Electron Energy Distribution Function Research Articles

Measurement of plasma electron energy distribution functions by Langmuir probe using a modified AC modulation method

Abstract In the diagnosis of vacuum discharge plasma using the Langmuir probe, the electron energy distribution function(EEDF) is closely related to the second derivative of current to voltage (d2I/dV2) on the Langmuir probe. While d2I/dV2 is very sensitive to probe noise, its accuracy directly affects the measurement results of the electron energy distribution function. In this paper, a modified AC modulation method is proposed to improve the measurement accuracy of the electron energy distribution function. First, two small AC signals of different amplitudes are modulated on the measured DC scanning voltage of the Langmuir probe, and the probe current signal is measured. Then, the fundamental amplitudes of the two AC signals are corrected by spectral analysis and using the all-phase Fast Fourier Transformation - Fast Fourier Transformation(apFFT-FFT) amplitude correction algorithm. Then the accurate first-order derivative of the probe current to voltage (dI/dV) is obtained using the AC modulation derivative correction algorithm, and finally the electron energy distribution function is obtained by numerically differentiating dI/dV to obtain d2I/dV2. The method of this paper is compared with the traditional data processing method through experiments, and the results show the superiority and effectiveness of the method.

A global model and two-dimensional simulation study of a low-pressure inductively coupled CF4 plasma considering non-Maxwellian EEDF

We analyze the discharge characteristics of a low-pressure inductively coupled CF4 plasma using a global model and a two-dimensional (2D) simulation. We first conducted a study comparing the experimental results with the global model, which makes it easier to compare the trend concerning external parameters and less computationally expensive, to validate the chemical reaction data, and then, compared the experimental results with the 2D simulation results. We then analyzed the discharge characteristics by comparing the 2D model results with the global model at various gas pressures and powers. The simulations were performed using COMSOL software, which is based on a fluid model. The electron energy distribution function (EEDF) was solved self-consistently using the Boltzmann equation solver, and then, coupled with the fluid model. The results were more consistent with the experimental results when the EEDF was calculated by solving the Boltzmann equation than for assuming the Maxwellian EEDF. Furthermore, the global model results were similar with the mean values obtained from the 2D model. This indicates that it is efficient to first validate the electron collision cross sections and reaction coefficients using the global model. Our approach is expected to be utilized in the analysis of new gases.

Scattering of e∓ in beryllium isonuclear series: cross sections and transport characteristics

The elastic scattering of electrons and positrons by beryllium atoms and its isonuclear ion states is described in this paper in terms of differential and various angle integrated cross sections. For this element, the critical minima in the elastic differential cross sections and the optimum spin polarization sites are found. These calculations are performed using the Dirac partial wave analysis (DPWA) and a projectile-target modified complex optical model potential. Further, the Monte Carlo method is used to calculate the transport characteristics of electrons in a mixture of inert gas (He, Ar) and beryllium vapor for electric field values E/N = 1-100 Td, taking into account inelastic collisions. We studied the effect of metal vapor concentration on drift velocity, average electron energy, diffusion and mobility coefficients. Finally, we investigated the effect of beryllium vapor on the electron energy distribution function in the inert gas. On comparing present work with existing theoretical calculation, a reasonable agreement is observed.

Numerical investigation of plasma properties in Ar/SiH4 inductively coupled plasmas considering electron energy distribution functions

In thin film deposition, Ar/SiH4 mixtures are widely used to make polysilicon (poly-Si) and hydrogenated amorphous silicon (a-SiH) layers. Despite extensive research conducted on this mixture, little research has focused on the variations in plasma properties, radicals, and ions that occur during plasma discharge in inductively coupled plasma (ICP) equipment compared to capacitive coupled plasma equipment. In this paper, we investigate the properties of the plasma generated through mathematical modeling of Ar/SiH4 inductive coupled plasma discharge by using the electron energy distribution function (EEDF) obtained by solving the Boltzmann equation. We closely examine the variation in plasma properties and the correlation of plasma variables by controlling the radio frequency power and gas pressure during the process conditions. The Boltzmann equation was computed by assuming the two-term approximation, resulting in a Druyvesteyn-like EEDF due to the high-pressure conditions. To validate the simulation model, the 2D simulation results were compared with probe measurements performed in a two-turn ICP chamber. The results demonstrated encouraging agreement with the measured data. This research not only enhances our comprehension of the discharge characteristics but also establishes a framework for optimizing the discharge conditions to enhance the process and effectively regulate external variables.

