Modified Diffusion Approximation Research Articles

Highly Ionized Arc He Plasma: Nonequilibrium, Nonideality, and Kinetics

Experimental findings suggest that a strongly ionized, arc He plasma of atmospheric pressure does not exist in the state of the local thermodynamic equilibrium (LTE) expected for a plasma with an electron concentration above 1016 cm–3. This is found to be caused by transverse plasma nonuniformity and density effects. The plasma quasistatic microfield destroys the upper electron levels of He atoms, and the radial ambipolar diffusion flow transports the charged particles from the narrow (1–2 mm) plasma channel on the chamber wall. In the distribution of atoms and the ions over the excited levels, strong ionization nonequilibrium and a large gap of the ground state are observed; these factors cause substantial difficulties in the spectral diagnostics of the plasma parameters due to the inapplicability of the relations taking into account the equilibrium conditions. A method is proposed to measure the concentration of double-charged ions He++ (α particle), which is inaccessible by direct spectral registration, as well as a simple kinetic model of strongly ionized He plasma with the use of a modified diffusion approximation; the model adequately describes the plasma parameters.

Study on mechanism of ultrasonic fluorescence modulation in light scattering medium based on diffusion approximation with varying refractive index

In this study, we propose a model to describe the mechanism of ultrasonic fluorescence modulation based on the application of a modified diffusion approximation, which is derived from the radiative transfer equation with consideration of the varying refractive index. The model was evaluated by computation with finite element method (FEM) to simulate the physical phenomena of our previous experiments. The simulation shows that the measured power of the modulated fluorescence signal at the boundary of 40-mm-thick light scattering medium (scattering coefficient and anisotropy factor of 1.36mm−1 and 0.67, respectively) with the fluorophore located at the center was 10−20 of the incident laser power. The analysis based on the simulation results indicates the significant property of the modulation in which the modulated signal is combination including two processes generated from the variation of the refractive index and fluorophore concentration (the contributions of these are equivalent), whereas the contribution of the variation of the scattering coefficient is negligibly small. The profile of the fluorescence image and the characteristics of the quadratic relationship between the modulated intensity signal and the sound pressure are consistent with our previous experimental results.

Study of diffuse reflectance based on a hybrid diffusion approximation and simulating experiment

A modified diffusion approximation is investigated. In this theoretical model, diffusion coefficient D of the standard diffusion approximation is substituted by diffusion coefficient Dasym of P3 approximation. Analytic solution RHybrid(ρ) of this hybrid diffusion for reflectance in single source approximation and steady-state case with extrapolated boundary is obtained; influences of the transport albedo a′ on the standard diffusion approximation RDA(ρ) and the hybrid diffusion approximation RHybrid(ρ) are compared; recovering of optical parameters from diffuse reflectance RHybrid(ρ) is demonstrated, and the errors and application ranges are studied. The results show that this hybrid diffusion approximation RHybrid(ρ) can be used in strong absorption media and at short source-detector separation.

适用于强吸收的混合漫射近似及其光源近似的影响

A modified diffusion approximation model called the hybrid diffusion approximation that can be used for highly absorbing media is investigated. The analytic solution of the hybrid diffusion approximation for reflectance in two-source approximation and steady-state case with extrapolated boundary is obtained. The effects of source approximation on the analytic solution are investigated, and it is validated that two-source approximation in highly absorbing media to describe the optical properties of biological tissue is necessary. Monte Carlo simulation of recovering optical parameters from reflectant data is done with the use of this model. The errors of recovering \mu_{a} and \mu_{s} are smaller than 15% for the reduced albedo between 0.77 and 0.5 with the source-detector separation of 0.4-3 mm.

Recombination properties of Rydberg nonequilibrium plasma created by dye laser

Ultracold Rydberg plasma formed by a dye laser has been studied theoretically. Recombination properties in the presence of three-body collisions in hydrogen-like plasma have been investigated. We have shown that the existing calculation models for three-body recombination (Thomson model, diffusion approximation, and modified diffusion approximation) work only in the high-electron-temperature region—more than or equal to 1 eV. When the electron temperature is substantially less 1 eV, we have found the strong dependence of process probability on the energy of free particle. As a result, there is a drastic slowdown recombination in the region, where the three-body recombination dominates. Another reason for this slowdown of the recombination deals with the increment nonideality parameter. Effect of slowdown of recombination with free-body collisions can be reduced to the situation when the thermal equilibrium is set earlier than the ionization equilibrium, and, hence, the formation of metastable structure is possible in the plasma. Also this effect can cause the inverse population on Rydberg levels.

Effects of refractive index on near-infrared tomography of the breast

Near infrared (NIR) optical tomography is an imaging technique in which internal images of optical properties are reconstructed with the boundary measurements of light propagation through the medium. Recent advances in instrumentation and theory have led to the use of this method for the detection and characterization of tumors within the female breast tissue. Most image reconstruction approaches have used the diffusion approximation and have assumed that the refractive index of the breast is constant, with a bulk value of approximately 1.4. We have applied a previously reported modified diffusion approximation, in which the refractive index for different tissues can be modeled. The model was used to generate NIR data from a realistic breast geometry containing a localized anomaly. Using this simulated data, we have reconstructed optical images, both with and without correct knowledge of the refractive-index distribution to show that the modified diffusion approximation can accurately recover the anomaly given a priori knowledge of refractive index. But using a reconstruction algorithm without the use of correct a priori information regarding the refractive-index distribution is shown as recovering the anomaly but with a degraded quality, depending on the degree of refractive index mismatch. The results suggest that provided the refractive index of breast tissue is approximately 1.3-1.4, their exclusion will have minimal effect on the reconstructed images.

