Resonance Radiation Transport Research Articles

Superdiffusive Transport Based on Lévy Walks in a Homogeneous Medium: General and Approximate Self-Similar Solutions

The general and approximate self-similar solutions for the Green’s function have been obtained for a wide class of integrodifferential equations for the two- and three-dimensional (in spatial coordinates) nonstationary superdiffusive transport of a perturbation of a homogeneous medium for a finite fixed velocity of carriers. This problem concerns the transport of resonance radiation in astrophysical gases and plasma, migration of animals, and the transfer of energy of electromagnetic waves in the plasma. The case of a model free path distribution function decreasing by a power law with increasing distance has been considered. Numerical calculations have been performed for two particular types of free path distribution functions, including the case with a Lorentzian shape of wings of the spectral line profile for the emission of photons by atoms or ions. The method developed in [A.B. Kukushkin and P.A. Sdvizhenskii, J. Phys. A: Math. Theor. 49, 255002 (2016)] for an infinite velocity of carriers has been used to construct the approximate self-similar solution. The inclusion of a finite velocity corresponds to the generalization of transport based on Levy flights to transport based on “Levy walks with stops.” The self-similar solution for arbitrary one-dimensional superdiffusive transport obtained in [A.B. Kukushkin and A.A. Kulichenko, Phys. Scripta 94, 115009 (2019)] has been applied to the case of the two- and three-dimensional transports. The accuracy of the self-similar solution has been tested by comparing it to the numerically calculated general solution.

VUV radiation flux from argon DC magnetron plasma

Vacuum ultraviolet (VUV) flux of argon plasma radiation in a DC magnetron discharge with a plane circular titanium cathode is measured. It is found that the intensity of VUV radiation, mainly indicated by the resonance lines of argon atoms at 104.8 and 106.7 nm and ions at 92 and 93.2 nm, is proportional to the discharge current and decreases with pressure. Following the results of the measurements, a numerical model of resonance radiation transport is developed to determine the VUV flux to the substrate placed near the sputtering cathode where direct measurements are impossible due to the fast contamination of the detector by sputtered atoms. In the case of a substrate located 10 cm opposite the cathode surface, the upper limit of estimated VUV flux is of the order of 1015 photons cm−2 s−1 at a coating deposition rate of 1.5 nm s−1 for 2 and 12 mTorr gas pressures. Based on the measurements, the damage to a porous low-k dielectric by VUV radiation during the deposition of barrier layers in the DC magnetron discharge is first estimated.

Influence of Resonance Radiation Transport on Chemical Equilibrium in an Argon Arc

Deviations from chemical equilibrium in argon arc plasma are analysed by means of collisional-radiative model. Corresponding comprehensive kinetic scheme has been developed and applied form study of free-burning arc at the conditions typical for welding applications. While the natural lifetime have been used for radiation emitted from highly excited argon states, the resonance radiation was described taking into account the radiation transport effects. Resulting spatial distributions of excited argon atoms are compared for the cases of LTE and two-temperature plasma using different approaches for the description of the resonance radiation transport.

Spatially resolved LAAS/OES diagnostics of a free-burning Ar arc: measurements of excited atom densities

Spatially resolved optical diagnostics are applied to a free-burning DC arc in argon at atmospheric pressure. Densities of metastable and resonance -atoms are measured by laser atomic absorption spectroscopy (LAAS). The novel LAAS design allowed for an extended range of wavelength scan covering the complete Stark broadened line profile (∼ nm). High spatial resolution of 0.2 mm allowed measurements of atom densities and line profiles in the regions of high-temperature gradients. Besides absorbing -states, the radiating -states were measured using optical emission spectroscopy (OES). Results of the LAAS and OES measurements are compared with the nonequilibrium collisional-radiative model. Measurement of metastable states in the non-radiating regions near the cathode reveals the existence of a ‘collar’ effect. The interpretation of the effect with a focus on transport of resonance radiation is given, quantitative agreement between simulations and experiment is reached.

The effect of photoemission on nanosecond helium microdischarges at atmospheric pressure

Atmospheric-pressure microdischarges excited by nanosecond high-voltage pulses are investigated in helium-nitrogen mixtures by first-principles particle-based simulations, which include VUV resonance radiation transport via the tracing of photon trajectories. The VUV photons, of which the frequency redistribution in the emission processes is included in some detail, are found to modify the computed discharge characteristics remarkably, due to their ability to induce electron emission from the cathode surface. Electrons created this way enhance the plasma density, and a significant increase of the transient current pulse amplitude is observed. The simulations allow the computation of the density of helium atoms in the 21P resonant state, as well as the density of photons in the plasma and the line shape of the resonant VUV radiation reaching the electrodes. These indicate the presence of significant radiation trapping in the plasma and photon escape times longer than the duration of the excitation pulses are found.

