Excited State Number Densities Research Articles

Three-Dimensional Radiation Analysis of the Hypersonic Jules Verne Reentry Spectra

The automatic transfer vehicle (ATV) Jules Verne, developed by the European Space Agency, played a crucial role in resupply missions to the International Space Station from 2008 to 2015. Following its resupply missions, Jules Verne was programmed to execute a planned destructive reentry into Earth’s atmosphere. To better understand the spectra generated by the Jules Verne, three-dimensional hypersonic flowfield and radiation analyses are performed at the 75 km trajectory point of the ATV. Results are compared to measurements obtained at 78 and 73 km by a miniature Echelle spectrograph operated from an airborne platform. Incorporating three-dimensional effects into the radiation analysis results in an overall reduction of the total radiation spectra and a decrease in atomic and molecular features, leading to a closer alignment between the observed and simulated values. Comparable effects are observed by making minor adjustments to the internal mode temperatures and modifying the model for the population of excited state number densities.

Collisional-radiative modeling of shock-heated nitrogen mixtures

A three-temperature collisional-radiative model for shock-heated nitrogen–argon mixtures is developed to facilitate the study of nonequilibrium electronic excitation and ionization behind strong shock waves. Model predictions accurately reproduce measurements of N2 dissociation for mixtures of 2%–10% N2 in argon, with some discrepancies observed for 20% N2 mixtures. Potential causes of the discrepancies are discussed. Net dissociation in mixtures containing 20% N2 is significantly impacted by the dissociation of N2(A), the first excited electronic state of N2, indicating that molecular electronic excitation can affect net dissociation in shock-heated nitrogen flows. The collisional-radiative model successfully predicts the three-stage behavior and induction time observed in concentration measurements of atomic nitrogen in its fourth excited state, the 3s4P level, behind reflected shocks. Mechanisms for the observed behavior are discussed, which deviate from those inferred using a simpler kinetic model. Excited state number density predictions are strongly influenced by the modeling of radiation self-absorption and the inclusion of the measured non-ideal pressure rise. At higher N2 concentrations, the measured data indicate increased efficiency of atomic nitrogen electronic excitation in collisions with N as compared to collisions with N2 and Ar. A global sensitivity analysis of the excited state predictions is then performed, identifying the processes in the kinetic model that most sensitively influence the predicted excited state time history and further clarifying the dominant mechanisms affecting the experimental observables.

In-situ quantification of alkali metals from biomass combustion by optical emission spectroscopy

In this study, an in-situ method was developed to quantify the alkali metal emissions and its speciation from the combustion of biomass in a 150 kWth furnace. An optical emission spectrometer was used to detect the spontaneous atomic emissions of the potassium and sodium in the flame. A calibration is performed to obtain the radiation intensities of potassium and sodium, which are precursive values needed to quantify each alkali metals’ relative ground state number densities. The results show that the spontaneous emissions of the alkali metals appear as doublet lines in the spectra. The calibrated radiation intensities for sodium were converted to relative values via Lorentzian fitting. The relative excited state number densities for sodium and potassium were within the range of 0.536 to 0.791 cm−3 and 23.468 and 30.320 cm−3 respectively. This shows that potassium vapours and its compounds were higher compared to sodium. These number densities will be compared to the sodium and content in the ash for further discussion and validation.

