Electron-impact Excitation Processes Research Articles

Evaluating plasma fluctuation by collisional-radiative model using Malliavin derivative

Abstract Non-equilibrium plasma has garnered significant attention due to its involvement in short-term phenomena. One example is plasma fluctuation, encompassing variations in electron temperature or density. This phenomenon is explored not only in nuclear fusion but also in semiconductor etching and thin film deposition. This study introduces an evaluation method employing Malliavin derivatives to predict plasma fluctuations based on a collisional-radiative model. This model delineates the chemical kinetics of excited states within the plasma. Given that electron impact excitation and atomic collisional processes are stochastic, they exhibit characteristics similar to a Wiener process. Furthermore, the properties of fractional Brownian motion are applied to the Malliavin derivative. The revised Wiener process is utilized to analyze the changes in excited-level populations within short durations. This approach assesses electron or atomic density fluctuations by considering the contributions of electron collisions and those of ground-state atoms.

Spectroscopic diagnosis and simulation analysis of tungsten cathode erosion during the start-up process for a magnetoplasmadynamic thruster

Measurement of tungsten density during the start-up process plays a vital role in monitoring real-time cathode mass loss in the study of plasma discharge instrument structure optimization. The relative intensity of the W II 239.71 nm spectral line, collected at the exit by the monochromator, is used to estimate the W II density in combination with the collision radiative model. The model of a small amount of tungsten in high-density plasma takes into account the main kinetic processes including the electron impact excitation process, electron impact de-excitation process, and electron impact ionization process. Additionally, A two-dimensional axisymmetric quasi-neutral fluid model, coupled with a thermal model of the cathode into a self-consistent model, is also constructed to analyze the mass loss mechanism of tungsten cathode during the start-up process. In the initial stage, the cold-state cathode has a large potential drop in the sheath region to accelerate the ion bombardment of the cathode for the requirement of electron emission, and a large number of tungsten atoms removal from the cathode surface due to sputtering and evaporation. In the steady-state operating phase, the primary reason for the mass loss of tungsten cathodes is attributed to thermal evaporation. Both experimental and simulation results indicate that the mass loss rate during the start-up phase is higher than that during steady-state operation phase by 1 to 2 orders of magnitude.

Collision Strengths of Astrophysical Interest for Multiply Charged Ions

The electron impact excitation and ionization processes are crucial for modeling the spectra of different astrophysical objects, from atmospheres of late-type stars to remnants of supernovae and up to the light emission from neutron star mergers, to name just a few. Despite their significance, however, little is known quantitatively about these processes for low- and medium-impact energies of, say, Ekin≲5000 eV of the free incident electron. To further explore the role of impact excitation, we here expanded Jac, the Jena Atomic Calculator, to the computation of distorted wave collision strengths for fine-structure-resolved, as well as configuration-averaged transitions. While we excluded the formation of dielectronic resonances, these tools can be readily applied for ions with a complex shell structure and by including the major relativistic contributions to these strengths. Detailed computations of the collision strengths are shown and explained for the impact excitation of lithium- and chlorine-like ions. When compared with other, well-correlated methods, good agreement was found, and hence, these tools will support studies of effective collision strengths for a wide range of electron impact energies, levels, and ionic charge states.

Electron impact excitation cross section calculations of the fine structure transitions of Mo and their applications in the diagnostics of the laser induced Mo plasma