Contraction of the positive column of a glow discharge in inert gases with account of resonance radiation transport

A previously proposed method for accurate description of resonance radiation transport in solving self-consistent problems is applied to a model of the contraction of the positive column of a glow discharge in argon. The exact solution to the problem and the solution obtained within the framework of the traditional approximation of local effective transition probability according to Biberman are compared. The influence of radiation transport on various plasma parameters is demonstrated

Mutual influence of higher diffusion and radiation modes on the contraction of the positive column discharge

Fourier analysis of various plasma components in contracted discharge is made by an expansion over diffusion and radiation modes. Resonance atoms transport is traditionally described by an approximation of the effective lifetime by Holstein which considers only a fundamental radiation mode. Proposed method makes it possible to estimate the role of resonance radiation transport quantitatively by comparing the mode spectra. Behavior of resonance atoms successively considered on simple three-level energy models in a linear Shottky theory and in a semi-analytical non-linear diffusion-recombination theory, describing a discharge contraction. Suggested Fourier analysis method has been applied to a detailed model of the DC column contraction in Argon glow discharge. An expansion of different plasma components (electron density, metastable and resonance atoms densities) over the corresponding orthonormal set of diffusion or radiation modes is performed. The comparison of spectra obtained using the traditional Holstein approximation and in case of accurate treatment of resonance radiation transport shows an increase of fundamental diffusion and radiation modes and an effect of higher harmonics suppression in the modes spectra when the resonance radiation transport is described precisely. The role of higher radiation modes in formation of radial profiles of the electron density, metastable and resonance atoms densities as well as current–voltage characteristics is demonstrated by specific examples.

Excited atoms in the free-burning Ar arc: treatment of the resonance radiation

The collisional–radiative model with an emphasis on the accurate treatment of the resonance radiation transport is developed and applied to the free-burning Ar arc plasma. This model allows for analysis of the influence of resonance radiation on the spatial density profiles of the atoms in different excited states. The comparison of the radial density profiles obtained using an effective transition probability approximation with the results of the accurate solution demonstrates the distinct impact of transport on the profiles and absolute densities of the excited atoms, especially in the arc fringes. The departures from the Saha–Boltzmann equilibrium distributions, caused by different radiative transitions, are analyzed. For the case of the DC arc, the local thermodynamic equilibrium (LTE) state holds close to the arc axis, while strong deviations from the equilibrium state on the periphery occur. In the intermediate radial positions the conditions of partial LTE are fulfilled.

The influence of resonance radiation transport on the contraction of a glow discharge in argon

The role of resonance radiation transport in the contraction of a positive column in an argon glow discharge is studied numerically. The theory is based on the self-consistent solution of the ambipolar diffusion equation for electrons, the diffusion equation for metastable atoms and the Biberman–Holstein equation for resonance atoms. To calculate the ionization and excitation rates, the Boltzmann equation is solved in a local approximation taking into account elastic, inelastic and electron–electron collisions. A solution method for a boundary problem is developed which allows one to obtain a hysteresis of the parameters during a continuous transition from a diffuse mode to a contracted mode through an unstable branch. At small currents there is a diffuse discharge where the role of radiation transport is inessential because the radial distributions of electrons and excited atoms are close to the fundamental modes of the corresponding equations. Under these conditions, the traditional approximation of ‘effective lifetime’ is accurate enough. For a contracted discharge, this approximation is not applicable because the higher diffusion and radiation modes play a notable role and a more strict description of radiation transport is required. It is shown that, when radiation transport is taken into account, the width of a filament in a contracted discharge significantly exceeds that obtained in the traditional ‘effective lifetime’ approximation. The critical current, when the discharge abruptly turns into a contracted mode, is shifted towards higher current values. The results obtained in this paper can also relate to a discharge in other inert gases.

The role of visible and resonance radiation in the energy balance of LTE plasma in argon

Energy losses due to radiation in an LTE arc plasma in argon are investigated in the temperature range from 5000 to 15 000 K. Calculations of the radiation transport require us to know the absorption spectra; for that purpose, free–free, bound–free and bound–bound transitions are taken into account. The energy losses due to resonance transitions with large absorption coefficients are analyzed. The transport of visible radiation with small absorption coefficients is calculated by accurate integration over a whole spectrum. The resonance radiation transport in LTE plasma is described by the Biberman–Holstein equation, which is usually used in non-equilibrium plasma. As the temperature grows, radiation processes become the main channel of energy losses. It is shown that, despite the resonance radiation being trapped, the energy losses due to resonance radiation escape can achieve 10% of the total radiation losses.