Comparisons and analyses of the aluminum K-shell spectroscopic models

Comparing different collisional-radiative models is of great importance for validating the models for plasma spectroscopy and improving the diagnostic accuracy of plasma parameters. In this paper, the widely applied K-shell spectroscopic models, FAC and FLYCHK, are compared based on their calculation results of the aluminum K-shell emissivity and absorption coefficient. The state abundances, K-shell line ratios, K-shell emissivities and absorption coefficients in a wide range of plasma temperatures and densities are calculated and compared, and the reasons for the differences between these two models are discussed. In an electron temperature range from 200 to 800 eV, and an electron density range from 1017 to 1024 cm-3, the Al ions in the plasma are mainly composed of H-like and He-like ions. The ground-state populations of the H-like and He-like ions, calculated from FAC model, are in good agreement with the results from FLYCHK. Number densities of the excited states are two orders or more less than those of the ground states from both the models, and significant differences are observed in the number densities of n=2 and n=3 states of both the H-like and He-like ions. These differences will further result in the differences in spectral line emissivity and their line emissivity ratio, such as He-IC/He-αup and H-βup/He-βup, which are key parameters used to diagnose the electron temperature and density. The line emissivity ratio Ly-αup/(He-αup+He-IC) is less dependent on the electron density, and the difference in line emissivity ratio between the two models mainly lies in the parameter region where both the electron temperature and density are high. The ratio He-IC/He-αup is less dependent on the electron temperature when the electron density is more than 1019 cm-3 while significant differences are observed at a lower electron density.#br#The reason for the difference between the number densities of the low-energy excited states from FAC and FLYCHK models is analyzed by comparing the rate coefficients of various collisional and radiative processes in the rate equation of each state. The differences in the n=2 excited states of H-like ions come from the fact that FAC and FLYCHK models use the detailed-level model and the super-configuration model respectively to construct the rate equations of these states. The FAC model ignores the collisional excitation and de-excitation processes between the n=3 state and higher excitation states (e.g. n = 4) in H-like and He-like ions, which are responsible for the density difference in the n=3 excited state. Higher Rydberg states considered in FLYCHK model do not have any significant influence on the density of the ground-states. The difference in the absorption coefficient between the two models is smaller than that in the emissivity as discussed above, for the absorption coefficient mainly depends on the number density of the ions in ground state.

Elaboration of collisional–radiative models for flows related to planetary entries into the Earth and Mars atmospheres

The most relevant way to predict the excited state number density in a nonequilibrium plasma is to elaborate a collisional–radiative (CR) model taking into account most of the collisional and radiative elementary processes. Three examples of such an elaboration are given in this paper in the case of various plasma flows related to planetary atmospheric entries. The case of theoretical determination of nitrogen atom ionization or recombination global rate coefficients under electron impact is addressed first. The global rate coefficient can be implemented in multidimensional computational fluid dynamics calculations. The case of relaxation after a shock front crossing a gas of N2 molecules treated in the framework of the Rankine–Hugoniot assumptions is also studied. The vibrational and electronic specific CR model elaborated in this case allows one to understand how the plasma reaches equilibrium and to estimate the role of the radiative losses. These radiative losses play a significant role at low pressure in the third case studied. This case concerns CO2 plasma jets inductively generated in high enthalpy wind tunnels used as ground test facilities. We focus our attention on the behaviour of CO and C2 electronic excited states, the radiative signature of which can be particularly significant in this type of plasma. These three cases illustrate the elaboration of CR models and their coupling with balance equations.

Modeling of microwave-induced plasma in argon at atmospheric pressure

A two-dimensional model of microwave-induced plasma (field frequency 2.45 GHz) in argon at atmospheric pressure is presented. The model describes in a self-consistent manner the gas flow and heat transfer, the in-coupling of the microwave energy into the plasma, and the reaction kinetics relevant to high-pressure argon plasma including the contribution of molecular ion species. The model provides the gas and electron temperature distributions, the electron, ion, and excited state number densities, and the power deposited into the plasma for given gas flow rate and temperature at the inlet, and input power of the incoming TEM microwave. For flow rate and absorbed microwave power typical for analytical applications (200-400 ml/min and 20 W), the plasma is far from thermodynamic equilibrium. The gas temperature reaches values above 2000 K in the plasma region, while the electron temperature is about 1 eV. The electron density reaches a maximum value of about 4 × 10(21) m(-3). The balance of the charged particles is essentially controlled by the kinetics of the molecular ions. For temperatures above 1200 K, quasineutrality of the plasma is provided by the atomic ions, and below 1200 K the molecular ion density exceeds the atomic ion density and a contraction of the discharge is observed. Comparison with experimental data is presented which demonstrates good quantitative and qualitative agreement.

NLTE analysis of Co i /Co ii lines in spectra of cool stars with new laboratory hyperfine splitting constants

