Optical Escape Factor Research Articles

Improved Line Intensity Analysis of Neutral Helium by Incorporating the Reabsorption Processes in a Helium Collisional-Radiative Model

In this study, eight emission lines in the visible wavelength range of neutral helium were used to diagnose the electron density and temperature of the Large Helical Device (LHD) helium plasma instead of the conventional three-line method. The collisional-radiative (CR) model for low-pressure helium plasma was revised to include the optical escape factors for spontaneous transition from the n1P states to the ground state so that the influence of the absorption effect under optically thick conditions could be considered. The developed algorithm was based on fitting the number densities of eight excited states obtained using optical emission spectroscopy (OES). The electron density, electron temperature, ground-state density, and optical escape factors were selected as the fitting parameters. The objective function was set as the summation of the residual errors between the number densities measured in the experiment and those calculated using the revised model. A regularization term was introduced for the optical escape factor and optimized through bias and variance analyses. The results show that the agreement between the number density calculated by the algorithm and its counterpart measured in the experiment was generally improved compared to the method using three lines.

Evaluation of self-absorption effect of He I resonance line by measurement of forbidden emission in helium arc jet plasma

We have proposed a new method to estimate the optical escape factor (OEF) in high-density helium (He) plasma. Plasma with an electron temperature of ca. 3 eV and density of 5 × 1013 cm−3 was generated by a cascaded arc discharge and rapidly cooled by the introduction of additional He gas, which resulted in a transition from ionizing to recombining plasma. With an increase in the gas pressure, the plasma became optically thick, and the He I forbidden line (spin-exchange intercombination line, 1 1S-2 3P: 59.1 nm) with resonance lines were simultaneously observed using a vacuum ultraviolet spectrometer. Comparison of the intensity ratio of the He I 58.4 nm resonance line to the forbidden emission with those by determined from the collisional-radiative model considering the self-absorption enabled the successful estimation of the OEF. The OEF was decreased with the ambient He gas pressure and was 6.6 × 10−4 and 3.5 × 10−5 for He gas pressures of 1.59 and 20.22 Pa, respectively.

Development of High-Performance Cascade Arc Discharge Device for Applications to Plasma Window

We fabricated a cascade arc discharge source with a channel diameter of 8 mm for application to plasma window as an alternative differential pumping. Helium arc plasmas up to a discharge current of 100 A were generated, and the performance as the plasma window was investigated. The pressure ratio of high-pressure discharge section to low-pressure vacuum side was about 200 at a gas flow rate of 0.05 L/min. In order to characterize the plasma parameters around the anode electrode, vacuum UV and visible emissions of He I were measured. The electron density was determined to be 4 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">13</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> for a discharge current 100 A and a gas flow rate of 0.05 L/min, while the electron temperature was 0.11 eV. Moreover, the forbidden transition of He I 2s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> S- <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> P was observed. The effect of radiation trapping of He I Ly-α was studied by the intensity ratio of Lyα to forbidden line and the collisional radiative (CR) model. As a result, it was found that the plasma generated was optically thick with an optical escape factor of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> .

Helium atom line-intensity ratios as an integrated diagnostic tool for low-pressure and low-density plasmas

The intensity ratios between specific pairs of helium atom (HeI) emission lines are functions of the electron temperature (Te) and density (ne), and these functions have been used for the analysis of Te and ne in various types of discharge plasma. We applied this method to a low-density (ne &amp;lt; 1018 m−3) plasma, where the procedure of the analysis is markedly different from that of higher-density plasmas. The 21S and 23S metastable atom densities are affected by transport, making it practically necessary to set Te, ne, the metastable atom densities, and the optical escape factors, which represent the effect of photoexcitation, as unknown variables and determine them simultaneously. Conversely, the transport of metastable atoms can be evaluated from the analysis.

Calculation of spatial distribution of optical escape factor and its application to He I collisional-radiative model

An integral analytical formula for a spatial distribution of the optical escape factor (OEF) in an infinite cylindrical plasma is derived as a function of an arbitrary upper state spatial density profile, the temperature ratio of the upper state to the lower state, and the optical depth of the corresponding transition. Test calculations are carried out for three different upper state profiles, i.e., uniform (rectangular), parabolic, and Gaussian upper state profiles. The OEF takes on negative values at the periphery of the parabolic and Gaussian upper state profiles. These characteristics cannot be expressed by the conventional OEF formulas derived for the center of the plasma, even though the optical depth is increased. In addition to the analytical derivation of the formula, two practical formulas are proposed: an empirical formula of the spatial distribution of the OEF for the Gaussian upper state density profile and a linear formula of the OEF distribution for upper state profiles that are expressed as linear combinations. These formulas enable us to calculate the spatial distribution of the OEF for the multiple-Gaussian upper state profile without the need for time-consuming integral calculations.