The current work reports a detailed calculation of electron impact excitation cross sections for the fine structure transitions of Mo from the manifolds 4d 55s, 4d 45s 2, 4d 6 and 4d 55p to the manifolds 4d 55s, 4d 45s 2, 4d 6, 4d 55p, 4d 45s5p, 4d 55d, 4d 56s, 4d 45s6s, and 4d 57s, using the relativistic distorted wave approximation for the applications in plasma modelling. Multi-configurational Dirac–Fock wave functions are used in the calculations. The oscillator strength and cross section results are compared with the previous calculations and measurements. A comprehensive collisional radiative (CR) model is developed and used to characterize laser induced molybdenum plasma to ensure that the calculated cross sections can be used for various plasma modelling applications. The current CR model has taken into account the electron impact excitation and de-excitation processes using the calculated consistent cross sections. The electron induced processes are dominant kinetic processes in the laser induced plasma. Furthermore, the diagnostics of the laser induced Mo plasma is done by coupling the current CR model with the experimental laser induced breakdown spectroscopic measurements of Mal et al (2021 Appl. Phys. B 127 52). The plasma parameter, i.e., electron temperature has been calculated using nine measured intensities of the emission lines of Mo, with wavelengths 406.9, 423.3, 438.2, 453.7, 476.0, 550.7, 553.3, 557.0 and 592.9 nm. The results are also compared with the values reported in the Boltzmann plot at various delay times ranging from 0.5 to 5.0 μs.

Vibrational excitation cross sections for non-equilibrium nitric oxide-containing plasma

A full set of vibrationally-resolved cross sections for electron impact excitation of NO(X2Π, v) molecules is calculated from ab initio molecular dynamics, in the framework of the local-complex-potential approach. Electron–vibration energy exchanges in non-equilibrium thermodynamic conditions are studied from a state-to-state model accounting for all electron impact excitation and de-excitation processes of the nitric oxide vibration manifold, and it is shown that the calculated vibration relaxation times are in good agreement with the experimental data. The new vibrational excitation cross sections are used in a complete electron impact cross section set in order to obtain non-equilibrium electron energy distributions functions and to calculate electron transport parameters in NO. It is verified that the new cross sections bring a significant improvement between simulations and experimental swarm data, providing an additional validation of the calculations, when used within the complete set of cross sections investigated in this work.

Calculations of electron-impact excitation and dielectronic recombination rate coefficients of highly charged silicon ions

The rate coefficients for dielectronic recombination and electron-impact excitation processes with H-like to Be-like silicon ions (${\mathrm{Si}}^{13+}\text{\ensuremath{-}}{\mathrm{Si}}^{10+}$) are calculated using relativistic distorted-wave approach. The prominent $▵n=1$ and the weaker $▵n=2$ and 3 dielectronic recombination (DR) resonances with $K$-shell excitations are presented, and compared with the existing DR experimental rate coefficients of ${\mathrm{Si}}^{13+}, {\mathrm{Si}}^{12+}$, and ${\mathrm{Si}}^{11+}$ ions, it is found that the theoretical DR rate coefficients are in very good agreement with the experimental results. With the same approach, the direct and resonant electron-impact excitation (EIE) cross sections associated with $1s\ensuremath{-}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}$ core excitations are calculated for the ground states of ${\mathrm{Si}}^{13+}\text{\ensuremath{-}}{\mathrm{Si}}^{10+}$ ions and found in excellent agreement with the available experiment. Finally, we present the synthesized DR and EIE rate coefficients for the sum of all detected $(13+\ensuremath{\sim}10+)$ charge states of Si and these agree well with the experimental results.

Debye-screening effect on electron-impact excitation of helium-like Al11+ and Fe24+ ions

Debye-screening effects on the electron-impact excitation (EIE) processes for the dipole-allowed transition 1s2 1 S → 1s2p 1P in He-like Al11+ and Fe24+ ions are investigated using the fully relativistic distorted-wave methods with the Debye–Hückel (DH) model potential. Debye-screening effects on the continuum-bound (CB) interaction and target ion are discussed, both of which result in reduction of EIE cross sections. This reduction due to screening on the CB interaction is dominant. The non-spherical and spherical DH potentials are adopted for considering the screening effect on the CB interaction. It is found that the spherical DH potential could significantly overestimate the influence of plasma screening on EIE cross sections for multielectron He-like ions.

