STUDY OF ELECTRON – ATOM (ION) SCATTERING AND PLASMA MODELING

Abstract

The study of electron-atom (ion) scattering is of great importance in different fields of physics, viz., the production of collision data for the modelling of low temperature and fusion plasma, astrophysics, laser physics, and the physics of planetary atmospheres, etc. Particularly, the cross-section corresponding to electron impact excitations (EIE) of atoms and ions have significant applications in the modeling of low temperature (laboratory and industrial) plasma. In such plasma, the electron-atom (ion) collision processes are dominant. Thus, the EIE cross-sections are utilized to incorporate in various models for the diagnostics of plasma. Low-temperature plasmas have various applications and the diagnostics of such plasmas become very important to characterize them and optimize their parameters, viz., electron temperature (Te), electron density(ne), etc., to make them suitable for various plasma-assisted applications. There are optical diagnostic methods, e.g., optical emission spectroscopy (OES) and optical absorption spectroscopy (OAS), for the characterization of plasmas. In these methods, line emission intensities of emitting species are measured. However, to extract information about the plasma from these measurements, a suitable population kinetic model is required. From the model, the emission intensities and populations are obtained theoretically and matched with the corresponding measurements to extract information about real plasma. Among the population kinetic models, the collisional radiative (CR) models are the most generalized and comprehensive which considers all the collisional and radiative processes inside the plasma. In these models, a population balance equation is solved to obtain the excited level populations and line emission intensities from the emitting species. To develop an efficient CR model, accurate rate coefficients for different processes occurring in the plasma are required. In the low-temperature plasmas, EIE processes are dominant, and calculating their rate coefficients requires consistent and detailed set of EIE cross-section data from the ground as well as excited fine structure levels. The EIE cross sections are available, hardly, for few transitions at selected energies which are totally insufficient to develop a CR model. In such a situation, the required large set of excitation cross-section for several fine structure transitions had relied on the theoretical calculations. The relativistic distorted wave (RDW) method has been found to be one of the most practical approaches for calculating reliable and consistent fine structure resolved EIE cross-sections for plasma modeling. In the RDW approach, the bound states of the target atom or ion are represented as multiconfiguration Dirac-Fock (MCDF) wave functions and ii the projectile electron distorted wave functions are obtained by solving the Dirac equations. This fully relativistic approach intrinsically considers the all-order spin-orbit interaction as well as other relativistic effects and produces fine structure resolved EIE cross-section suitable for the plasma modeling. The aim of the present thesis is the development of comprehensive CR models for the optical diagnostics of some of the selected low-temperature plasmas. For this purpose, the calculations of the complete set of the required EIE cross-section data set have been carried out and these are incorporated in the CR model for the plasma characterization. Consequently, in the thesis, the detailed electron impact excitation cross-sections for magnesium (Mg), neon (Ne), and silicon ion (Si+2) atoms are calculated using RDW theory from their ground as well as excited states. These cross-sections have been used to obtain the rate coefficients of EIE processes, which are dominant in low-temperature plasmas. Utilizing the rate coefficients, The CR models have been developed for pure as well as mixture plasmas, e.g., laser-produced magnesium and silicon plasmas, radio-frequency-produced inductively coupled pure neon and neon-argon mixture plasmas, and capacitively coupled neon-oxygen/hydrogen mixture plasmas. These CR models have been applied to suitable OES or OAS measurements on low temperature plasmas and by utilizing their measured intensities to evaluate the various plasma parameters, e.g., electron temperature, electron density, rate coefficients, line emission intensities, and fine structure level populations of emitting species, etc. In the process of calculating cross sections, the rigorous atomic structure calculations have been performed, and the obtained atomic and ionic data viz. energy levels, transition probabilities, and oscillator strengths, are also reported in this work. The whole work of the thesis has been presented through seven chapters as described below. Chapter 1 gives a brief introduction of the complete thesis. In this chapter, a brief overview is given of the