Application of optical emission spectroscopy for He I considering the spatial structure of radiation trapping in MAP-II divertor simulator

The He I optical emission spectroscopy that considers the spatial structure of radiation trapping was proposed by us and was applied to a MAP-II divertor simulator. The spatial distribution of the optical escape factor was calculated from the n (1)P (n≥3) state profiles measured by visible spectroscopy. The profile of 2 (1)P, which is immeasurable by visible spectroscopy, needs to be broader than that of the 3 (1)P state. The sensitivity of the 2 (1)P profile to the T(e) value estimated by He I spectroscopy is investigated.

Ray tracing simulation for radiation trapping of the He I resonance transitions in a linear plasma device

A ray tracing code combined with a He I collisional-radiative (CR) model has been developed to investigate effects of radiation trapping on the population distribution of He atoms in a weakly ionized plasma. The code accurately reproduces experimentally observed vertical profiles of emission intensities in a linear plasma device. On the other hand, the CR code and that modified with the optical escape factor method to include the radiation trapping effects show that vertical profiles significantly deviate from measured ones at the periphery of the plasma column. This work therefore demonstrates that accurate matching of line intensity profiles over the entire plasma column requires a ray tracing code, not just an optical escape factor approximation.

Composition of homogeneous quasi-stationary nitrogen arc plasma by collisional–radiative model

A collisional–radiative model (CRM) is developed to study nitrogen arc plasma. The model is based on solution of the rate equations of ν species chosen for the study. The species chosen are: electrons e, atomic ions N + , atoms N, diatomic molecules N 2, and molecular ions N 2 + , we have then ν=5 species. The CRM is applied to homogeneous and quasi-stationary state (HQSS) plasma for electron temperature T e upto 12 000 K. All heavy particles are assumed to have the same kinetic temperature T g such that T g = T e , this means the temperature of the all five species is identical and is called plasma temperature T. The total pressure of the plasma is considered between 1 and 4 atm. The plasma composition is calculated taking into account all significant collisional and radiative mechanisms. The local effect of radiation absorption is described by the optical escape factors Λ j and Λ jk for free–bound and bound–bound transitions. Results show significant deviation from local thermodynamic equilibrium (LTE). It was also shown that the plasma pressure p has a strong influence on deviation from LTE. To assess the relative speeds of recombination reactions in nitrogen arc plasma we have calculated the relaxation time τ (or time constant) as a function of temperature.

Determination of the optical escape factor in the He I line intensity ratio technique applied for weakly ionized plasmas

Radiation trapping of the He I UV resonance transition (λ = 53.7 nm) has been experimentally confirmed in weakly ionized (ionization degree of ∼1–10%)helium plasmas in the PISCES-A linear divertor plasma simulator by using visible line emission with the same upper state as the UV transition. To study the effect of UV opacity on visible line ratios, the radiation trapping of UV resonance transitions was included in a He I collisional–radiative code with the optical escape factor method. The modified code is used to derive electron density ne and temperature Te with the standard He I line intensity ratios, 667.8 nm/728.1 nm and 728.1 nm/706.5 nm. The predicted values of ne and Te are compared with Langmuir probe measurements. Best agreement (within ±30%) is obtained when including radiation trapping and the correct (measured) neutral temperature and using the vacuum chamber radius (as opposed to the smaller plasma radius) for the characteristic length of the system. Neglecting radiation trapping entirely is found to give errors as large as 10 × (3 ×) in the predicted values of ne (Te).

Comparison of He I line intensity ratio method and electrostatic probe for electron density and temperature measurements in NAGDIS-II

The electron density and temperature obtained from the line intensity ratio method of HeI (λ=667.8, 706.5, and 728.1nm) are compared to the probe method in a divertor simulator. When a collisional radiative model that does not include the effect of the radiation transport was used for the analysis, ne obtained from the spectroscopic method was significantly higher than that from the electrostatic probe method. The discrepancy between the two methods increases with the gas pressure; in other words, it increases with the optical thickness. In the case that the effect of the radiation trapping is taken into consideration using optical escape factor, the discrepancy becomes moderate. And then, the parameters obtained from the line intensity ratio method agree with the probe method within a factor of 2 in the case that the radiation trapping was introduced with R=0.05m, which corresponds to the column radius of the spatial profile of the excited population density. In recombining plasmas, however, it was shown that the line intensity ratios might not be appropriate because the recombining component broke the monotonic increase/decrease dependences of the line intensity ratios on ne and Te. A measurement of another HeI line intensity of 447.1nm (2P3←4D3) is proposed for solving the problem.