Enhanced escape rate for Hg 254 nm resonance radiation in fluorescent lamps

The potential of the low-cost MAGIS isotopic separation method to improve fluorescent lamp efficacy is explored using resonance radiation transport simulations. New Hg isotopic mixes are discovered that yield escape rates for 254 nm Hg I resonance radiation equal to 117% to 122% of the rate for a natural isotopic mix under the same lamp conditions.

Spatial distribution of metastable and resonance atoms in a low-pressure He–Xe discharge in spot mode

A dc low-pressure discharge in a helium–xenon mixture with a hot spot on a flat oxide cathode is investigated. The zone around this cathode spot is an interesting source of excitation of metastable and resonance atoms and can be effectively used for the study of fundamental aspects, e.g. transport phenomena of these excited atoms. The method of laser atomic absorption spectroscopy is used to measure the spatial distribution of these atoms. Since excitation sources are significantly distinct from the diffusion and radiation fundamental modes there is a need for correct interpretation of the experimental results based on simultaneous solution of the diffusion equation and the equation of radiation transport. It is shown that the conventional method for the description of resonance radiation transport, which uses the effective lifetime approximation according to Holstein–Biberman, cannot reproduce the spatial distribution of excited atoms in this type of discharge. The influence of various transport mechanisms and of the collisional coupling between the two lowest excited states of xenon on the spatial distribution of these densities is analysed. It is found that the excited atoms appear on the discharge periphery mainly due to resonance radiation transport.

Fractional Boltzmann equation for multiple scattering of resonance radiation in low-temperature plasma

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start with the standard Boltzmann equation; averaging over photon frequencies leads to the appearance of a fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of a fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solving the obtained equation and demonstrate numerical results in some simple cases.

Radiation trapping in 1D using the Markov chain formalism: a computational physics project

A computational model study for atomic radiation trapping is presented with an audience non-specialized in radiation transport in mind. The level of presentation is adequate for a final undergraduate or beginning graduate project in a computational physics instruction. The dynamics of resonance radiation transport is discussed using a theoretical model known as the multiple scattering representation. This model is compared with the alternative Holstein's ansatz, reinterpreting the fundamental mode as the one associated with a relaxed stationary spatial distribution of excitation. Its computational implementation is done making use of the stochastic Markov chain formalism. A comprehensive discussion of its rationale as well as fine implementation details are presented. The simplest case of complete frequency redistribution in a two-level system is considered for a unidimensional geometry. Nevertheless, the model study discusses at length the influence of the spectral distributions, overall opacity and emission quantum yield for trapping distorted ensemble quantities stressing physical insight and using only straightforward algorithmic concepts. Overall relaxation parameters (ensemble emission yield and lifetime) as well as steady-state quantities (spectra and spatial distribution) are calculated as a function of intrinsic emission yield, opacity and external excitation mode for Doppler, Lorentz and Voigt lineshapes, respectively, with the fundamental mode contribution singled out.

Metastable and resonance atom densities in a positive column: I. Distinctions in diffusion and radiation transport

The distinctions in the mechanisms of diffusive transport and resonance radiation transport leading to different population of the metastable and resonance levels are discussed. The analysis is based on a uniform solution of the diffusion equation and the Holstein–Biberman equation. The Green functions of the diffusion and radiation transport operators are shown to be markedly different. The Green function for the integral operator is close to the delta function and that for the diffusion operator shows a smooth logarithmic decrease. The eigenfunctions of the two operators are similar but the eigenvalues differ strongly. For this reason the density of the metastable atoms is determined by the first few modes and the density of the resonance atoms is influenced by a large number of higher modes. Diffusion carries the metastable atoms far out of the excitation zone. Resonance atoms are concentrated in the vicinity of the excitation source. The joint influence of diffusion and radiation transport is considered in the presence of intermixing channels on the basis of a constricted positive column of a discharge.

Metastable and resonance atom densities in a positive column: II. Application to light source modelling

Methods for the detailed description of new radiation and light sources based on low-pressure plasmas are required which also consider the spatial structure and the mechanisms of resonance radiation transport without considerable increase of computational effort. A general solution technique based on the reduction of the Holstein–Biberman integral equation to a system of linear equations is introduced to treat the radiation transport. This technique is applied in the framework of a self-consistent radially resolved model of the positive column of a cylindrical dc glow discharge at low pressure. A helium–xenon discharge which can be used as an efficient VUV-radiation source is studied as an example. The theoretical results for the radial density profiles of the resonance and metastable atoms of xenon are compared with absorption measurements providing atomic number densities for the levels of the 1s manifold. In addition, the solution technique for the Holstein–Biberman equation is validated by means of a comparison with Monte-Carlo simulations.