Preliminary Exploration of Low Frequency Low-Pressure Capacitively Coupled Ar-O2 Plasma

Non-thermal plasma as an emergent technology has received considerable attention for its wide range of applications in agriculture, material synthesis, and the biomedical field due to its low cost and portability. It has promising antimicrobial properties, making it a powerful tool for bacterial decontamination. However, traditional techniques for producing non-thermal plasma frequently rely on radiofrequency (RF) devices, despite their effectiveness, are intricate and expensive. This study focuses on generating Ar-O2 capacitively coupled plasma under vacuum conditions, utilizing a low-frequency alternating current (AC) power supply, to evaluate the system’s antimicrobial efficacy. A single Langmuir probe diagnostic was used to assess the key plasma parameters such as electron density (ne), electron temperature (Te), and electron energy distribution function (EEDF). Experimental results showed that ne increases (7 × 1015 m−3 to 1.5 × 1016 m−3) with a rise in pressure and AC power. Similarly, the EEDF modified into a bi-Maxwellian distribution with an increase in AC power, showing a higher population of low-energy electrons at higher power. Finally, the generated plasma was tested for antimicrobial treatment of Xanthomonas campestris pv. Vesicatoria. It is noted that the plasma generated by the AC power supply, at a pressure of 0.5 mbar and power of 400 W for 180 s, has 75% killing efficiency. This promising result highlights the capability of the suggested approach, which may be a budget-friendly and effective technique for eliminating microbes with promising applications in agriculture, biomedicine, and food processing.

Energy efficient F atom generation and control in CF4 capacitively coupled plasmas driven by tailored voltage waveforms

Abstract Neutral radicals generated by electron impact dissociation of the background gas play important roles in etching and deposition processes in low pressure capacitively coupled plasmas (CCPs). The rate and energy efficiency of producing a given radical depend on the space- and time-dependent electron energy distribution function (EEDF) in the plasma, as well as the electron energy dependent cross sections of the electron-neutral collisions that result in the generation of the radical. For the case of a CCP operated in CF4 gas, we computationally demonstrate that the energy efficiency of generating neutral radicals, such as F atoms can be improved by controlling the EEDF by using tailored voltage waveforms (TVW) instead of single-frequency driving voltage waveforms and that separate control of the radical density and the ion energy can be realized by adjusting the waveform shape at constant peak-to-peak voltage. Such discharges are often used for industrial etching processes, in which the F atom density plays a crucial role for the etch rate. Different voltage waveform shapes, i.e. sinusoidal waveforms at low (13.56 MHz) and high (67.8 MHz) frequencies, peaks- and sawtooth-up TVWs, are used to study their effects on the energy cost / energy efficiency of F atom generation by PIC/MCC simulations combined with a stationary diffusion model. The F atom density is enhanced by increasing the voltage amplitude in the single frequency cases, while the energy cost per F atom generation increases, i.e. the energy efficiency decreases, because more power is dissipated to the ions, as the sheath voltages and the ion energy increase simultaneously. In contrast, using TVWs can result in a lower energy cost and provide separate control of the F atom density and the ion energy. This is explained by the fact that tailoring the waveform shape in this way allows to enhance the high-energy tail of the EEDF during the sheath expansion phase by inducing a non-sinusoidal sheath motion, which results in acceleration of more electrons to high enough energies to generate F atoms via electron-neutral collisions compared to the single frequency cases. Similar effects of TVWs are expected for the generation of other neutral radicals depending on the electron energy threshold and the specific consequences of TVWs on the EEDF under the discharge conditions of interest.

Heating mode transitions in capacitively coupled CF4 plasmas at low pressure

Abstract Capacitively coupled plasmas operated in CF4 at low pressure are frequently used for dielectric plasma etching. For such applications the generation of different ion and neutral radical species by energy dependent electron impact ionization and dissociation of the neutral background gas is important. These processes are largely determined by the space and time dependent electron energy distribution function and, thus, by the electron power absorption dynamics. In this work and based on a particle-in-cell/Monte Carlo collision model, we show that the electron heating mode in such plasmas is sensitive to changes of the gap at a constant pressure of 3 Pa. At a gap of 1.5 cm, the dominant mode is found to be a hybrid combination of the Drift-Ambipolar (DA) and the α-mode. As the gap is increased to 2 cm and 2.5 cm, the bulk power absorption and ambipolar power absorption decreases, and the DA mode decays. When the gap reaches 3 cm, the α-mode becomes more prominent, and at a gap of 3.75 cm the α-mode is dominant. These mode transitions are caused by a change of the electronegativity and are found to affect the discharge characteristics. The presence of the DA-mode leads to significant positive electron power absorption inside the bulk region and negative power absorption within the sheaths on time average, as electrons are accelerated from the bulk towards the collapsed sheath. The heating mode transitions result in a change from negative to positive total electron power absorption within the sheaths as the gap increases. When accounting for secondary electron emission, the transition of the heating mode can occur at shorter gaps due to the enhanced plasma density and decreased electronegativity.