We investigate the statistical equilibrium of Co in the atmospheres of cool stars, and the influence of NLTE and HFS (hyperfine splitting) on the formation of Co lines and abundances. Significant departures from LTE level populations are found for Co I, also number densities of excited states in Co II differ from LTE at low metallicity. The NLTE abundance of Co in solar photosphere is 4.95 +/- 0.04 dex, which is in agreement with that in C I meteorites within the combined uncertainties. The spectral lines of Co I were calculated using the results of recent measurements of hyperfine interaction constants by UV Fourier transform spectrometry. For Co II, the first laboratory measurements of hyperfine structure splitting A and B factors were performed. A differential abundance analysis of Co is carried out for 18 stars in the metallicity range -3.12 < [Fe/H] < 0. The abundances are derived by method of spectrum synthesis. At low [Fe/H], NLTE abundance corrections for Co I lines are as large as +0.6 >... +0.8 dex. Thus, LTE abundances of Co in metal-poor stars are severely underestimated. The stellar NLTE abundances determined from the single UV line of Co II are lower by ~0.5-0.6 dex. The discrepancy might be attributed to possible blends that have not been accounted for in the solar Co II line and its erroneous oscillator strength. The increasing [Co/Fe] trend in metal-poor stars, as calculated from the Co I lines under NLTE, can be explained if Co is overproduced relative to Fe in massive stars. The models of galactic chemical evolution are wholly inadequate to describe this trend suggesting that the problem is in SN yields.

Electron-driven excitation of O 2 under night-time auroral conditions: Excited state densities and band emissions

Electron impact excitation of vibrational levels in the ground electronic state and seven excited electronic states in O 2 have been simulated for an International Brightness Coefficient-Category 2+ (IBC II+) night-time aurora, in order to predict O 2 excited state number densities and volume emission rates (VERs). These number densities and VERs are determined as a function of altitude (in the range 80–350 km) in the present study. Recent electron impact excitation cross-sections for O 2 were combined with appropriate altitude dependent IBC II+ auroral secondary electron distributions and the vibrational populations of the eight O 2 electronic states were determined under conditions of statistical equilibrium. Pre-dissociation, atmospheric chemistry involving atomic and molecular oxygen, radiative decay and quenching of excited states were included in this study. This model predicts relatively high number densities for the X 3 Σ g - ( v ′ ⩽ 4 ) , a 1 Δ g and b 1 Σ g + metastable electronic states and could represent a significant source of stored energy in O 2* for subsequent thermospheric chemical reactions. Particular attention is directed towards the emission intensities of the infrared (IR) atmospheric (1.27 μm), Atmospheric (0.76 μm) and the atomic oxygen 1 S→ 1 D transition (5577 Å) lines and the role of electron-driven processes in their origin. Aircraft, rocket and satellite observations have shown both the IR atmospheric and Atmospheric lines are dramatically enhanced under auroral conditions and, where possible, we compare our results to these measurements. Our calculated 5577 Å intensity is found to be in good agreement with values independently measured for a medium strength IBC II+ aurora.

Analysis of excitation processes and electron temperature changes from spectral data in a dc micro plasma discharge

A micro scale dc plasma discharge was studied to determine the potentialities for lab-on-the-chip applications. Different working conditions for the micro plasma discharge were considered: the pressure was varied between 2.7 and 5.3 kPa and the applied dc voltage was between 400 and 540 V, generating a discharge current in the range of 0.02–0.09 mA. The electrode distance was maintained at 0.025 cm and argon was used as the gas for the formation of plasma discharges. The number densities of excited states were determined by spectral emission data (400–1000 nm) and then were calculated by introducing a few assumptions: comparison of experimental and calculated number densities allowed an analysis of a volume averaged electron energy distribution function. Also, it was possible to estimate an effective electron temperature for different conditions of pressure and applied voltage.

Two-dimensional self-consistent microwave argon plasma simulations with experimental verification

Optical emission spectroscopy (OES), absorption measurements, and thermal energy rate analysis were used in tandem with numerical models to characterize microwave argon plasmas. A WAVEMAT (model MPDR-3135) microwave diamond deposition system was used to generate argon plasmas at 5 Torr. Three excited state number densities (4p, 5p, and 5d) were obtained from the OES measurements, and a fourth excited state number density (4s) was obtained from the absorption measurements. Further, power absorbed in the substrate was monitored. A self-consistent two-dimensional argon model coupled with an electromagnetic field model and a 25-level two-dimensional (2D)-collisional-radiative model (CRM) was developed and validated with the experimental measurements. The 2D model provides the gas and electron temperature distributions, and the electron, ion, and 4s state number densities, which are then iteratively fed into the electromagnetic and CRM models. Both the numerically predicted thermal energy rates and excited state densities agreed, within the experimental and numerical uncertainties, with the experimental results.

