the Li2S phase and the combined region of LiCoO2/CoO2 phases do not have a common overlap area in the same log a(Li) vs. log p(O2) plot. Three dimensional diagrams of the Li–Co–S–O system and the Li–Co–P–S–O system were constructed by fixing log a(Li) at selected values. Based on the constructed diagrams, the chemical nature of the sulfide electrolyte–oxide electrode interface could be considered from both the high temperature electrochemical and chemical points of view. This aided the interpretation of recently reported microscopic analyses on the interfaces. The causes of the “high resistive layer” and cobalt diffusion can be reasonably interpreted as chemical processes, caused by the high Li potential during charging. The results present in this paper are also compared to recent results from theoretical calculations on the energetics of interface structure. The possible applications of the here presented chemical diagrams are discussed in terms of the stoichiometric numbers and energies of the local interface atomic arrangement.

SPECTRO-POLARIMETRIC SIMULATIONS OF THE SOLAR LIMB: ABSORPTION-EMISSION Fe I 6301.5 Å AND 6302.5 Å LINE PROFILES AND TORSIONAL FLOWS IN THE INTERGRANULAR MAGNETIC FLUX CONCENTRATIONS

Using radiative magneto-hydrodynamic simulations of the magnetised solar photosphere and detailed spectro-polarimetric diagnostics with the FeI $6301.5\mathrm{\AA}$ and $6302.5\mathrm{\AA}$ photospheric lines in the local thermodynamic equilibrium approximation, we model active solar granulation as if it was observed at the solar limb. We analyse general properties of the radiation across the solar limb, such as the continuum and the line core limb darkening and the granulation contrast. We demonstrate the presence of profiles with both emission and absorption features at the simulated solar limb, and pure emission profiles above the limb. These profiles are associated with the regions of strong linear polarisation of the emergent radiation, indicating the influence of the intergranular magnetic fields on the line formation. We analyse physical origins of the emission wings in the Stokes profiles at the limb, and demonstrate that these features are produced by localised heating and torsional motions in the intergranular magnetic flux concentrations.

Critical value of volume ignition and condition of nonequilibriem burning of DT in inertial confinement fusion

In the local thermodynamic equilibrium approximation, we study the problems on low-temperature volume ignition of DT fuel. The temperature and compression threshold of volume ignition are given by solving the ion, electric and radiation energy equation. The ignitions points are affected by the albedo, DT mass, abundance ratio, etc. At the point of ignition, the temperature reduces with the increase of areal density. The trends of variations in radiation and electron temperature become closer to each other. The most important fact is that the subsequent development of the system can be given by analyzing the stationary solution based on the linear stability method. In other words, we can estimate whether the system can enter into a deep-burning state by using this method.

A conservative multicomponent diffusion algorithm for ambipolar plasma flows in local thermodynamic equilibrium

The usage of the local thermodynamic equilibrium (LTE) approximation can be a very powerful assumption for simulations of plasmas in or close to equilibrium. In general, the elemental composition in LTE is not constant in space and effects of mixing and demixing have to be taken into account using the Stefan–Maxwell diffusion description. In this paper, we will introduce a method to discretize the resulting coupled set of elemental continuity equations. The coupling between the equations is taken into account by the introduction of the concept of a Péclet matrix. It will be shown analytically and numerically that the mass and charge conservation constraints can be fulfilled exactly. Furthermore, a case study is presented to demonstrate the applicability of the method to a simulation of a mercury-free metal-halide lamp. The source code for the simulations presented in this paper is provided as supplementary material (stacks.iop.org/JPhysD/47/425202/mmedia).

Numerical modeling of a cutting torch

A two-dimensional turbulent model of a low-current intensity (30 A) cutting plasma torch was developed using the local thermodynamic equilibrium approximation. A good agreement was found between measured and modelled results of plasma temperature and velocity, the latter of which has not been previously reported in the literature for high energy density torches. The cutting performance was also studied in terms of the heat flux to the work-piece and the value of the force exerted by the impinging plasma jet.