Data‐model comparison search analysis of coincident PBO Balmer α, EURD Lyman β geocoronal measurements from March 2000

Recent Lyman series and Balmer series airglow measurements provide a fresh opportunity to investigate the density distribution and variability of atomic hydrogen in the upper atmosphere. Dedicated nightside Balmer α Fabry‐Perot spectrometer measurements at the Pine Bluff Observatory (PBO), University of Wisconsin‐Madison, have been acquired since late 1999 taking advantage of several technological advances. Extreme ultraviolet spectral radiance measurements by the Espectrógrafo Ultravioleta extremo para la Radiación Difusa (EURD) instrument on the Spanish MINISAT‐1 satellite from October 1997 to December 2001 provide extensive sets of geocoronal Lyman β, Lyman γ and He 584 Å emission intensities. In this paper, coincident EURD Lyman β and PBO Balmer α radiance measurements from the early March 2000 new moon period are presented. In addition to serving as examples of the data sets now available, the data volume poses an analysis challenge not faced in prior geocoronal studies. A data‐model comparison search procedure employing resonance radiation transport results for extensive sets of parametric density distribution models is being developed for use in analyses of multiple large data sets; this is described, and example results for the PBO and EURD March 2000 data sets are presented. The tightness of the constraints obtained for the solar line‐center Lyman β irradiance and the atomic hydrogen column abundance is somewhat surprising, given the crudeness of the parameter binning in the search procedure and the fact that a small number of recognized corrections remain to be made to each data set.

Geocoronal Hα intensity measurements using the Wisconsin Hα Mapper Fabry‐Perot facility

The Wisconsin Hα Mapper (WHAM), a remotely operable, semi‐automated Fabry‐Perot located at Kitt Peak Observatory, has been making an all‐sky survey of interstellar hydrogen Balmer α(Hα) emissions since 1997. Using the annular summing spectroscopy technique, WHAM has acquired ∼37,000 spectra to date, spanning almost 100 nights of observations. Since all of the galactic emission spectral data contain the terrestrial Hα (6562.7 Å) emission line, these measurements constitute a rich source of geocoronal data for investigating natural variability in the upper atmosphere. The WHAM observations also serve as a benchmark for comparison with future data. Analysis of the first year of WHAM data shows only small day‐to‐day variations after shadow altitude variations are taken into account. For example, at shadow altitudes of 2000 and 3000 km, the RMS scatter is within approximately +/− 20%; this variability is expected to be reduced with accurate accounting of the smaller‐scale effects of observational slant path, zenith angle, and azimuth on the Hα intensity. This result is consistent with past midlatitude Wisconsin data sets but different from observations made by other observers and instruments at the low‐latitude Arecibo site. The multiple viewing geometries of the observations provide stringent modeling constraints, useful in testing current modeling capabilities. Modeling of the WHAM data with a global nonisothermal resonance radiation transport code (lyao_rt) indicates that the signal‐to‐noise of the data is sufficient to determine relative variations in upper atmospheric atomic hydrogen column densities to better than 5%. This paper describes the WHAM aeronomy program and its observational scheme, analysis procedures, and results from data taken in 1997. Case study comparisons are made with past data sets and with predictions from the lyao_rt resonant radiation transport modeling code of Bishop [1999].

Resonance radiation transport in plasma display panels

In fluid models of the gas discharges in plasma display panels, the trapping of resonance radiation is usually accounted for by a trapping factor. In this work, we present a Monte Carlo model for resonance photons, which gives a much more accurate description. First, we compare the results of this Monte Carlo model with the results of the fluid model trapping factor approach. Although the trapping factor approach does not yield the same spatial distribution for the density of the resonant state atoms, the spatially integrated density is in good agreement with the results of the Monte Carlo model. Next, we compare the results of the Monte Carlo model with measured spectra of emitted resonance radiation. The agreement is very good. Thus we provide, via the Monte Carlo model, experimental support for the widely used trapping factor approach.

74 nm Radiative Efficiency of a DC Neon Glow Discharge

Radiative efficiency of resonance line emission of a dc glow discharge plasma is derived from experimentally determined profiles of atoms in resonant states. Spatial density profiles were determined by diode laser atomic absorption spectroscopy and laser induced fluorescence. Absorption measurements were used for absolute calibration. The influence of the shape of spatial density profiles was considered. Investigations show that power dissipation by resonance radiation transport remains nearly constant for the currents investigated (i = 1 ... 20 mA). Total power loss due to resonance radiation was found to be about 25% of electrical power input.