Escape Factor Research Articles

Calculation of self-absorption coefficients of calcium resonance lines in the case of a CaCl 2–water plasma

The resonance escape factors for the lines emitted by a neutral calcium atom Ca I at 4226.73 Å and of ionic calcium Ca II at 3933.66 Å and at 3968.47 Å are calculated assuming a Voigt profile and in the case of CaCl 2–water plasma. The dependence of the escape factor on the optical thickness ґ 0 from the line center which itself depends on the two main spectral line shape broadening mechanisms (pressure and Doppler effects) are considered. The variation of the resonance escape factors with the temperature, the CaCl 2 molar proportion and the size of the plasma are also investigated. This calculation is useful for the application of Laser-Induced Breakdown Spectroscopy in the quantitative analysis of elemental composition. Its application allows us to reduce the non-linearities in the relation between resonance lines intensities of calcium in our case and its concentration.

Theory of the resonance escape factors of plasma resonance lines basing on the exact Voigt profile

In this paper, based on the exact Voigt profile we obtained, we derive the theory of resonance escape factors of plasma resonance lines, for both Lorentzian profile and Voigt profile. The oscillator strength, the number density of the absorbing atoms in the ground state, and the optical depth in the line center are discussed. As an example, the helium He I 1083.0 nm, lithium Li I 670.970 nm and carbon C I 111.74 nm are discussed for infrared, visible and ultraviolet regions. The results we calculated are in good agreement with the experimental results. These calculations will be significant in the theoretical analysis of plasma.

Backscattering of secondary electrons to the cathode in the oblique electric field in dielectric barrier discharge systems

In dielectric barrier discharge systems, where the cathode is covered with the dielectric layer, electric field lines may cross the cathode surface at an oblique angle θ. The secondary electrons emitted from this surface either return to the cathode due to collisions with atoms of the background gas or escape from the cathode vicinity. Using the two-term approximation to the Boltzmann equation for electrons, we have found that, for Ramsauer gases, the electron escape factor fes as a function of the angle θ unexpectedly exhibits non-monotonic behaviour. Monte Carlo simulations of backscattering of electrons performed for xenon and argon have confirmed the theoretical results and shown similar trends for non-Ramsauer gases.

A robust method to measure metastable and resonant state densities from emission spectra in argon and argon-diluted low pressure plasmas

A simple robust method is presented to determine the densities of metastable and resonant species in low temperature, low pressure argon and argon-diluted plasmas. The ratios of spectral lines which correspond to transitions from common upper states to resonant or metastable lower states are measured with low resolution optical spectrographs. Photon reabsorption makes these ratios sensitive to the population densities of the lower states. The concept of escape factors is used to develop a set of nonlinear equations for the line ratios, which does not depend on the densities of the upper states. By means of a least squares method, the equations can be solved for metastable and resonant state population densities. The method does not depend on the nature of the excitation process, which makes it superior to other spectroscopic techniques in situations where the electron energy distribution is not known.

Decay of the excited state 32 P 3/2 of sodium atoms taking into account radiation trapping

The effective lifetime of the excited state 32P3/2 of sodium atoms corresponding to the transition with λ = 589 nm has been studied numerically. It is shown that the nonmonotonic behavior of the dependence of the Biberman-Holstein escape factor on the optical thickness of sodium vapor measured in the experiment (A. Romberg and H.-J. Kunze, J. Quant. Spectrosc. Radiat. Transfer 39 (2), 99 (1988)) should not be attributed to the manifestation of the effects of partial frequency redistribution.

Escape factors in zero-dimensional radiation-transfer codes

Several zero-dimensional non-LTE radiation-transfer codes are in common use within the laser-plasma community (for example, RATION, FLY, FLYCHK and GALAXY). These codes are capable of generating calculated emission spectra for a plasma of given density and temperature in the presence of a radiation field. Although dimensionless in nature, these codes can take into account the coupling of radiation and populations by use of the escape factor method, and in this sense the codes incorporate the finite size of the plasma of interest in two ways – firstly in the calculation of the effect of the radiation on the populations and secondly when using these populations to generate a spectrum. Different lengths can be used within these two distinct operations, though it has not been made clear what these lengths should be. We submit that the appropriate length to use for the calculation of populations in such zero-dimensional codes is the mean chord of the system, whilst when calculating the spectrum the appropriate length is the size of the plasma along the line of sight. Indeed, for specific plasma shapes using the appropriate escape factors it can be shown that this interpretation agrees with analytic results. However, this is only the case if the correct escape factor is employed: use of the Holstein escape factor (which is in widely distributed versions of the codes mentioned above) is found to be significantly in error under most conditions. We also note that for the case where a plasma is close to coronal equilibrium, some limited information concerning the shape of the plasma can be extracted merely from the ratio of optically thick to optically thin lines, without the need for any explicit spatial resolution.