Angular Distribution of Characteristic Radiation Following the Excitation of He-Like Uranium in Relativistic Collisions

In this paper, we present an experimental and theoretical study of excitation processes for the heaviest stable helium-like ion, that is, He-like uranium occurring in relativistic collisions with hydrogen and argon targets. In particular, we concentrate on angular distributions of the characteristic Kα radiation following the K → L excitation of He-like uranium. We pay special attention to the magnetic sub-level population of the excited 1s2lj states, which is directly related to the angular distribution of the characteristic Kα radiation. We show that the experimental data can be well described by calculations taking into account the excitation by the target nucleus as well as by the target electrons. Moreover, we demonstrate for the first time an important influence of the electron-impact excitation process on the angular distributions of the Kα radiation produced by excitation of He-like uranium in collisions with different targets.

Outer midplane neutral density measurements and H-mode fueling studies in NSTX-U

Neutral density profiles are measured on the outboard midplane of the National Spherical Torus Experiment Upgrade (NSTX-U) using a two dimensional camera (ENDD, edge neutral density diagnostic) filtered for deuterium Balmer α (D α ) emission interpreted via simulations using the Monte Carlo neutral transport code DEGAS 2. Deuterium atomic densities n D are calculated by inverting the line-integrated D α brightness and using local measurements of electron density n e and temperature T e to determine atomic rate coefficients. The assumptions used in the derivation of n D from D α emissivity are validated using DEGAS 2 to estimate contributions to emissivity due to electron impact excitation and molecular processes. Experimental measurements and DEGAS 2 simulations are compared over a database of L- and H-mode discharges, showing good agreement in D α emissivity profiles. Residual disagreement between experiment and simulations is suggestive of the possible role of intermittent transport and uncertainties in the molecular data. DEGAS 2 simulations are further used to complement the ENDD diagnostic, extracting neutral (atomic and molecular) densities at locations where the ENDD measurement are not made or where the assumptions used in the ENDD analysis are not valid. Deuterium atomic densities and ionization profiles on the outer midplane are compared for L-mode and H-mode discharges in NSTX-U. One-way coupling of DEGAS 2 to UEDGE multi-fluid simulations constrained by experimental data is used to study edge fueling and neutral penetration in NSTX-U discharges.

Semiclassical theory of resonant dissociative excitation of molecular ions by electron impact

We have developed a semiclassical approach to the description of resonant dissociative excitation of a molecular ion induced by collisions with plasma free electrons and accompanied by the non-adiabatic transitions between its different electronic terms. It is based on the quasistatic treatment of nuclear particles relative motion in a molecular ion combined with the approximation of a quasicontinuum for rovibrational states. We have derived the semianalytic expressions for the Boltzmann-averaged cross sections, , and rate constants, α de(T, T e), of this process. The resulting expressions for and α de(T, T e) with explicit dependencies on the electron energy, ɛ, the gas, T, and electron, T e, temperatures are valid when the thermal energy k B T exceeds the value of the lowest vibrational quantum, ℏω e, of a molecular ion. The theory developed is applied to studying the resonant dissociative excitation of homo-nuclear , and ions as well as the hetero-nuclear rare gas ions RgXe+ (Rg = Ne, Ar, and Kr) with significantly different values of the dissociation energy. The efficiencies of the electron-impact dissociative excitation process and dissociative recombination leading to the population of the Rydberg states are compared. Our results of calculations are in good agreement with the available experimental data.

Characterization of a transient spark micro-discharge in nitrogen using simultaneous two-wavelength diagnostics

A transient spark micro-discharge in nitrogen is investigated between two sharpened electrodes at a pressure of 0.5 bar. The plasma parameters (gas temperature, electron density and reduced electric field) are determined using optical emission spectroscopy (OES) and numerical simulations. The gas temperature of 3500 ± 100 K is determined by the comparison of the measured and simulated rotational distributions of the photoemission spectra of neutral molecular nitrogen N2(C-B,0–0). Both direct and stepwise electron impact excitation are considered in the collision-radiative model. The rate constants for electron impact excitation processes are calculated for different electric field values using the electron velocity distribution function, which is simulated by solving the Boltzmann equation. The applied broadband echelle spectrometer is absolutely calibrated in a spectral range of 200 nm to 800 nm, using two standard light sources, a deuterium lamp and a tungsten ribbon lamp, which are certificated by the Physikalisch-Technische Bundesanstalt (PTB), Germany. With the aid of this absolutely calibrated echelle spectrometer and a microwave atmospheric plasma source operated in a nitrogen flow, the intensified charge-coupled device (ICCD) camera, provided with an in-house made optical arrangement for simultaneous two-wavelength diagnostic is calibrated. The spatial resolution of this diagnostic system under the studied plasma conditions amounts to 13 µm. The accurate examination of the experimental results allows determining the dominant process of electron impact excitation of molecular nitrogen ion from ionic ground state. Applying the chosen excitation model of the nitrogen photoemission, the spatially resolved reduced electric field and the electron density are determined. This is done by using the inverse Abel transformation of the absolute intensities of molecular nitrogen bands N2(C-B,0–0) and (B-X,0–0), which were measured with the calibrated ICCD camera. The measured electric current of the micro-discharge is compared with the calculated one using the measured plasma parameters and a good coincidence is established.

