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A Global Enhanced Vibrational Kinetic Model for Radio-Frequency Hydrogen Discharges and Application to the Simulation of a High

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A Global Enhanced Vibrational Kinetic Model for Radio-Frequency Hydrogen Discharges and Application to the Simulation of a High A Global Enhanced Vibrational Kinetic Model for Radio-Frequency Hydrogen Discharges and Application to the Simulation of a High Current Negative Hydrogen Ion Source by Sergey Nikolaevich Averkin A Dissertation Submitted to the Faculty of the WORCESTER POLYTECHNIC INSTITUTE in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Aerospace Engineering by _____________________________ February 27, 2015 APPROVED: ______________________________________________________________________________ Dr. Nikolaos A. Gatsonis, Advisor Professor, Aerospace Engineering Program, Mechanical Engineering Department ______________________________________________________________________________ Dr. John J. Blandino, Committee Member Associate Professor, Aerospace Engineering Program, Mechanical Engineering Department ______________________________________________________________________________ Dr. Lynn Olson, Committee Member Senior Scientist, Busek Co. Inc., Natick, MA ______________________________________________________________________________ Dr. Seong-kyun Im, Graduate Committee Representative Assistant Professor, Aerospace Engineering Program, Mechanical Engineering Department 2 Abstract A Global Enhanced Vibrational Kinetic (GEVKM) model is presented for a new High Cur- rent Negative Hydrogen Ion Source (HCNHIS) developed by Busek Co. Inc. and Worcester Pol- ytechnic Institute. The HCNHIS consists of a high-pressure radio-frequency discharge (RFD) chamber in which the main production of high-lying vibrational states of the hydrogen molecules occurs and a bypass system. The RFD chamber is connected via a nozzle to a low-pressure nega- tive hydrogen ion production (NIP) region where negative ions are generated by the dissociative attachment of low energy electrons to rovibrationally excited hydrogen molecules. Two configu- rations of the HCNHIS have been developed, one with the long NIP region (HCNHIS-1) and a second with a short NIP region (HCNHIS-2). Operation of the HCNHIS covered inlet flow rates from 300 to 3000 sccm and absorbed power of 430-600 W. Experiments using Faraday cups downstream the NIP region have shown the saturation of negative current in the presence of an electron filter. Negative currents attributed to negative hydrogen ions of 2-6 mA were measured for the HCNHIS-1 and 4 μA for the HCNHIS-2. The GEVKM is developed from moment equations for multi-temperature chemically react- ing plasmas derived from the Wang Chang-Uhlenbeck equations for a cylindrical geometry of an inductively coupled discharge chamber. The species included into the model are ground state hy- drogen atoms H and molecules H2 , 14 vibrationally excited hydrogen molecules H()2 v , v 1 14 , electronically excited hydrogen atoms H(2) , H(3) , ground state positive ions H , H2 , H3 , ground state negative ions H , and electrons e . The power deposition is considered to be primarily due to Joule heating of electrons by RF electric field while the stochastic heating is disregarded. The species temperature in the GEVKM is considered to be uniform in the plasma reactor. The spatial variation of the number densities of the plasma components is assumed to follow the product of two one-dimensional distributions corresponding to infinite long cylinder and two infinite plates. Heuristic expressions derived from exact and numerical solutions of the momentum and continuity equations covering low to high-pressure regimes are used in order to relate the wall, centerfield and average number densities of the plasma components. The volume- averaged steady-state continuity equations coupled with the electron energy equation, the total energy equation and heat transfer to the chamber walls are solved simultaneously in order to ob- 3 tain the volume-averaged number densities of the plasma components, the electron and heavy- particle temperatures as well as the wall temperature. The GEVKM is supplemented by a com- prehensive set of surface and volumetric chemical processes governing vibrational and ionization kinetics of hydrogen plasmas. The reaction rates when not available are calculated based on the available cross section-data and fitted to analytical expressions. The input conditions to the GEVKM are the inlet flow rate of the feedstock gas, absorbed power, geometry configuration and material properties of the plasma reactor. The GEVKM is implemented into a robust computational tool written in Fortran 90. It consists of the non-linear algebraic system of equations solver which utilizes the Newton- Raphson method. The GEVKM includes also a solver framework for the continuity and energy