Effective deexcitation time of lithium vapor

The method of numerical simulation was used to study the effective deexcitation time of the resonance transition in lithium vapor at the wavelength λ = 670.776 nm. Taking into account the partial frequency redistribution and the cylindrical geometry of the medium, the rate equations of the population balance of a two-level atom were solved along with the equation of radiation transfer. The light scattering by an atom was simulated by a linear combination of the angle-averaged frequency distribution functions R II and R III. The Biberman-Holstein escape factor was calculated as a function of the optical thickness of lithium vapor for different geometries of the luminescing gas and different models of the frequency redistribution functions.

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).

Escape factors in spherically symmetric plasmas

In this paper we present explicit formulas for the escape factors of strong spectral lines in spherical-symmetric plasmas. The plasma does not necessarily have a homogeneous density. The calculations include two new elements: the first incorporates an accurate calculation of the angle-averaged areal density of ions from any internal point to the edge of the sphere. The second is the use of a saddle point method to carry out the integration over the line profile. Approximate expressions for the asymptotic behavior of the escape factor are given for Gaussian, Lorentzian and Holtsmarkian line shapes.

Line mixing and collision‐induced absorption by oxygen in the A band: Laboratory measurements, model, and tools for atmospheric spectra computations

The absorption by oxygen in the region of the O2 A band near 760 nm has been measured in the laboratory under various conditions of pressure (20–200 atm) and temperature (200–300 K) for both pure O2 and O2‐N2 mixtures. In order to calculate the contribution of the “allowed” A band transitions, Lorentzian profiles and a model accounting for line‐mixing (LM) effects using the energy corrected sudden (ECS) approximation have been used. The differences between computed spectra and measured values enable extraction of the collision‐induced absorption (CIA) contribution. It is shown that neglecting line mixing overestimates absorption in the wings and underestimates absorption at the P and R branch peaks, whereas the CIA extracted by the line‐mixing approach shows the “smooth” profile expected. Applying this approach to our spectra enables determination of the CIA and allowed contributions for both O2‐O2 and O2‐N2 collisions versus temperature and pressure. The resulting model and data are then used to build a database and some software suitable for the calculation of oxygen (in air) atmospheric absorption and for easy inclusion in radiative transfer codes (available upon request). These tools are then applied to a theoretical study of the influences of both line‐mixing and collision‐induced processes on atmospheric photon path escape factors and on cloud‐top altitude retrievals. It is shown that LM and CIA make significant contributions and explain a large part of the discrepancies between measured and calculated atmospheric absorption observed recently.

Escape factors for thermionic cathodes in atomic gases in a wide electric field range

An approximate analytical expression is obtained for the escape factors for thermionically emitting cathodes in atomic gases that is uniformly valid at all values of the reduced electric field. This expression is used for evaluation of the escape factors in neon, helium and mercury. An independent evaluation is performed by means of Monte Carlo simulations. The analytical results are in good agreement with the results of Monte Carlo simulations, both for reflecting and non-reflecting cathodes.

The calculation of the resonance escape factor of helium for Lorentzian and Voigt profiles

The resonance escape factors of helium 10830.34 Å, 10830.25 Å and 10829.08 Å that making up the 10830 Å emission lines are calculated, for both Lorentzian profile and Voigt profile. The total number of absorbing atoms in the ground state is calculated. The dependence of the escape factors on the optical depth in the line center is considered. The resonance escape factors of helium 3889 and 3118 emission lines are discussed also. This calculation is useful in the research on the helium in the sun and remote stars from the helium emission lines.

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.

Screening techniques and sources of resistance against parasitic weeds in grain legumes

A number of parasitic plants have become weeds, posing severe constraints to major crops including grain legumes. Breeding for resistance is acknowledged as the major component of an integrated control strategy. However, resistance against most parasitic weeds is difficult to access, scarce, of complex nature and of low heritability, making breeding for resistance a difficult task. As an exception, resistance against Striga gesnerioides based on a single gene has been identified in cowpea and widely exploited in breeding. In other crops, only moderate to low levels of incomplete resistance of complex inheritance against Orobanche species has been identified. This has made selection more difficult and has slowed down the breeding process, but the quantitative resistance resulting from tedious selection procedures has resulted in the release of cultivars with useful levels of incomplete resistance. Resistance is a multicomponent event, being the result of a battery of escape factors or resistance mechanisms acting at different levels of the infection process. Understanding these will help to detect existing genetic diversity for mechanisms that hamper infection. The combination of different resistance mechanisms into a single cultivar will provide durable resistance in the field. This can be facilitated by the use of in vitro screening methods that allow highly heritable resistance components to be identified, together with adoption of marker-assisted selection techniques.