Polarization of x-ray radiation after electron-impact excitation of ions in plasmas

A new relativistic model for calculating (magnetic sublevel) electron-impact excitation process in plasmas is proposed in this paper, which is essential to predict the polarization property of x-ray radiation. Our model focuses on weakly coupled plasmas (assuming that the plasma is of low density and very hot), where we use a Debye-Hückel potential to represent the interactions among the charged particles, in order to calculate plasma shielding effects. As a practical example, we present results of accurate calculations of transition energy, cross section, and linear polarization of the photon emission following EIE of 1s2→1s2p3,1P1 lines of He-like Ar16+ ion over a broad range of energies and Debye lengths, i.e., 16 times ionized atom of Ar. Such highly-ionized species can exist in many environments, such as in laser-produced plasmas, x-ray laser, astrophysics, and inertial confinement fusion experiments. The energies and cross sections are found to be decreased with decreasing Debye length, these general characteristics also lead to a reduction in the linear polarization of the photon emission. The present approach compares well, with existing methods and experimental data. Apart from other applications, results obtained in this work should be useful in plasma diagnostic.

Polarization of fluorescence radiation following electron impact excitation of ions immersed in strongly coupled plasmas

An investigation on the electron impact excitation and subsequent radiative decay process of He-like Fe24+ ions immersed in strongly coupled plasmas is made, using the 1s2p P3,11 → 1s2 S10 characteristic lines as an example. The shielded nuclear potential of the uniform electron gas model (UEGM) type experienced by the electron is parameterized by the ion-sphere radius. For the target structure, accuracies of wave functions are justified by evaluating the energies of the relevant states. To serve as an independent check of the results, self-consistent calculations are carried out using the multiconfiguration Dirac-Fock relativistic configuration interaction method incorporating the same potential. For the impact excitation process, the UEGM potential is also employed to screen the projectile electron from the nucleus and target electrons. A distorted-wave method in the framework of the relativistic theory is developed to include the effect of plasma background, in which the continuum wave function of the projectile electron is evaluated by solving numerically the modified Dirac equations. The plasma effects on the total excitation cross section, magnetic sublevel cross section, and linear polarization of fluorescence radiation are investigated. The comparison with the available theoretical and experimental results is satisfactory.

Study on electrons conduction paths in Hall thruster ignition processes with the cathode located inside and outside the magnetic separatrix

A high speed charged coupled device (CCD) camera was used to examine the plume features over time when the cathode was located inside and outside the magnetic separatrix. Due to the different positions of the cathode, there are obvious differences in the electron impact excitation process, the characteristics of the plasma bridge, and the transition process from the end of ignition to the steady-state discharge process. The main reason for these differences may be due to the different conduction paths followed by emitted electrons into the acceleration channel. The CCD images method can be used as a technique to characterize the ignition process of Hall thruster.

