Modeling of transport properties of ions of krypton and xenon for optimization of cold rare-gas plasmas generators

Cyril Van de Steen

Doctoral thesis

Abstract:

The use of cold plasmas based on rare gases (Rg) in biomedical applications as well as in space propulsion is clearly evolving. To optimize these plasma reactors, a fine understanding of the processes taking place in these reactors is necessary. This thesis aims to provide the missing data in the literature (transport coefficients and reaction) through mesoscopic data (cross-sections) obtained from microscopic data (interaction potentials) for xenon and krypton in their parent gas. Only cold plasmas composed of a single type of atom are considered. Both are rare gases, and so have, in the neutral state little / no interaction between them. Therefore, only ion – atom collisions will be considered. Due to the low ion energies in the cold plasma, only the first 6 excited states of the Rg2+ pair will be taken into account. These 6 states will be classified in two groups, 2P1/2 and 2P3/2. In this work, two different interaction potentials available in the literature are used and compared for the Kr+/Kr and Xe+/Xe collision systems in the calculation of cross sections. For collisions involving ionic dimers (Kr2+/Kr and Xe2+/Xe), the interaction potentials are calculated from the DIM model (Diatomics In Molecules) which is a combination of the atomic potentials of neutral – neutral and ionic – neutral interaction. The cross-sections required to obtain the missing mesoscopic data are calculated from three different methods. The first method is the quantum method which allows, by a resolution of the Schrödinger equation, to obtain exactly the cross sections from the interaction potentials. This exact method, which consumes a lot of computation time, is used as a reference to validate the two other approximate methods. The second method, called semiclassical, is based on the same expression as the quantum cross section but uses an approximate phase shift (JWKB approximation), induced by the interaction potential, between the scattered wave and the incident wave. This method has the advantage of being faster than the quantum method while having very close results. The last method is the hybrid method of treating atoms by a classical method and electrons by quantum formalism. This method is the only one of the approximate methods which makes it possible to treat the collisions between dimer and atom taking into account the vibration and the rotation of the dimer. In a dimer-atom collision, fragmentation of the dimer may occur and thus the dissociative dissociation cross-section of the dimer appearing from an energy threshold has been taken into account in the Monte Carlo calculations. The diffusion coefficients as well as the mobility of the ions in their parent gases are calculated from the cross-sections with a Monte Carlo code. The mobilities thus calculated are compared with the experimental measurements available in the literature. For dimer calculations, rotation and vibration in the molecule must be taken into account. All the results shown are made on the ground state of the dimer. The mobilities thus calculated by the available methods give results close to the experimental values, allowing us to reinforce our other coefficients of transport and reaction.

Abstract:

The use of cold plasmas based on rare gases (Rg) in biomedical applications as well as in space propulsion is clearly evolving. To optimize these plasma reactors, a fine understanding of the processes taking place in these reactors is necessary. This thesis aims to provide the missing data in the literature (transport coefficients and reaction) through mesoscopic data (cross-sections) obtained from microscopic data (interaction potentials) for xenon and krypton in their parent gas. Only cold plasmas composed of a single type of atom are considered. Both are rare gases, and so have, in the neutral state little / no interaction between them. Therefore, only ion – atom collisions will be considered. Due to the low ion energies in the cold plasma, only the first 6 excited states of the Rg2+ pair will be taken into account. These 6 states will be classified in two groups, 2P1/2 and 2P3/2. In this work, two different interaction potentials available in the literature are used and compared for the Kr+/Kr and Xe+/Xe collision systems in the calculation of cross sections. For collisions involving ionic dimers (Kr2+/Kr and Xe2+/Xe), the interaction potentials are calculated from the DIM model (Diatomics In Molecules) which is a combination of the atomic potentials of neutral – neutral and ionic – neutral interaction. The cross-sections required to obtain the missing mesoscopic data are calculated from three different methods. The first method is the quantum method which allows, by a resolution of the Schrödinger equation, to obtain exactly the cross sections from the interaction potentials. This exact method, which consumes a lot of computation time, is used as a reference to validate the two other approximate methods. The second method, called semiclassical, is based on the same expression as the quantum cross section but uses an approximate phase shift (JWKB approximation), induced by the interaction potential, between the scattered wave and the incident wave. This method has the advantage of being faster than the quantum method while having very close results. The last method is the hybrid method of treating atoms by a classical method and electrons by quantum formalism. This method is the only one of the approximate methods which makes it possible to treat the collisions between dimer and atom taking into account the vibration and the rotation of the dimer. In a dimer-atom collision, fragmentation of the dimer may occur and thus the dissociative dissociation cross-section of the dimer appearing from an energy threshold has been taken into account in the Monte Carlo calculations. The diffusion coefficients as well as the mobility of the ions in their parent gases are calculated from the cross-sections with a Monte Carlo code. The mobilities thus calculated are compared with the experimental measurements available in the literature. For dimer calculations, rotation and vibration in the molecule must be taken into account. All the results shown are made on the ground state of the dimer. The mobilities thus calculated by the available methods give results close to the experimental values, allowing us to reinforce our other coefficients of transport and reaction.

Keywords

Physicochemical modeling, basic data, atomic ion (Kr+ and Xe+) and diatomic (Kr2+ and Xe2+), ion-neutral interaction, interaction potential, collision cross section and dissociation, quantum method, semiclassical method (JWKB) method hybrid, Monte Carlo simulation, transport coefficients, reaction rate

Keywords

Physicochemical modeling, basic data, atomic ion (Kr+ and Xe+) and diatomic (Kr2+ and Xe2+), ion-neutral interaction, interaction potential, collision cross section and dissociation, quantum method, semiclassical method (JWKB) method hybrid, Monte Carlo simulation, transport coefficients, reaction rate

Language used: English

Date on which the thesis was submitted / produced: 13. 11. 2018

Thesis defence

• Date of defence: 5. 12. 2018
• Supervisor: René Kalus
• Reader: Ahmed Rhallabi, Ivana Paidarová, Ivan Janeček

VŠB - Technical University of Ostrava

Univerzitní studijní programy

Doctoral programme / field:
Výpočetní vědy / Výpočetní vědy