Asymptotic calculation of escape factor in atomic plasmas

Simple analytical expressions are obtained for the escape factor for low-energy electrons in an atomic plasma at intermediate and high values of the reduced electric field in the near-cathode region, when the dominating electron energy losses are due to inelastic collisions of electrons with atoms. An approximate account of the reflection of electrons by the cathode surface is introduced. Calculated escape factors are in reasonable agreement with the results of the Monte Carlo simulations available in the literature. When applied to cathodes of high-pressure arc discharges, the obtained results indicate that the escape factor is close to unity in cases where the near-cathode space-charge sheath is collision-free or moderately collisional. If the sheath is collision-dominated, the escape factor may be different from unity; for example, this is the case under conditions of a 100 bar mercury plasma of a mercury arc lamp.

Non-local radiation transport via coupling constants for the radially inhomogeneous Hg–Ar positive column

A model is presented for the radially inhomogeneous Hg–Ar positive column discharge with properties similar to the standard fluorescent lamp. The model combines the electron excitation reactions and radiation trapping to self-consistently solve the spatially dependent species rate equations. Collision rates are evaluated from the electron distribution function determined from the inhomogeneous Boltzmann equation with the gradient term. Radiation processes are evaluated through frequency dependent cell-to-cell coupling constants. This general radiation transport method accounts for non-local photo-pumping, line overlap within the isotopic structure of the Hg resonance lines, and an emission line profile subject to partial frequency redistribution. The coupling constants agree with a more computationally intensive Monte Carlo code. The emission line profile provides an effective decay rate for the 185 nm line, which follows trends in measurements. In contrast, the use of a uniform constant escape factor for radiation trapping leads to centrally constricted profiles for the Hg excited states. Model results for the mean electron energy, distribution function and density distribution of Hg triplet levels are found to agree with existing spatially resolved data. Predicted and measured broad profiles for the Hg triplet levels are attributed to photo-pumping of the outer plasma regions by inner ones.

Two-bands charge transport in silicon nitride due to phonon-assisted trap ionization

The charge transport in the amorphous Si3N4 is studied experimentally and theoretically. We have found, that widely accepted Frenkel model of the trap ionization gives the unphysical low value of the attempt to escape factor, and the enormously high value of the electron tunnel mass. Experimental data are well described by theory of the two-bands conduction and the phonon-assisted trap ionization in Si3N4.

Enhancement of Optically Thick to Thin Line Intensities in Solar and Stellar Coronal Plasmas through Radiative Transfer Effects: An Angularly Resolved Study

An analysis of radiative transfer effects present in the Fe XV ion stage of solar and stellar coronal plasmas provides a general explanation of line radiation intensity enhancement above the optically thin limit. Full linearization radiation transfer is compared with the escape factor method and found to be in good agreement at the lower column densities. An angular study of the enhancement shows that symmetry factors are of great importance. This gives a possible reason for the indeterminate status of opacity in relation to coronal lines of distant stellar sources, where only emission integrated across the whole surface is detected.

A collisional-radiative model for simulation of Ne-like and F-like resonance lines emitted from laser produced plasmas

We describe a collisional radiative code to simulate the Ne-like and F-like resonance lines emitted from laser produced plasmas. Ions and excited levels densities are calculated by solving rate equations using an implicit-finite difference method for steady state, quasi steady state and time-dependent conditions. The code calculates intensities of Ne-like 1s 22s 22p 6→1s 22s 22p 5 nl and F-like 1s 22s 22p 5→1s 22s 22p 4 nl resonance lines emitted from various species, Z=18 to 32, i.e., from argon to germanium. Intensities of photons emitted between Ne-like 1s 22s 22p 5 n′ l′→1s 22s 22p 5 nl and F-like 1s 22s 22p 4 n′ l′→1s 22s 22p 4 nl excited levels are also calculated. Doppler broadened line shapes are assumed. Absorption of resonance lines is determined using an escape factor approximation. The ratios of optically thin various F-like to Ne-like resonance lines are calculated with the aim that such ratios can serve as a diagnostic to measure electron temperatures.

The mean probability of photon capture of resonance radiation in atomic absorption spectroscopy

The mean probability of photon capture Ψ, obtained via an approximation to the complementary escape factor Λ, for calcium and zinc resonance lines at 4226.73 and 2138.56 A ̊ have been determined from their atomic absorption measurements. Calculations are performed for Gaussian, Lorentzian, and Voigt spectral line shapes. Tabulations and graphical plots of the mean probability of photon capture, Ψ, with the optical depth in the center of Doppler profile, τ D, and the number density of free atoms in the ground state N, are provided.