equations with self-consistency checks to guarantee conservation of charge, particles and energy in the system. The GEVKM is verified and validated in the low-pressure (0.2-100 mTorr) and low ab- sorbed power density (0.053-0.32 W/cm3) regime by comparing simulation results with experi- mental measurements of the low-pressure negative hydrogen ion source DENISE. The electron temperature and number density predicted by the GEVKM agree very well with the Langmuir probe measurements taken in the DENISE source. In the intermediate to high-pressure regime (1-100 Torr) and high absorbed power density (8.26-22 W/cm3) the GEVKM is verified and validated by comparisons with the numerical simu- lations and experimental measurements of a microwave generated plasma reactor. The GEVKM predictions of gas temperature are found in good agreement with the measurements. The GEVKM is applied to the simulation of the RFD chamber of the HCNHIS in both the HCNHIS-1 and HCNHIS-2 configurations. Analytic boundary conditions are developed for the flow in the bypass tubes based on the Fanno theory with the modifications due to rarefactions effects. The analytical boundary conditions are developed for the nozzle flow based on isentropic flow theory with corrections for high Knudsen numbers effects. These analytical outlet boundary conditions are validated by comparison of the pressures predicted by the GEVKM with the pres- sure measurements of the HCNHIS-1 RFD chamber undertaken at Busek Co. Inc. The GEVKM is used for simulations of the HCNHIS-2 RFD chamber at inlet flow rate of 1000 sccm and ab- sorbed power of 341 W. The GEVKM predictions of negative hydrogen ions number densities and electron temperatures in the RFD chamber of the HCNHIS-2 are used to estimate the nega- 4 tive hydrogen ion current using the Bohm flux approximation. The estimated negative current compares well with the Faraday Cup measurements and provides additional validation of the model. The GEVKM is used in a parametric investigation of the RFD chamber of the HCNHIS-2 with hydrogen inlet flow rates 5-1000 sccm and absorbed powers 200-1000 W. These simula- tions examine the effects of inlet flow rate and absorbed power on the production and destruction of vibrationally excited hydrogen molecules, the plasma composition, the production and de- struction of negative hydrogen ions, the electron and heavy particles temperature, and the maxi- mum extractable negative hydrogen ion current in the RFD chamber. Simulations show that the inlet flow rate has a major impact on the number densities of plasma species in the RFD cham- ber. The negative hydrogen ions production and the shape of the vibrational distribution function of hydrogen molecules depend on the inlet flow rate. At high flow rates and discharge pressures the distribution function is near Boltzmann while at low flow rates and discharge pressures the distribution is Bray-like distribution. The form of the distribution function affects the production of negative hydrogen ions through dissociative attachment mechanism. In addition, simulations show that the inlet flow rate affects the electron and heavy particles temperatures in a non- monotonic way. This parametric investigation provides the optimum operational parameters which result in the maximum relative concentration of high-lying vibrationally excited hydrogen molecules responsible for the negative hydrogen ion production. 5 Acknowledgments First of all, I would like to express my sincerest gratitude to my advisor Prof. Nikolaos Gatsonis. His continued guidance, support, encouragement, and inspiration provided throughout the whole period of my research allowed me to gain priceless experience. It was a privilege to work with him; his contribution to this work and my education in general will be always appreci- ated. In addition, I would like to thank Prof. Gatsonis and his wife Maria Kefallinou for their help and concern to my family and me. Special thanks are given to my committee members for their time and effort spent on my dissertation. I also would like to thank Siamak Najafi, Randy Robinson, Barbara Edilberti, Barbara Furman, and Donna M. Hughes. I would like to extend my gratitude to Dr. Raffaele Potami. Our fruitful discussions and his advices led me through my work at my thesis. My gratitude is extended to Prof. Alexander Fedorov and Prof. Ivan Egorov for giving the start of my career in Moscow Institute of Physics and Technology. I would also like to thank my friends from the CFPL laboratory. We spent an awesome time together. The last but not the least I would like to thank my parents, my son, and my wife for their patience, support, and believing in me. This work has been partially supported through a Subcontract from Busek Co. Inc. with prime sponsor the Phase I and Phase II DOE SBIR Grant No. DE-SC0004199. My thesis is dedicated to my son, my wife, and my parents. 6 Table of Contents
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