Effect of Electron Energy Distribution Function on Spectroscopic Characteristics of Microwave Discharge Argon Plasma

We discuss the effects of electron energy distribution function (EEDF) on the number densities of excited states of Ar I in a microwave discharge argon plasma in the pressure range of 0.1 to 10 Torr. We experimentally generate the microwave discharge argon plasma and find the electron temperature and density to be 5–12 eV and (1 -4)×1011 cm-3, respectively. Single probe analysis also shows that its EEDF is approximately Druyvesteynian, but with a large uncertainty. We measure the number densities of excited states of Ar I by spectroscopic examination. For numerical analysis, we obtain the number densities of the excited states by using a collisional radiative model, substituting experimentally observed electron temperature and density. The number densities of excited states calculated by the collisional radiative model agree well with the experimental ones when we adopt the Druyvesteynian distribution as EEDF, whilst the Maxwellian distribution gives poor results.

Modeling Cladding-Pumped Er/Yb Fiber Amplifiers

This paper presents a new computational strategy for efficient and stable modeling of rare-earth-doped fiber amplifiers and illustrates the strategy with results for a cladding-pumped erbium/ytterbium-doped fiber amplifier. The computational strategy allows arbitrary radial dependence for the optical fields and rare-earth densities, arbitrary wavelength resolution for amplified spontaneous emission (ASE) at pump and signal wavelengths, and arbitrary numbers of rate equations with arbitrary dependence on ground- and excited-state number density. Numerical results are presented for cladding-pumped Er/Yb-doped fiber amplifiers that illustrate how to reach the conversion efficiency limited by the quantum defect, how power conversion and the intensity of the ASE depend on operating wavelength, and how secondary loss mechanisms such as distributed loss, upconversion, and pairing/clustering affect the efficiency of the amplifier.

Nitric oxide excited under auroral conditions: Excited state densities and band emissions

Electron impact excitation of vibrational levels in the ground electronic state and nine excited electronic states in NO has been simulated for an IBC II aurora (i.e., ∼10 kR in 3914 Å radiation) in order to predict NO excited state number densities and band emission intensities. New integral electron impact excitation cross sections for NO were combined with a measured IBC II auroral secondary electron distribution, and the vibrational populations of 10 NO electronic states were determined under conditions of statistical equilibrium. This model predicts an extended vibrational distribution in the NO ground electronic state produced by radiative cascade from the seven higher‐lying doublet excited electronic states populated by electron impact. In addition to significant energy storage in vibrational excitation of the ground electronic state, both the a 4Π and L2 Φ excited electronic states are predicted to have relatively high number densities because they are only weakly connected to lower electronic states by radiative decay. Fundamental mode radiative transitions involving the lowest nine excited vibrational levels in the ground electronic state are predicted to produce infrared (IR) radiation from 5.33 to 6.05 μm with greater intensity than any single NO electronic emission band. Fundamental mode radiative transitions within the a 4Π electronic state, in the 10.08–11.37 μm region, are predicted to have IR intensities comparable to individual electronic emission bands in the Heath and ε band systems. Results from this model quantitatively predict the vibrational quantum number dependence of the NO IR measurements of Espy et al. [1988].

Excited state density distributions of H, C, C2, and CH by spatially resolved optical emission in a diamond depositing dc-arcjet reactor

Spatially resolved optical emission spectroscopy is used to investigate excited species in a dc-arcjet diamond depositing reactor. Temperature measurements indicate a cold plasma with electrons, excited states, and gas in nonthermal equilibrium. The H, C, C2, and CH excited state number densities decrease exponentially with the distance from the nozzle and have a pronounced increase in the shock structure above the substrate. The H emission increases throughout the boundary layer to the substrate surface, whereas emission from other species has a maximum in the boundary layer and then decreases again towards the substrate. The reconstructed radial distribution of excited state concentrations are Gaussian, with the C and C2 distributions broader than the H and CH ones. The optical emission is calibrated with either Rayleigh scattering or laser-induced fluorescence to furnish absolute number densities. We find all the excited species to be present in concentrations two or more orders of magnitude smaller than the corresponding ground states measured in the same reactor and conditions. We find that C2(d-a) emission intensity correlates well with laser-induced fluorescence measurements of C2(a) concentration in the arcjet plume. Ground state concentrations of the other species do not vary as their emission intensity except near the substrate, where the variations of CH(A-X), CH(B-X), and C2(d-a) emission intensities are good monitors of the corresponding concentration changes.

