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The approach, which was developed earlier for modeling chemical reactions in laser induced plasmas, is applied to radio-frequency discharge plasmas. The model is based on the assumption that all ionization processes and chemical reactions are at local thermodynamic equilibrium. A chemical composition of an argon-hydrogen plasma with an Addition of boron trichloride is studied as a function of plasma temperature and mole ratio H2∕BCl3. It is established that more than twenty simple and composite molecules and ions can be formed in the course of chemical reactions. The results are compared with those obtained earlier by means of another equilibrium model that uses ab-initio quantum chemical computations of thermochemical and kinetic data and a 0D thermochemical quilibrium solver.
The equation of state for plasmas containing negative and positive ions of elements and molecules formed by these elements is modeled under the assumption that all ionization processes and chemical reactions are at local thermal equilibrium and the Coulomb interaction in the plasma is described by the Debye–Hückel theory. The hierarchy problem for constants of molecular reactions is resolved by using three different algorithms for high, medium, and low temperatures: the contraction principle, the Newton–Raphson method, and a scaled Newton–Raphson method, respectively. These algorithms are shown to have overlapping temperature ranges in which they are stable. The latter allows one to use the developed method for calculating the equation of state in combination with numerical solvers of Navier–Stokes equations to simulate laser-induced Plasmas initiated in an atmosphere and to study formation of molecules and their ions in such plasmas. The method is applicable to a general chemical network. It is illustrated with examples of Ca–Cl and C–Si–N laser-induced plasmas.
Data processing in the calibration-free laser-induced breakdown spectroscopy (LIBS) is usually based on the solution of the radiative transfer equation along a particular line of sight through a plasma plume. The LIBS data processing is generalized to the case when the spectral data are collected from large portions of the plume. It is shown that by adjusting the optical depth and width of the lines the spectra obtained by collecting light from an entire spherical homogeneous plasma plume can be least-square fitted to a spectrum obtained by collecting the radiation just along a plume diameter with a relative error of 10 −11 or smaller (for the optical depth not exceeding 0.3) so that a mismatch of geometries of data processing and data collection cannot be detected by fitting. Despite the existence of such a perfect least-square fit, the errors in the line optical depth and width found by a data processing with an inappropriate geometry can be large. It is shown with analytic and numerical examples that the corresponding relative errors in the found elemental number densities and concentrations may be as high as 50% and 20%, respectively. Safe for a few found exceptions, these errors are impossible to eliminate from LIBS data processing unless a proper solution of the radiative transfer equation corresponding to the ray tracing in the spectral data collection is used.
Data processing in the calibration-free laser-induced breakdown spectroscopy (LIBS) is usually based on the solution of the radiative transfer equation along a particular line of sight through a plasma plume. The LIBS data processing is generalized to the case when the spectral data are collected from large portions of the plume. It is shown that by adjusting the optical depth and width of the lines the spectra obtained by collecting light from an entire spherical homogeneous plasma plume can be leastsquare fitted to a spectrum obtained by collecting the radiation just along a plume diameter with a relative error of 10−11 or smaller (for the optical depth not exceeding 0.3) so that a mismatch of geometries of data processing and data collection cannot be detected by fitting. Despite the existence of such a perfect least-square fit, the errors in the line optical depth and width found by a data processing with an inappropriate geometry can be large. It is shown with analytic and numerical examples that the corresponding relative errors in the found elemental number densities and concentrations may be as high as 50% and 20%, respectively. Safe for a few found exceptions, these errors are impossible to eliminate from LIBS data processing unless a proper solution of the radiative transfer equation corresponding to the ray tracing in the spectral data collection is used.
The equation of state for plasmas containing negative atomic and molecular ions (anions) is modeled. The model is based on the assumption that all ionization processes and chemical reactions are at local thermal equilibrium and the Coulomb interaction in the plasma is described by the Debye–Hu¨ckel theory. In particular, the equation of state is obtained for plasmas containing the elements Ca, Cl, C, Si, N, and Ar. The equilibrium reaction constants are calculated using the latest experimental and ab initio data of spectroscopic constants for the molecules CaCl2, CaCl, Cl2, N2, C2, Si2 , CN, SiN, SiC, and their positive and negative ions. The model is applied to laserinduced plasmas (LIPs) by including the equation of state into a fluid dynamic numerical model based on the Navier–Stokes equations describing an expansion of LIP plumes into an ambient gas as a reactive viscous flow with radiative losses. In particular, the formation of anions Cl-, C-, Si-, Cl2, Si2, C2 , CN-, SiC-, and SiN- in LIPs is investigated in detail.
