Collisional-radiative modeling with multitemperature thermodynamic models

To control the H(0) atom production profile in the H(-) ion sources is one of the important issues for the efficient and uniform surface H(-) production. The purpose of this study is to construct a collisional radiative (CR) model to calculate the effective production rate of H(0) atoms from H2 molecules in the model geometry of the radio-frequency (RF) H(-) ion source for Linac4 accelerator. In order to validate the CR model by comparison with the experimental results from the optical emission spectroscopy, it is also necessary for the model to calculate Balmer photon emission rate in the source. As a basic test of the model, the time evolutions of H(0) production and the Balmer Hα photon emission rate are calculated for given electron energy distribution functions in the Linac4 RF H(-) ion source. Reasonable test results are obtained and basis for the detailed comparisons with experimental results have been established.

An algorithm for diagnosing the electron density and temperature of helium plasma at atmospheric pressure has been developed based on a revised helium collisional-radiative (CR) model. Atomic collision processes are included, and part of the atomic data of electron collision processes in the conventional CR model has been updated to expand its valid pressure. The algorithm uses eight emission lines in the visible-wavelength range as inputs to determine the electron density, electron temperature, and number density of the two metastable states by fitting the number density of the states corresponding to the emission lines. The algorithm has a considerably small theoretical error. In the microwave-discharged low-pressure helium plasma experiment, the results obtained with the algorithm agreed well with the results obtained with the probe method. The electron density and temperature of the atmospheric-pressure helium plasma obtained with the algorithm agreed well with the results of the continuum spectrum analysis.

To examine the influence of radiative transitions on the performance of nonequilibrium seed-free argon plasma magnetohydrodynamic (MHD) generators, we developed MHD numerical simulation technique with a collisional-radiative (C-R) model, where neutral argon atoms with 45 discrete effective electronic excitation levels, singly ionized argon ions, and free electrons were considered under a two-temperature, low-magnetic Reynolds number MHD approximation. Furthermore, a so-called escape factor was implemented in the C-R model to consider the effects of radiation trapping by ground-state neutral atoms. Using the developed technique, we computed the performance characteristics of a nonequilibrium seed-free argon plasma MHD generator. The numerical results showed that the generator performance gets higher as the escape factor decreases, i.e., the optical thickness for radiative transitions to the ground state of neutral atoms increases. The numerical results also suggested that when the escape factor is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.0\times 10^{-3}$ </tex-math></inline-formula> or less, the generator performance is almost the same as that for the escape factor of 0 corresponding to completely optical-thick plasma case for the radiative transitions to the ground state of neutral atoms. Furthermore, realistic escape factor values for resonance lines in the power generation channel were evaluated using a well-known estimation model. Consequently, the estimated values had the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-4}$ </tex-math></inline-formula> . We also showed that under such relatively optically thick plasma cases, a collisional (C) model and a widely used global ionization-recombination rate model with no explicit consideration of electronically excited-state neutral atoms can reproduce the generator performance predicted by the C-R model with relatively good accuracy.

Collisional-radiative (CR) models describe the atomic processes in a plasma by tracking the population density in the ground and excited states for each charge state of the atom/ion. These models predict important plasma properties such as charge state distributions and radiative emissivity and opacity. Accurate descriptions of the CR balance of the plasma are essential in fusion whole device modeling, especially when significant impurities are introduced into the plasmas. In an integrated fusion plasma and CR simulation, a CR model, which is a high-dimensional stiff ODE, needs to be solved on each grid point in the configuration space, and can overwhelm the overall computational cost. In this work, we propose a machine-learning-based method that discovers a latent space and learns its corresponding latent dynamics, which can capture the essential physics to make accurate predictions at much lower online computational cost. The proposed approach is physics-assisted, due to its combination of a physical latent space and a data-driven latent space. It has been demonstrated that the proposed architecture can predict both the full-order CR dynamics and a physical quantity of interest accurately.

In plasmas the population densities are affected by electron collisions and by photon emission and absorption. In low temperature plasmas such as divertor or process plasmas, emissions from impurities are important for plasma diagnostics and plasma modeling. We study the density effect on population densities, effective ionization and recombination rate coefficients and emission lines from carbon ions. Especially we studied recombination processes for L-shell carbon ions because atomic data for dielectronic recombination for L-shell ions have recently become available. We made collisional radiative (CR) models for carbon L-shell ions including both ionization/excitation and recombination processes. Our CR model can calculate the line emission associated with recombination as well as that associated with excitation. In this work we apply these models to measured spectra from LHD (Large Helical Device) in the National Institute for Fusion Science. The spectra in recombining phase are measured in LHD and they are compared with our CR model.