Influence of concentration on the values of recombination and ionization rate coefficients of atoms S and F

In our previous papers we have published theoretical results of recombination and ionization rate coefficients computed by the method of modified diffusion approximation. These values depend on concentrations of electrons, ions and neutral atoms. In first approximation, we have considered the equilibrium concentrations at given temperature and pressure, and used these values of reaction rate coefficients in the model of reaction kinetics to compute the nonequilibrium composition of the SF6 system during are extinction in gas self-blasted high-voltage circuit breakers. In this paper we have improved our calculations of the composition. We have included the calculation of reaction rate coefficients into the chemical kinetics model; in each computational step current values of reaction rate coefficients are computed according to the current concentrations in the system. Results are compared.

Ionization and Recombination Kinetics in a Plasma Accelerator Channel

A number of theoretical approaches to the investigation of ionizing gas flows are analyzed and compared with reference to a plasma accelerator channel. The transition from a weakly ionized gas to a plasma is considered within the framework of the complete system of equations. The ionizing gas flow model is based on the magnetogasdynamic equations of a continuum and the equation of ionization and recombination kinetics. The corresponding coefficients are determined both within the framework of the standard theory and within a modified diffusion approximation, including possible variations. In addition, for comparison purposes some results of numerical experiments on the ionization process under conditions of local thermodynamic equilibrium are given.

Microscale Heat Conduction in Dielectric Thin Films

Heat conduction in dielectric thin films is a critical issue in the design of electronic devices and packages. Depending on the material properties, there exists a range of film thickness where the Fourier law, used for macroscale heat conduction, cannot be applied. This paper shows that in this microscale regime, heat transport by lattice vibrations or phonons can be analyzed as a radiative transfer problem. Based on Boltzmann transport theory, an equation of phonon radiative transfer (EPRT) is developed. In the acoustically thick limit, ξL ≫ 1, or the macroscale regime, where the film thickness is much larger than the phonon-scattering mean free path, the EPRT reduces to the Fourier law. In the acoustically thin limit, ξL ≪ 1, the EPRT yields the blackbody radiation law q = σ (T14 − T24) at temperatures below the Debye temperature, where q is the heat flux and T1 and T2 are temperatures at the film boundaries. For transient heat conduction, the EPRT suggests that a heat pulse is transported as a wave, which becomes attenuated in the film due to phonon scattering. It is also shown that the hyperbolic heat equation can be derived from the EPRT only in the acoustically thick limit. The EPRT is then used to study heat transport in diamond thin films in wide range of acoustical thicknesses spanning the thin and the thick regimes. The heat flux follows the relation q = 4σT3ΔT/(3ξL/4 + 1) as derived in the modified diffusion approximation for photon radiative transfer. The thermal conductivity, as currently predicted by kinetic theory, causes the Fourier law to overpredict the heat flux by 33 percent when ξL ≪ 1, by 133 percent when ξL = 1, and by about 10 percent when ξL increases to 10. To use the Fourier law in both ballistic and diffusive transport regimes, a simple expression for an effective thermal conductivity is developed.

Analysis of Radiative Heat Transfer in Ultra-Fine Powder Insulations Under Variation of Radiative Boundary Conditions

This paper reports the theoretical investigation of radiative heat transfer through the ultra-fine powder insulation (UFPI) Aerosil 380. The radiative transport process is modeled by the modified diffusion approximation solution and the two-flux solu tion of the equation of transfer. Accuracy of those two approximate methods are in vestigated by comparing the results with those of the Differential-Discrete-Ordinate (DDO) method. The radiative properties of UFPI for dependent effect consistent with these solutions have been determined based on the independent scattering and absorption coefficient which can be calculated by the Rayleigh scattering theory. The influences of the boundary emissivity on radiative heat transfer are also studied. The results show that the radiative thermal conductivity increases very sharply for the black boundary and has a very low value for the low-emissivity boundary. It is sug gested that UFPI systems should always be provided with low-emissivity boundaries around the aerosil powders.

Recombination of a Xenon Plasma Jet

AbstractAs pointed out in a previous paper, stable spherical plasma configurations can be produced by pulsed injection of a plasma into an ambient gas. It is shown here that the observed long plasma lifetime of several milliseconds is in agreement with collisional‐radiative recombination theories. We used the modified diffusion approximation by Biberman et al. involving thermal non‐equilibrium, recombination heating of electrons, heat conduction, radiation and other details. Under the assumption of a pure xenon plasma, the calculated plasma lifetime is even longer than the observed one. This discrepancy can be explained by the presence of molecules and turbulent mixing with the outer gas, which are not considered in the recombination calculation.

KINETICS OF IMPACT-RADIATION IONIZATION AND RECOMBINATION

The theory of impact-radiation recombination (ionization) in a low-temperature plasma is based on the representation of this process as a random walk of a recombining (released) electron in the discrete space of the atom's energy levels. Different methods of studying recombination (ionization) are considered. The described modified diffusion approximation, combining the possibilities of the previously developed approaches, takes into account the real energy structure of the atom, the influence of the radiative transitions, and the relationship between the non-equilibrium distributions of the atoms over the levels and of the electrons over the energies. A solution is presented for the Fokker-Planck equation expressed in finite-difference form, and analytic expressions are obtained for the ionization and recombination coefficients. The results are compared with the published experimental data.