Collisional radiative model for Ar-O2 mixture plasma with fully relativistic fine structure cross sections

A collisional radiative (C-R) model has been developed to diagnose the rf generated Ar-O2 (0%–5%) mixture plasma at low temperatures. Since in such plasmas the most dominant process is an electron impact excitation process, we considered several electron impact fine structure transitions in an argon atom from its ground as well as excited states. The cross-sections for these transitions have been obtained using the reliable fully relativistic distorted wave theory. Processes which account for the coupling of argon with the oxygen molecules have been further added to the model. We couple our model to the optical spectroscopic measurements reported by Jogi et al. [J. Phys. D: Appl. Phys. 47, 335206 (2014)]. The plasma parameters, viz. the electron density (ne) and the electron temperature (Te) as a function of O2 concentration have been obtained using thirteen intense emission lines out of 3p54p → 3p54s transitions observed in their spectroscopic measurements. It is found that as the content of O2 in Ar increases from 0%–5%, Te increases in the range 0.85–1.7 eV, while the electron density decreases from 2.76 × 1012–2.34 × 1011 cm−3. The Ar-3p54s (1si) fine-structure level populations at our extracted plasma parameters are found to be in very good agreement with those obtained from the measurements. Furthermore, we have estimated the individual contributions coming from the ground state, 1si manifolds and cascade contributions to the population of the radiating Ar-3p54p (2pi) states as a function of a trace amount of O2. Such information is very useful to understand the importance of various processes occurring in the plasma.

Hyperfine structure effect on circular polarization of X-ray radiation

During the last decades, the electron impact excitation (EIE) process has aroused much interest in various research areas. This process is crucial to the diagnoses of astrophysical and laboratory plasmas. Moreover, the EIE studies play an important role in understanding the quantum electrodynamic, many-electron, and hyperfine interaction effects in heavy atomic systems. As is well known, when ions are excited by collisions with a unidirectional beam of electrons, the magnetic sublevels of the excited state may be populated with nonstatistical probability. In the decay of the excited state, the emitted radiation is found to be anisotropic and polarized. From the analysis of the polarization, valuable information can be obtained. These properties have become indispensable tools for the diagnosis of plasma state and the analysis of complex spectrum formation mechanism. Up to now, however, most of studies have dealt with the linear polarization of X-ray radiation. Fewer publications have reported the circular polarization. Moreover, theoretical studies of the characteristic X-ray emission have just dealt with ions having zero nuclear spin, or have simply omitted all contributions that arise from such a spin. It is known that some kinds of ions each have a nuclear spin I 0. Owing to the hyperfine coupling, new decay channel will be open, namely, hyperfine-induced transition. It is thus important to analyze how the hyperfine interaction affects the polarization properties of X-ray radiation. In this study, we present a systematically theoretical analysis of the polarization and angular distribution of X-ray radiation during the hyperfine-induced transition. The calculations are performed by using a fully relativistic distorted-wave method. Special attention is paid to the studies of angular correlations and polarization properties of the 1s2p 3P2 Fi=3/2 1s2 1S Ff=1/2 decay for highly charged He-like Sc19+ and 205Tl79+ ions with nuclear spin I=1/2 following impact excitation by a completely longitudinally-polarized electron beam. Two effects, i.e.the BI and the mutipole mixing between the leading M2 decay and hyperfine-induced E1 decay, on the polarization of the emitted radiation are discussed. Our results show that both the BI and the E1-M2 interference effects may significantly affect the polarization and angular emission pattern of the transition line. For example, the BI and the E1-M2 mixing lead the circular polarization to increase by about 50% and 40% for 205Tl79+ ions, respectively. With the development of the X-ray detectors, the measurement on the polarization during the hyperfine-induced transition becomes feasible. We hope that the present results would be useful in resolving some disagreement between the theories and experiments relating to the polarization properties of the X-ray radiation.

Influence of Breit interaction on the linear polarization of radiation following electron impact excitation of B-like ions

SynopsisThe influences of Breit interaction on the total cross section and linear polarization of highly charged Ca15+, Xe49+, and W69+ ions in the electron impact excitation process are calculated by fully relativistic distorted-wave program REIE06. It is found that the influence of Breit interaction on the linear polarization is more obvious with the increase of atomic number Z.