We develop a collisional radiative (CR) model of high-Z multiple charge ions based on computational atomic data. We use an algorithm to determine a set of atomic energy levels in the model with significant population in the plasmas and contribute to the dielectronic recombination (DR) processes. The model is validated through participation to the non-LTE kinetics workshops. At the nLTE workshop, an alternative method for the analysis of the spectrum from plasmas based on genetic algorithm (GA) is also discussed. An application of the present model to calculate the ion abundance and radiative power loss of Gd and Nd plasmas is also shown.

SPIDER is the full scale prototype for the ITER Heating Neutral Beam (HNB) source. The production of negative ions in the source mostly relies on the conversion of H/D atoms and positive ions on a 1.6 m <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times0.8$ </tex-math></inline-formula> m converter surface, which is covered with cesium in order to reduce its work function and maximize the conversion efficiency. In SPIDER, optical emission spectroscopy (OES) is used to study the light emitted by the plasma. In particular, the intensities of the cesium emission lines are tracked and used to reconstruct the distribution of its excited states. By coupling these measurements with a collisional radiative (CR) model, estimates of the cesium ground-state density and plasma parameters can be obtained in various parts of the source which are unreachable by other diagnostics. This work describes such a model and its use in conjunction with OES during the first operation with cesium in SPIDER. The electron density at the bottom of the source was found to be much larger than the rest, as a consequence of vertical drifts caused by the horizontal filter field, which would likely indicate a lower negative-ion availability for the beam. The effect of increasing the cesium evaporation rate on the negative-ion and electron densities was also investigated.

A collisional radiative (CR) model has been developed for the diagnostics of Ne–Ar mixture plasma. The 40 fine‐structure resolved energy levels of neon corresponding 2p53s, 2p53p, 2p53d, 2p54s, and 2p54p along with ground state (2p6) and ion state (2p5) have been considered. All the essential population and de‐population channels viz. electron impact excitation‐de‐excitation, ionization, two/three‐body recombination, radiative decay, self‐absorption correction, diffusion, etc., have been considered in the model. The quenching of relatively higher lifetime states 2p53s due to interaction with Ar atoms through associative and Penning ionization is also included in the model. The applicability of the CR model is demonstrated by performing the optical diagnostic of rf induced inductively coupled Ne–Ar mixture plasma. The plasma parameters viz. electron temperature, electron density, and population distribution of levels at various mixture conditions are extracted by coupling the present CR model predictions with emission and absorption measurements by Boffard et al. [J. Phys. D: Appl. Phys., 45, 382001 (2012) and private communication]. The results are also compared with earlier optical models and Langmuir probe measurements. The self‐absorption correction (escape) factors and electron impact excitation rates at various Ne–Ar mixture concentrations are also presented.

Summary form only given. X-pinch experiments using 188 alloy and combined Mo/W wires were implemented at the Cornell 450 kA XP facility. The spatially resolved, time-gated and integrated X-ray line spectra have been recorded using different crystal spectrometers (time-gated ADP and time-integrated mica crystal spectrometers). In particular, K-shell and L-shell X-ray line spectra from Cr, Co, and Ni ions as well as M-shell spectra from W ions have been recorded through different filters in the same shot from the 188 wire alloy X-pinch. In addition, L-shell spectra of Mo ions and M-shell spectra of W ions have been studied produced from X-pinches composed from two different wires of Mo and W. Non-LTE collisional-radiative (CR) atomic kinetic models of Ni and Co have been developed earlier to identify the useful K- and L-shell diagnostic features in X-pinch plasmas from nichrome and conichrome alloys produced at the same Cornell XP device. These models along with the Mo model were used in the present work to interpret X-ray spectra from 188 alloys and to isolate M-shell spectra of W ions. The newly developed non-LTE CR model of W has been applied to identify and diagnose the spectral features of W ions in both types of X-pinches. The distinct features, similarities, and differences of these M-shell spectra of W ions have been analyzed and compared for both types of X-pinches. The future development of this work is discussed.

Collisional-radiative (CR) models for neutral and singly ionized xenon have been constructed for applications to Hall thruster diagnostics. The models use primarily theoretical electron-impact excitation cross sections calculated using the Dirac B-spline R-matrix method. This paper describes the models’ construction and their validation against heritage CR models and previously published Hall thruster data, and then outlines several applications. The baseline 0D steady-state models are used to investigate electron density dependence in neutral xenon emission line intensity ratios commonly used to measure electron temperature, and also to demonstrate that stepwise ionization through excited states is an important process in Hall thrusters. The models are extended to evaluate impacts of neutral and ion transport on 0D CR model applicability, intrinsic bandwidth limits for time-dependent line intensity measurements, and errors introduced when the plasma is assumed to be optically thin.