Helium metastable density determination in the COST reference source by absolutely calibrated optical emission spectroscopy

Helium metastable densities in the COST Reference Microplasma Jet are estimated for a variety of He/N2 admixtures and dissipated powers by applying a collisional-radiative model to absolutely calibrated optical emission spectroscopy measurements. This is accomplished by delineating the excitation mechanisms that result in the N2(C–B) and N2+(B–X) emission bands, the latter of which is strongly coupled to the presence of helium metastables. A number of other plasma parameters are established and discussed for each operating condition including the electron energy distribution function, reduced electric field, rate constants, and electron density. With these parameters, the reaction rates for the primary ionization pathways are also calculated, emphasizing the importance of helium metastables for discharge sustainment. Good agreement with the existing literature is found for most plasma parameters and for helium metastable densities, in particular. A clear [N2]−1 relationship between the nitrogen concentration and density of helium metastables is demonstrated, as has been identified in previous studies in analogous atmospheric pressure plasma jets. This validates the efficacy of this optical technique for determining helium metastable densities and establishes it as a viable, and in many cases, more accessible alternative to other means of quantifying helium metastables in low-temperature plasmas.

Machine learning-based prediction of the electron energy distribution function and electron density of argon plasma from the optical emission spectra

Machine learning-based prediction of the electron energy distribution function and electron density of argon plasma from the optical emission spectra

Retraction Note to: Determination of Electron Energy Distribution Function in Tokamak Plasma

Retraction Note to: Determination of Electron Energy Distribution Function in Tokamak Plasma

Transmissions of an x-ray free electron laser pulse through Al: Influence of nonequilibrium electron kinetics.

A theoretical model for investigating the radiative transfer of an x-ray free electron laser (XFEL) pulse is developed based on a one-dimensional radiative transfer equation. The population dynamics of energy levels is obtained by rate equationapproximation coupling with the Fokker-Planck equation, in which the electron energy distribution function (EEDF) is self-consistently determined. As an illustrative example, XFEL pulse propagation through a solid-density aluminum (Al) is investigated. The characteristics of the temporal evolution of the x-ray pulse shape, level population, and EEDF are demonstrated. The EEDF usually has two parts in XFEL-Al interactions: the near equilibrium part in the lower energy regions and the nonequilibrium part in the higher energy region. The deep gap between the two parts is quickly filled in the solid-density Al plasma. The pulse shape is distorted and the duration shortens as the x-ray pulse propagates through the Al sample. The x-ray transmission spectra were compared with experimental and other theoretical results, and good agreement was found. There are slight discrepancies between the transmission obtained by solving the Fokker-Planck equationand Maxwellian assumptions because nonequilibrium electrons in the higher energy region account for only a small fraction of the total electrons.

Time-dependent electron Boltzmann equation for hypersonic plasmas

The electron kinetics in hypersonic plasmas is modeled by solving the time-dependent electron Boltzmann equation for the electron energy distribution function (EEDF). This plasma is created by strong shock compression of the gas in front of a vehicle moving with hypersonic speed. The main source of energy for the electrons is gas heating due to elastic collisions and second-kind collisions (de-excitation) from vibrationally excited states of N2. We established that the electron energy distribution function is most sensitive to vibrational level populations. At mid-altitudes (tens of kilometers), the electron temperature equilibrates with the vibrational temperature on a microsecond timescale. The electron distribution function reaches steady state on a comparable timescale. Numerical simulations of air plasma showed that the electron energy distribution function is far from Maxwellian and the collision rates differ by orders of magnitude from those computed with a Maxwellian distribution. The two most important parameters for the electron kinetics and the electron energy distribution function are the vibrational temperature and ionization degree.