Radiative emission analysis of an expanding hydrogen arc plasma—II. Plume region diagnostics through radial emission

An experimental investigation of the plasma plume of a 1 kW class radiatively-cooled hydrogen arcjet thruster is presented. The line-of-sight emission of the Balmer-alpha line is measured at several radial positions using a high resolution monochromator and photon counting detection. The line-of-sight spectra are deconvolved radially into Voigt profiles, from which radial distributions of translational temperature and electron number density are determined. Absolute intensity calibration is also performed providing radial distributions of atomic hydrogen m = 3 excited state number density. Electron temperature profiles are calculated using a non-equilibrium collisional-radiative model. The hydrogen translation temperature displays good agreement with previous measurements. The electron number density profiles are consistent with Langmuir probe measurements made downstream of the exit plane. The results of the model indicate that the plasma at the nozzle exit plane is strongly recombining.

The role of two-step ionization in numerical predictions of electron energy distribution functions

Spectroscopic emission measurements have been made in a microwave plasma and have been compared with results from a collisional-radiative model—one that accounts for a non-Maxwellian electron energy distribution function (EEDF)—to assess the effects of nonequilibrium. Typical operating conditions are 40 Torr pressure, 300 sccm hydrogen, and 3 sccm methane flow rates, and 1.6 kW deposited power. Optical emission measurements of atomic hydrogen’s excited state number densities indicate values that are inconsistent, by orders of magnitude, with those predicted by an atomic hydrogen collisional-radiative model if numerically estimated EEDFs (average energy near 2.5 eV) taken from the published literature are used as input. Satisfactory agreement between the experimental and numerical results, however, is obtained if two-step ionization is accounted for in a self-consistent coupled numerical solution for the free and bound–excited electron densities, the electric field, and the EEDF. Two-step ionization is the dominant electron production mechanism and thereby greatly impacts numerical predictions of the electric field, the electron average energy, and thus the EEDF. Self-consistently accounting for two-step ionization reduces the predicted sustaining electric field by 55% and thereby results in a predicted EEDF with an average energy near 1.1 eV.

Population densities and rate coefficients for electron impact excitation in singly ionized oxygen

In non-LTE arc plasmas, O II excited state number densities were measured relative to the O II ground and metastable states. The results were compared with collisional-radiative code calculations on the basis of the JET ADAS programs. Stationary He plasmas with small oxygen admixtures, generated in a 5 mm diameter cascade arc chamber (pressures 13-70 hPa, arc current 150 A), were investigated spectroscopically in the visible and the VUV spectral range. The continuum of a 2 mm diameter pure He arc (atmospheric pressure, current 100 A) served for calibration of the VUV system response. Plasma diagnostics on the basis of H beta Stark broadening yielded electron densities between 2.4*1014 and 2.0*1015 cm-3 for the low-pressure O II mixture plasmas. The intensities of a He II line were analysed with respect to electron temperatures, resulting in values from 3.5 to 8.2 eV. The O II ground and metastable number densities were derived from resonance lines in the VUV on the basis of the corona excitation balance and the relevant rate coefficients. Subsequently, the population of five 3p levels and one 3d level was obtained from lines in the visible spectrum. The agreement of measured and calculated excited state populations is generally very satisfactory, thus confirming the rate coefficients in the code. This is of particular interest in this intermediate region between corona balance and LTE, where many atomic data are required in the simulation. Clear indications were found for the diffusion of metastables lowering their number densities significantly below their statistical values.

Optimization of quasi-three level end-pumped Q-switched lasers

Equations describing the pump excitation and Q-switched energy extraction of end-pumped, quasi-three level laser systems are collected. A transcendental expression relating the Q-switched laser output energy to the laser's initial gain and cavity transmission which is valid for arbitrary output coupling is derived. This expression simplifies sensitivity and optimization studies of such systems. A first order ordinary differential equation is derived which describes the rod-integrated excited state number density resulting from an arbitrary pump excitation pulse, The equation is valid for both single pass and double pass pump geometries. To illustrate the utility of the collected set of equations an end-pumped joule class, Q-switched Yb:YAG oscillator is optimized and studied.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonequilibrium effects in thermal plasmas

Abstract

Gas temperatures and Penning collision rates in hollow-cathode metal-ion lasers

Gas temperatures along the axis of a hollow-cathode He-Cd laser have been measured. The effect of gas temperature variations on calculations of both the excited-state number densities and the heavy-body Penning collision rates are assessed. Implications on the gas kinetics of these discharge types, in particular, on the role of Penning collisions in populating the 5s2 2D5/2 level of the cadmium ion are discussed.