Collisional-radiative model for neutral helium in plasma revisited

Atomic processes in Sn plasmas are investigated for application to extreme-ultraviolet (EUV) light sources used in microlithography. We develop a full collisional radiative (CR) model of Sn plasmas based on calculated atomic data using Hebrew University Lawrence Livermore Atomic Code (HULLAC). Resonance and satellite lines from singly and multiply excited states of Sn ions, which contribute significantly to the EUV emission, are identified and included in the model through a systematic investigation of their effect on the emission spectra. The wavelengths of the 4d−4f+4p−4d transitions of Sn5+ to Sn13+ are investigated, because of their importance for determining the conversion efficiency of the EUV source, in conjunction with the effect of configuration interaction in the calculation of atomic structure. Calculated emission spectra are compared with those of charge exchange spectroscopy and of laser produced plasma EUV sources. The comparison is also carried out for the opacity of a radiatively heated Sn sample. A reasonable agreement is obtained between calculated and experimental EUV emission spectra observed under the typical condition of EUV sources with the ion density and ionization temperature of the plasma around 1018 cm−3 and 20 eV, respectively, by applying a wavelength correction to the resonance and satellite lines. Finally, the spectral emissivity and opacity of Sn plasmas are calculated as a function of electron temperature and ion density. The results are useful for radiation hydrodynamics simulations for the optimization of EUV sources.

Based on the heat conduction equation, hydrodynamics equations, and radiation transport equation, a two-dimensional axisymmetric radiation hydrodynamics model is developed. The charge state distribution and energy level population in the plasma are solved by the collisional-radiative model using screened hydrogenic levels. The model is used to study the effect of excitation laser wavelength at 1064 and 266 nm on aluminum target evolution, plasma generation, laser absorption in the plasma, and the plasma characteristic during laser ablation in the presence of atmospheric pressure. For 1064 nm radiation, the evaporation of the target surface stops earlier and the plasma formation time is later. The plasma has higher temperature as well as density and the hottest region is at the forefront of the plasma. The plasma shielding effect resulted in a sharp decrease in the laser transmissivity of 1064 nm radiation to about 0.1%, while the transmissivity of 266 nm radiation only decreased to about 30%. The inverse bremsstrahlung is the most important laser absorption mechanism for 1064 nm, whereas photoionization dominates the entire absorption process in the case of 266 nm radiation. The effect of the plasma model on optical breakdown has been present. The results show that neither breakdown nor plasma formation is encountered if the local thermodynamic equilibrium model is used in 266 nm radiation.

The helium (He) non-thermal atmospheric pressure plasma jet (APPJ) source was configured, and the He spectra were measured by applying AC power to the source. A He collisional-radiative (CR) model was developed to investigate the He spectra obtained from the APPJ source. Different atmospheric pressure (AP) processes were evaluated, and the dominant processes among them that contribute to the He spectra were determined. The plasma parameters of the APPJ were determined using the He CR model, and the He spectra were successfully reproduced. The electron density was determined to be ∼2×1012 cm−3 between the electrodes of the APPJ, and ∼9×1011cm−3 outside the quartz tube, for a frequency and bias of an AC voltage source of 5 kHz and 10 kVp.p, respectively. A parametric study was performed to explain the behavior of the electron temperature and electron density of APPJ.

We present extreme ultraviolet spectra of highly charged tungsten ions (${\mathrm{W}}^{19+}\ensuremath{-}{\mathrm{W}}^{32+}$) in the wavelength range of $15\ensuremath{-}55\phantom{\rule{0.16em}{0ex}}\AA{}$ obtained with a compact electron-beam ion trap (CoBIT) and a grazing-incidence spectrometer at the National Institute for Fusion Science. The electron energy dependence of the spectra was investigated for electron energies from 490 to $1320\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$. Identification of the observed lines was aided by collisional-radiative (CR) modeling of CoBIT plasma. Good quantitative agreement was obtained between the CR-modeling results and the experimental observations. The ion charge dependence of the $6g\text{\ensuremath{-}}4f,\phantom{\rule{0.16em}{0ex}}5g\text{\ensuremath{-}}4f,\phantom{\rule{0.16em}{0ex}}5f\text{\ensuremath{-}}4d,\phantom{\rule{0.16em}{0ex}}5p\text{\ensuremath{-}}4d$, and $4f\text{\ensuremath{-}}4d$ transition wavelengths were measured.