On fundamental inconsistencies in a commonly used modification of a fluid model for glow discharge

This work considers the fundamental contradictions in the concept of one of the most well-known and widely used modifications of the fluid model for simulation of a glow discharge (GD), the ‘local mean energy approximation’ (LMEA). In this model, it is proposed to determine the kinetic coefficients in the electron particle and energy balance equations as functions of the electron mean energy (temperature) rather than local electric field, using a one-to-one correspondence between these parameters through the electron Boltzmann equation. It is shown that the scope of applicability of this model, like any other modification of the fluid model, is limited by the local mode of formation of the electron energy distribution function (EEDF). Therefore, as demonstrated by the examples of typical 1D and 2D problems for a GD in argon, its extension to the region of nonlocal EEDF is in no way justified and leads not only to serious errors in the results, but also to a logically intractable situation in attempts to apply the main postulate of the LMEA model to the region of a weak (or even reverse) electric field in a negative glow plasma. At the same time, the apparent reliability of calculations within the framework of the LMEA model for a number of parameters, in our opinion, only slows down progress in modeling of gas discharge plasma.

Study on Breakdown Characteristics and Attenuation Characteristics of Air Mixed Gas

Abstract Nowadays, the global demand for environmental protection and energy saving is getting higher and higher. In the past, SF6 gas was regarded as an environmentally unfriendly gas in the circuit breaker with SF6 gas as the insulating medium. In order to save energy and reduce emissions, this paper uses clean and environmentally friendly air as the arc extinguishing medium. The gas mixture studied contains N2, O2 and CO2. Through two approximate values of Boltzmann equation, we obtain the electron energy distribution function of air mixed gas under different electric field reduction conditions. By studying the changes of ionization and adsorption coefficients of particles under various collision conditions, we obtained the conversion breakdown field strength (E/N) Cr of air mixture. An arc attenuation model is built to characterize the arc attenuation characteristics using the prior transport characteristics as input. The arc attenuation process is broken down into three steps: heat recovery, pre-ignition, and arcing. All of these phases are determined by the changes in axial temperature and arc conductance over time. Analysis is done on the air and nitrogen thermal recovery and pre-dielectric recovery phases. This study explores the use of clean dielectrics to ensure optimum performance of primary equipment in the power system, based on current circumstances.

Self-consistent calculation of the optical emission spectrum of an argon capacitively coupled plasma based on the coupling of particle simulation with a collisional-radiative model

We report the development of a computational framework for the calculation of the optical emission spectrum of a low-pressure argon capacitively coupled plasma (CCP), which is based on the coupling of a particle-in-cell/Monte Carlo collision simulation code with a diffusion-reaction-radiation code for Ar I excited levels. In this framework, the particle simulation provides the rates of the direct and stepwise electron-impact excitation and electron-impact de-excitation for 30 excited levels, as well as the rates of electron-impact direct and stepwise ionization. These rates are used in the solutions of the diffusion equations of the excited species in the second code, along with the radiative rates for a high number of Ar-I transitions. The calculations also consider pooling ionization, quenching reactions, and radial diffusion losses. The electron energy distribution function and the population densities of the 30 excited atomic levels are computed self-consistently. The calculations then provide the emission intensities that reproduce reasonably well the experimentally measured optical emission spectrum of a symmetric CCP source operated at 13.56 MHz with 300 V peak-to-peak voltage, in the 2–100 Pa pressure range. The accuracy of the approach appears to be limited by the one-dimensional nature of the model, the treatment of the radiation trapping through the use of escape factors, and the effects of radiative cascades from higher excited levels not taken into account in the model.

Influence of energy transfer processes on the rovibrational characteristics of CO2 in low-temperature conversion plasma with Ar and He admixture.

The influence of argon and helium on the rovibrational kinetics of carbon dioxide (CO2) and CO in low-temperature conversion plasma is investigated. With this objective, a combined experimental and computational study is conducted, applying quantum cascade laser infrared absorption spectroscopy to a pulsed DC CO2 glow discharge with varying noble gas admixture and modeling it with a two-term Boltzmann solver. Time-resolved rovibrational temperatures and dissociation fractions are presented, exhibiting an increase in rotational-vibrational non-equilibrium and an increasing CO2 conversion with argon (Ar) and helium (He) admixtures. Results are discussed in the context of energy transfer processes for collisions involving electrons, corroborated by electron-kinetic modeling, and heavy particle collisions. With noble gas addition, an increase in the electron number density, promoting excitation, and the high-energy tail of the electron energy distribution function are found. Penning ionization processes are proposed as an explanation for the increase in conversion, showing higher conversion for Ar due to the lower excitation thresholds and, therefore, larger state population. In the context of rovibrational kinetics, processes leading to the gain or loss of vibrational energy of CO2 are analyzed, pointing out subtle differences in, for example, relaxation rate coefficients between Ar and He. However, the cooling of the gas through conductive heat transfer is identified as the most important influence of the Ar and He admixture, as it keeps the relaxation rate for vibrational quenching low.