study of electron-atom (ion) scattering and different methods for calculating the EIE cross-sections. Further, the RDW method, which has been adopted for calculating the EIE cross-sections for different atoms and ions, has been discussed in detail. Population kinetic models and CR models for plasma diagnostics are presented. Various collisional and radiative processes considered in the CR model and the population balance equation are given in detail. An outline of the thesis is also provided at the end of the Chapter. iii Chapter 2 presents the development of a detailed CR model for the diagnostics of laser-produced magnesium plasma. To develop the model, the EIE cross-sections have been calculated for the Mg atom from its ground state 3s2 (J = 0) to the 3s3p, 3s4s, 3s3d, 3s4p, 3s5s, 3s4d, 3s5p, 3s6s, 3s5d, and 3s6p excited states using the RDW method. The cross-sections among 3s3p manifolds and the above-mentioned configurations are also computed. The calculated cross-sections have been utilized to calculate the EIE rates which are incorporated in the model. The model is coupled with available OES measurements to extract the plasma parameters viz. the electron temperature (Te) and electron density (ne) for 100–700 ns time delays of plasma expansion. The evaluated electron temperatures from the CR model have been compared with the values obtained using Thomson scattering as well as the Boltzmann plot methods. Chapter 3 describes the calculation of EIE cross-sections of neon from its ground 2p6 (1S0) state to the excited 2p53s, 2p53p, 2p53d, 2p54s, and 2p54p states, as well as from the excited state 2p53s to the 2p53p and 2p54p excited states for projectile electron energy from threshold to 500 eV. A CR model has been developed for the diagnostics of inductively coupled neon plasma in the pressure range of 5–25 mTorr. The plasma parameters (ne, Te) are obtained by comparing the state population of 2p53s 1si (i = 2–5) levels of neon to the available OAS measurements. The calculated plasma parameters are compared with those obtained using Langmuir probe measurements. Also, intensities of 29-line emission corresponding to 2pi-1si transitions calculated from the CR model are also compared with the values obtained from OES measurements. Here, the 2pi and 1si are the states in Paschen’s notation. Chapter 4 presents a fine-structure resolved CR model for the diagnosis of Ne–Ar mixture plasma. This model considers the 40 energy levels of neon and all the important channels of excitation and de-excitation among these levels. In the model, various collisional and radiative processes, along with the quenching of neon 1s levels by Ar atoms through Penning, and associative ionization are considered. The plasma parameters (ne, Te) have been extracted for 1, 6, 14, 25, and 40% of argon in neon-argon mixture plasma at 10 mTorr pressure. The extracted parameters have also been compared with the Langmuir probe measurements. The intensities of 23 emission lines corresponding to 2pi-1si transitions are also calculated and compared with the available OES measurements. iv Chapter 5 describes the non-invasive diagnostic study of capacitively coupled Ne rf plasma with a trace amount of O2/H2 through optical emission spectroscopy (OES) coupled with a suitable CR model. In a vacuum chamber, a 13.56 MHz RF signal and a 120 W power supply were used to generate a capacitively coupled neon RF discharge (flowing downstream) with a small admixture of O2/H2 (1-4%).The pressure in the chamber has been observed in the intermediate range (500–25000 Pa) for different mixture concentrations. A CR model has also been developed that efficiently considers the quenching of Ne atoms 1s (1s5, 1s4, 1s3) by O2/H2 molecules. Five intense Ne-I emission lines at 594.48, 607.43, 633.44, 638.30, and 703.24 nm are used to extract plasma parameter information from OES measurements. The electron temperature (Te) and electron density (ne) of the plasma have been extracted for the different mixture concentrations of Ne-O2 and Ne-H2. Chapter 6 deals with the development of a time-dependent CR model for the diagnostics of laser-produced silicon plasma. This model incorporates the extensively calculated fine structure resolved EIE cross-sections of the Si+2 ion. The EIE cross-section of Si+2 from its ground state 3s2 (J = 0) to the 41 fine structure levels of the configurations 3s3p, 3p2, 3s3d, 3s4s, 3s4p, 3s5s, 3s4d, 3s4f, 3s5p, 3s5d, and 3s5f have been calculated using relativistic distorted wave RDW theory. The EIE cross-section from the excited species and the ionization cross-section from the ground and metastable states of Si+2 ions are also calculated. The developed CR model is coupled with the optical emission spectroscopic OES measurements to extract the electron temperature in the early-stage expansion (30–100 ns) of laser-ablated silicon plasma. Chapter 7 finally presents the summary of the thesis work, conclusions drawn, and future scope of the work carried out.