VUV lasing on puff metal vapor of neon-like aluminum ions produced by Z-pinch plasma

A collisional-radiative equilibrium model was developed to investigate the population inversion on metal vaporaluminum plasma. The population inversion has been establishedbetween lower3s(3P1 °, 1P1°) and upper 3p(3P0, 1S°) levels. The vacuumultra-violet lasing on neon-like aluminum ions provideswavelengths of 111.9, 143.2, and 157.3 nm. The rate of relativedensity population, between lower 3s1P1° and upper 3p3P0 levels, reaches its highest valueof 7.16 at the electron density of 1019 cm-3. Themodified expression of the optical escape factor, in the case of the Doppler profile, was introduced in the calculation of the opacityeffect on the gain magnitudes. The Holstein expressionunderestimates the optical escape factor in the region ofrelatively small thickness. The resonance radiation trapping by the 3dconfiguration drastically alters the gain values. A gain greater than 1 cm-1 was found between lasing levels 3s 3P1 ° and3p3P0. The enhancement of gain was due to the pumping of heupper level by a dielectronic recombination process from the groundstate of fluorine-like and by the inner-shell ionization processfrom excited levels of sodium-like ions.PACS No.: 52.00

VUV lasing on puff metal vapor of neon-like aluminum ions produced by Z-pinch plasma

A collisional-radiative equilibrium model was developed to investigate the population inversion on metal vaporaluminum plasma. The population inversion has been establishedbetween lower3s(3P1 °, 1P1°) and upper 3p(3P0, 1S°) levels. The vacuumultra-violet lasing on neon-like aluminum ions provideswavelengths of 111.9, 143.2, and 157.3 nm. The rate of relativedensity population, between lower 3s1P1° and upper 3p3P0 levels, reaches its highest valueof 7.16 at the electron density of 1019 cm-3. Themodified expression of the optical escape factor, in the case of the Doppler profile, was introduced in the calculation of the opacityeffect on the gain magnitudes. The Holstein expressionunderestimates the optical escape factor in the region ofrelatively small thickness. The resonance radiation trapping by the 3dconfiguration drastically alters the gain values. A gain greater than 1 cm-1 was found between lasing levels 3s 3P1 ° and3p3P0. The enhancement of gain was due to the pumping of heupper level by a dielectro...

Studies on Vuv Lasing with Neon-Like Aluminum Ions

The collisional-radiative equilibrium model has been developed in order to investigate the population inversion on aluminum plasma. The population inversion has been established between lower 3s ( 3Ρ01,1P01) and upper 3p (3 Ρ0 , 1 S0) levels. The vacuum ultra-violet lasing on neon-like aluminum ions provides wavelengths of 111.9 nm, 143.2 nm, 157.3 nm. The rate of relative density population, between lower 3S 1Ρ01 and upper 3p 3Ρ0 levels, reaches its highest value of 7.16 at the electron density of 10 19 cm -3 . The modified expression of optical escape factor, in the case of Doppler profile, was introduced in the calculation of opacity effect on the gain magnitudes. The resonance radiation trapping by 3d configuration alters drastically the gain values. A gain greater than 1 cm -1 was found between lasing levels 3s 3 P01 and 3p 3 Ρ0. The enhancement of gam was due to the pumping of the upper level by &electronic recombination process from the ground state of fluorine-like and by the inner-shell ionization process from excited levels of sodium-like ions. PACS numbers: 42.55.Lt, 52.20.Ηv

Magnesium as a representative analyte metal in argon inductively coupled plasmas. I. An extensive collisional-radiative model

An extensive collisional-radiative model for magnesium in an argon inductively coupled plasma is presented. Charge transfer reactions along with electron-impact and radiative processes are considered in this model, taking into account 30 effective levels for magnesium atoms and 30 effective levels for magnesium ions. Analytical expressions used for the corresponding cross sections are discussed in detail owing to the possibility of using the formulas recommended by us in kinetic modelling studies of inductively coupled plasmas and other discharges in mixtures including magnesium atoms and ions. The numerical method developed makes it possible to investigate the mechanisms by which the excited levels are populated under various conditions in an argon inductively coupled plasma characterized by a set of fundamental parameters, such as the electron temperature T e, the atom temperature T a and the electron number density n e, provided that the optical escape factors for Mg atoms ( Λ mn and Λ m ) and Mg + ions ( Λ mn + and Λ m +) are known, and the ground-state population of Mg atoms n 1, Mg + ions n 1 + and Mg 2+ ions n 1 2+ have been determined. © 1997 Elsevier Science B.V.