Modeling Study of Chemical Kinetics and Vibrational Excitation in a Volumetric DBD in Humid Air at Atmospheric Pressure

A zero-dimensionl model is developed to study the chemical kinetics of a volumetric dielectric barrier discharge (DBD) reactor operating with humid air at atmospheric pressure. This work focuses on the relation between molecular vibrational excitation, the plasma reactor input power and the number densities of several species that are known to play an important role in biomedical applications (e.g. O3,NO,NO2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{O}_{3},\ extrm{NO, NO}_{2}$$\\end{document}, ...). A preliminary study is carried out to observe the influence of water molecules on the electron energy distribution function for different values of water concentration and reduced electric field. A simplified approach is then adopted to quantify the contribution of vibrationally-excited O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{O}_{2}$$\\end{document} molecules to NO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{NO}$$\\end{document} formation. The results obtained using our detailed model suggest that for the physical conditions considered in this work O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{O}_{2}$$\\end{document} vibrational kinetics can be neglected without compromising the overall accuracy of the simulation. Finally, a reaction set is coupled with an equivalent circuit model to simulate the E-I characteristic of a typical DBD reactor. Different simulations were carried out considering different values of the average plasma input power densities. A particular focus was given to the influence of the Zeldovich mechanism on O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{O}_{3}$$\\end{document} and NOX\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{NO}_\ extrm{X}$$\\end{document} production performing simulations where this reaction is not considered. The obtained results are shown and the role of vibrationally excited N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{N}_{2}$$\\end{document} molecules is discussed. The simulation results indicate also that N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{N}_{2}$$\\end{document} vibrational excitation, and more precisely the Zeldovich mechanism, has a larger effect on O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{O}_{3}$$\\end{document} and NOX\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{NO}_\ extrm{X}$$\\end{document} production at intermediate input power levels.

Reducing the computational complexity of implicit schemes in the modeling of kinetic inelastic collisions in a partially ionized plasma

AbstractModeling the time evolution of atomic number densities and the kinetic (non‐Maxwellian) electron energy distribution function under the action of electron impact collisions by classical approaches requires an implicit time‐stepping scheme to maintain numerical stability. The resulting linear system that must be iteratively solved at each time step incorporates a dense (nonsparse) matrix. For variables being propagated, the computational cost is . We present an alternative approach with a computational cost of , which is the same order as the computational cost of an explicit method for propagating a system of this type. The approach relies on a combination of classical iterative derivative evaluations, combinatorial approximations, and some ideas from deep machine learning.

Plasma properties in the vicinity of the last closed flux surface in hydrogen and helium fusion plasma discharges

The origin of the bi-Maxwellian electron energy distribution function (EEDF) observed in the scrape-off layer (SOL) of tokamak plasmas by means of Langmuir probes is still under discussion. It has been assumed that the ionization of hydrogen and deuterium neutrals by thermal electrons penetrating the SOL from the bulk plasma is the main reason for the appearance of a second Maxwellian. To validate this assumption, radial measurements of the electron temperatures and densities, or the plasma properties in helium plasmas in the GOLEM tokamak and the TJ-II stellarator were performed. The radial profiles of the low-temperature electron group densities follow the trend of the calculated radial profiles of the electron sources arising from the ionization of neutrals in both deuterium and helium plasmas in TJ-II. The difference in the radial location where the bi-Maxwellian EEDF appears can be explained by the difference in the rate coefficients for ionization of deuterium and helium. The results of probe measurements in GOLEM and the WEST tokamak divertor, at one radial location in the SOL, are compatible with the hypothesis concerning the ionization of neutral atoms and the type of the EEDF.

Spectroscopic measurement of atmospheric-pressure non-equilibrium Ar plasma using continuum and line spectra

A robust method for determining the electron temperature and density of atmospheric-pressure non-equilibrium argon plasmas is reported. The methodology is based on the analysis of the continuum and line spectra of the plasma. Assuming that the electron energy distribution function (EEDF) is expressed as a two-temperature generalized EEDF (GEEDF), the gamma value of the GEEDF is determined through a grid search of the continuum spectrum analysis given by the bremsstrahlung process, which minimizes the mean-squared logarithmic error (MSLE). In addition, the relationship between the gamma value and the electron temperature and density is determined. Utilizing this relationship, the electron temperature and density are determined by minimizing the MSLE between the excited-state densities obtained from the line spectrum analysis and numerically calculated using the collisional-radiative model. This methodology yielded results that satisfied both continuum and line spectrum analyses. In addition, the same analysis was conducted either by continuum spectrum analysis or by line spectrum alone to compare the results.