Under the assumption of local thermal equilibrium, a numerical algorithm is proposed to find the equation of state for laser-induced plasmas (LIPs) in which chemical reactions are permitted in addition to ionization processes. The Coulomb interaction in plasma is accounted for by the DebyeHückel method. The algorithm is used to calculate the equation of state for LIPs containing carbon, silicon, nitrogen, and argon. The equilibrium reaction constants are calculated using the latest experimental and ab initio data of spectroscopic constants for the molecules N2 ,C2 ,Si2 ,CN,SiN,SiC and their ions. The algorithm is incorporated into a fluid dynamic numerical model based on the NavierStokes equations describing an expansion of LIP plumes into an ambient gas. The dynamics of LIP plumes obtained by the ablation of SiC, solid silicon, or solid carbon in an ambient gas containing N2 and Ar is simulated to study formation of molecules and molecular ions.
A dynamical model of a laser induced plasma with axial symmetry is developed to systematically study the effects of the plasma equation of state, radiation transfer, various transport phenomena (viscosity, thermal conductivity, diffusion), and the ablation surface on the observable quantities such as spectra emitted by LIBS plasmas containing multiple species. Theoretical and numerical foundations of the model are described in detail. It is shown that the plasma spectra simulated with the equation of state based on the energy balance that includes the kinetic (thermal) energy, ionization energy, and energy of electronic excitations in atoms and ions differ significantly from the spectra obtained for plasmas modeled in the ideal gas approximation (where only the kinetic energy is included into the energy balance). Various transport phenomena, such as viscosity, diffusion, and thermal conductivity, are shown to have a little effect on the spectra. Radiation losses are proved to have noticeable effects. The effects of various interactions (adhesion, heat exchange, mass inflows) of the evolving plasma with the ablation surface are also illustrated by numerical simulations for typical LIBS plasmas. The model provides a numerical tool to assess various settings for LIBS plasma experiments as well as to interpret experimental data.
The Radon transform tomography is used for reconstruction of the emissivity distribution in single- (SP) and double-pulse (DP) laser induced plasmas in orthogonal geometry. The orthogonal DP plasma is intrinsically asymmetric and thus suitable for the Radon reconstruction. The DP plasma consists of two plasmas separated by a short time interval of ~ 1 µs. The first plasma is created in air near the surface of a Si wafer and is followed (pre-ablation mode) or preceded (post-ablation mode) by the second plasma induced on this surface. A spectrometer moves in a semi-circular path around the plasma keeping the plasma in the rotation center. The optical detection is arranged so that a thin plasma layer parallel to the target surface is monitored. The axial symmetry of the SP plasma is investigated by comparing data from the Abel inversion taken at different angles and Radon reconstruction. The multi-angle measurements are used to estimate errors of the Abel reconstruction due to asymmetries of the plasma. Time-resolved Radon reconstruction in white light is performed for the DP plasma in both pre- and post-ablation modes. In the former case, the effect of ablated aerosol on the formation of the air plasma is monitored. In the latter case, a formation of an asymmetric compression shock created by the target plasma inside the air plasma is visualized. This observation is supported by computer simulations. An interaction of the two plasmas is studied by spectrally resolved Radon reconstruction revealing a complex distribution of target and ambient species inside the plasma at all studied delay times. Overall, it is demonstrated that Radon-based tomography is an informative tool to study transient asymmetric laser induced plasmas.
It is proposed to use apertures with large acceptance angles to reduce the integration time when studying the emissivity of laser induced plasmas by means of the Abel inversion method. The spatial resolution lost due to contributions of angled lines of sight to the intensity data collected along the plasma plume diameter is restored by a special numerical data processing. The procedure is meant for the laser induced plasma diagnostics and tomography when the integration time needed to achieve a reasonable signal to noise ratio exceeds a characteristic time scale of the plasma state variations which is short especially at early stages of the plasma evolution. It can also be used to improve the spatial resolution in a conventional experimental setup for plasma diagnostics.
Abel inversion applied to a transient laser induced plasma: implications from plasma modeling
(2011)
We test the effects of non-uniformity, non-transparency, and non-stationarity of a laser-induced plasma on the results obtained by the Abel inversion method. The method is commonly used for obtaining spatially resolved emissivity of axially symmetric non-homogeneous radiating objects. Besides the axial symmetry, the plasma is assumed to be optically thin. As the method addresses a certain plasma state, the plasma is required to be stationary during measurements. It is difficult to satisfy the aforementioned conditions for transient laser induced plasmas. As such the plasmas are not stationary; they have steep gradients of thermodynamic parameters that rapidly vary during the plasma evolution. Therefore, any conclusion based on time-integrated measurements and the corresponding data processing should account for these effects. In this work, we use the collision-dominated plasma model to generate time- and spatially resolved synthetic spectra. The spectra are processed by executing the Abel inversion using two numerical algorithms. Thus obtained spatially resolved plasma parameters (emissivity, temperature, and number density) are compared with the exact parameters used to set up the model. In doing so, the accuracy of the Abel inversion method is assessed. Special attention is paid to the dynamic aspect of the expanding plasma and possible errors which result from time-integrated measurements.