Time-integrated optical emission studies on laser-produced copper plasma in the presence of magnetic field in air ambient at atmospheric pressure

We report on the effect of laser fluence variation on ablation rate and the time-integrated optical emission of copper plasma in the presence of static transverse magnetic field in air. In the presence of magnetic field, the ablation rate at 14 Jcm−2 laser fluence is around two times higher than that in the absence of magnetic field. It is attributed to an increase in melt ejection caused by recoil pressure of ablated mass in the presence of magnetic field. We also simulated the laser ablation rate using finite element method to justify that the ablation rate is higher in the presence of magnetic field. The intensity of atomic/ionic transition is enhanced in the presence of magnetic field. The enhancement in the intensity of spectral line depends on laser fluence and it is pronounced at fluence 14 Jcm−2. The intensity enhancement is due to an increase in electron-impact excitation and recombination process as a result of magnetic confinement of plasma. The ionic line also showed intensity enhancement in the presence of the magnetic field. It is due to the increase in ionization of atom in the presence of magnetic field. The ionization potential is lowered in the presence of magnetic field which results in more ionization. The electron density and temperature initially increased with fluence and then decreased slightly at higher fluence. In the presence of magnetic field, the electron density and temperature followed the same trend; however, higher compared with that in the absence of magnetic field. It is attributed to magnetic confinement of plasma. The spatially resolved optical emission measurements showed that the intensity with magnetic field decreased with lateral distance. However, it is higher than that without magnetic field up to 2 mm and beyond that the intensity with and without magnetic field remained almost the same.

Electron impact excitation for He-like ions withZ= 20–42

Aims. Spectral lines of He-like ions are among the most prominent features in X-ray spectra from a large variety of astrophysical and high-temperature fusion plasmas. A reliable plasma modeling and interpretation of the spectra require a large amount of accurate atomic data related to various physical processes. In this paper, we focus on the electron-impact excitation (EIE) process. Methods. We adopted the independent process and isolated resonances approximation using distorted waves (IPIRDW). Resonant stabilizing transitions and decays to lower-lying autoionizing levels from the resonances are included as radiative damping. To verify the applicability of the IPIRDW approximation, an independent Dirac R-matrix calculation was also performed. The two sets of results show excellent agreement. Results. We report electron impact excitation collision strengths for transitions among the lowest 49 levels of the 1snl(n ≤ 5; l ≤ (n - 1)) configurations in He-like ions with 20 ≤ Z ≤ 42. The line ratios R and G are calculated for Fe XXV and Kr XXXV. Conclusions. Compared to previous theoretical calculations, our IPIRDWcalculation treats resonance excitation and radiative damping effects more comprehensively, and the resulting line emission cross sections show good agreement with the experimental observations. Our results should facilitate the modeling and diagnostics of various astrophysical and laboratory plasmas. (Less)

EUV induced low temperature SF6-based plasma

In this work spectral investigations of low temperature F-rich photoionized plasmas were performed. The photoionized plasmas were created by irradiation of SF6 gas with intense EUV (extreme ultraviolet) radiation pulses. Two laser plasma EUV sources of different parameters used in the experiments were based on 0.8 J /4ns and 10 J/ 10 ns Nd:YAG lasers respectively. Both sources operated at 10 Hz repetition rate. The EUV radiation was focused using a dedicated reflective collector onto the gas stream, injected into a vacuum chamber synchronously with the EUV pulses. Irradiation of the SF6 gas resulted in dissociative ionization of the molecules, leading to creation of SFn+ ions and fluorine atoms. Further photo- or electron impact ionization and excitation processes allow for formation of photoionized plasmas emitting radiation in the wide spectral range. Emission spectra were measured in the EUV and optical ranges. The EUV spectra contained multiple spectral lines, originating from F II, F III and S II ions. The UV/VIS spectra were composed of spectral lines corresponding to radiative transitions in F II, F I and S II species. A computer simulation of the F II spectrum was performed using a collisional-radiative PrismSPECT code. Parameters of the photoionized plasmas were estimated by fitting the spectrum obtained from the simulations to the experimental one. Apart from that, the electron temperature was estimated employing Boltzmann plots based on the UV/VIS spectrum.