Magnesium as a representative analyte metal in argon inductively coupled plasmas. II. Population mechanisms in analytical zones of different spectrochemical systems

The extensive collisional-radiative model is applied to the actual argon inductively coupled plasmas (ICP) in order to clarify consistently the mechanisms by which the excited levels of magnesium atoms and ions are populated in analytical zones of these ICP systems. Computations are carried out for various sets of input parameters, such as the electron temperature the T e , atom temperature T a , the electron number density n e and the optical escape factors A mn and A m for Mg atoms, and A mn + and A m + for Mg + ions. The predicted values of the populations in the excited levels and the quantities derived from them are fairly close to the corresponding experimental results. The effect of the changes in the discharge parameters T e , T a , n e , A 1 n , and A 1 n + on the population mechanisms, together with the role played by the upward excitation flows of electrons from the respective ground states and by the charge transfer between argon and magnesium, are also shown. © 1997 Elsevier Science B.V.

A collisional-radiative model applicable to argon discharges over a wide range of conditions. I. Formulation and basic data

A collisional-radiative model with an extended region of applicability is developed for an argon atom plasma. Atom-atom inelastic collisions and diffusion losses of the metastable states along with the electron-atom inelastic collisions and radiative processes are considered in this model, taking into account 65 effective levels. Among the analytical expressions used for the corresponding cross sections, special attention is paid to those determining the set of cross sections for excitation by electrons from the ground state, owing to the possibility of utilising the formulae recommended in kinetic modelling studies of discharges in argon or in mixtures including argon atoms. The numerical method developed makes it possible to investigate the mechanisms by which the excited levels are populated in a non-equilibrium argon plasma characterised (even in the case of a non-Maxwellian electron distribution) by a set of parameters, such as the electron kinetic temperature Te, the atom temperature Ta, the ion temperature Ti, the electron number density ne, the ground state atom population n1, the discharge tube (or the plasma column) radius R and the optical escape factors Lambda mn and Lambda m, which are dependent only on the quantities Ta, n1 and R in many cases of practical interest.

Spectroscopic Investigation of Recombination Process in a Pulsed Discharge Plasma Using Laser Induced Fluorescence Technique

The temporal behavior of the population density of the first excited level of the hydrogen atom in a pulsed discharge plasma of a helium and hydrogen mixture has been measured using the laser induced fluorescence technique, while the population densities of the higher excited levels have been determined from the emission measurements. The population density of each level shows a rapid enhancement in the early stage of afterglow. The experimental results are compared with the collisional-radiative model, including various dissociation processes of hydrogen molecules. The experimental results can be explained well with the model. The population mechanism of the first excited level in the afterglow is found to be sensitive to the optical escape factor of the Lα line

Population inversion in optically thick, recombining hydrogen plasmas

Abstract The plasma condition is investigated theoretically for population inversion between the first two excited states of hydrogen atoms in a recombining plasma. The rate equation, including atom-atom collision terms, is solved consistently with the optical escape factors. The upper bound of the ground level population density (n1)max necessary for inversion in the optically thick plasma at specified electron density and temperature is nearly inversely proportional to the mean radius of the plasma rO. With a decrease in the atom temperature, the upper bounds increase in the optically thin plasma but decrease in the optically thick plasma.

The relation between the optical escape factor and the thermalization length

The dependence of the optical escape factor on the thermalization length is discussed for a plane-parallel plasma composed of two-level atoms. Expressions for an upper and a lower bound for the escape factor are given. The radiative transfer equation is solved numerically in the case of a Doppler profile and escape factors on the midplane of the plasma slab are given. The variation of the escape factor with the thermalization length is very small; an expression given by Drawin has been found to be erroneous.

Optical escape factors and population densities for TPD-plasma

Optical escape factors and recalculated population densities are presented in connection with a remark by Hegde and Ghosh. It is shown that the optical escape factors given by these authors are too small for the experimental conditions used and, contrary to their results, the population densities for levels with principal quantum numbers larger than 4 of He(II) may be described by the optically-thin assumption.