Electromagnetic Particle-In-Cell Algorithms on Unstructured Meshes for Kinetic Plasma Simulations
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Electromagnetic Particle-in-Cell Algorithms on Unstructured Meshes for Kinetic Plasma Simulations Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Dong-Yeop Na, M.S. Graduate Program in Electrical and Computer Engineering The Ohio State University 2018 Dissertation Committee: Prof. Fernando L. Teixeira, Advisor Prof. Kubilay Sertel Prof. Robert Lee c Copyright by Dong-Yeop Na 2018 Abstract Plasma is a significantly ionized gas composed of a large number of charged parti- cles such as electrons and ions. A distinct feature of plasmas is the collective interac- tion among charged particles. In general, the optimal approach used for modeling a plasma system depends on its characteristic (temporal and spatial) scales. Among var- ious kinds of plasmas, collisionsless plasmas correspond to those where the collisional frequency is much smaller than the frequency of interests (e.g. plasma frequency) and the mean free path is much longer than the characteristic length scales (e.g. Debye length). Collisionless plasmas consisting of kinetic space charge particles interacting with electromagnetic fields are well-described by Maxwell-Vlasov equations. Electromag- netic particle-in-cell (EM-PIC) algorithms solve Maxwell-Vlasov systems on a com- putational mesh by employing coarse-grained superparticle. The concept of super- particle, which may represent millions of physical charged particles (coarse-graining of the phase space), facilitates the realization of computer simulations for under- scaled kinetic plasma systems mimicking the physics of real kinetic plasma systems. In this dissertation, we present an EM-PIC algorithm on general (irregular) meshes based on discrete exterior calculus (DEC) and Whitney forms. DEC and Whitney forms are utilized for consistent discretization of Maxwells equation on general ir- regular meshes. The proposed EM-PIC algorithm employs a mixed finite-element ii time-domain (FETD) field solver which yields a symplectic integrator satisfying en- ergy conservation. Importantly, we employ Whitney-forms-based gather and scatter schemes to obtain exact charge conservation from first principles, which had been a long-standing challenge for PIC algorithms on irregular meshes. Several further contributions are made in this dissertation: (i) We develop a local and explicit EM-PIC on unstructured grids using sparse approximate inverse (SPAI) strategy and study macro- and microscopic residual errors in motions of charged par- ticles affected by the approximate inverse errors. (ii) We extend the present EM-PIC algorithm to the relativistic regime with several relativistic particle-pushers and com- pare their performance. (iii) We implement a secondary electron emission (SEE) processor based on probabilistic Furman-Pivi model and numerically investigate mul- tipactor effects that are resonant electron discharges from conducting surfaces by external RF fields. (iv) We diagnose numerical Cherenkov radiation, which is a detri- mental effect frequently found in EM-PIC simulations involving relativistic plasma beams, for the present EM-PIC algorithm on general meshes. (v) We extend the FETD field solver for the solution of Maxwell's equations in circularly symmetric or body-of-revolution (BOR) geometries. (vi) Lastly, we combine the EM-PIC algo- rithm with the BOR-FETD field solver for the efficient analysis of vacuum electronic devices (VED). iii Dedicated to my beloved wife Da-Young and my family iv Acknowledgments First and foremost, I would like to express my sincere gratitude to my advisor, Prof. Fernando L. Teixeira, for the support, encouragement, and guidance during the years of my graduate study. It has been a great honor and privilege to work with him. His passion and immense knowledge in electromagnetics, mathematics, and physics, and kindness and commitment to his students will always inspire me. Besides, I would like to thank Dr. Yuri A. Omelchenko and Prof. Ben-Hur V. Borges for their helpful discussions and suggestions. My special appreciation also goes to the members of my doctoral committee, Prof. Kubilay Sertel and Prof. Robert Lee, for insightful comments. I would like to thank to many of ESL colleagues, past and present, Haksu Moon, WoonGi Yeo, Jungwhan Park, Carlos A. Viteri, Cagdas Gunes, Daniel O. Acero, and Julio L. Nicolini, and my friends, Yun-Shik Hahn, Chunghyun Lee, Jongchan Choi, Kyoung-Ho Jeong, and Huyngjun Kim. I wish to thank my family for their constant support and unconditional love. Last but not least, I would like to share this accomplishment with my beloved wife, Da-Young, and sincerely appreciate her her encouragement, support, and love. v Financial support from National Science Foundation grant ECCS-1305838, De- fense Threat Reduction Agency grant HDTRA1-18-1-0050, Ohio Supercomputer Cen- ter grants PAS-0061 and PAS-0110, and The Ohio State University Presidential Fel- lowship Program are gratefully acknowledged. vi Vita March 30, 1987 . Born - Seoul, Korea Feburary, 2012 . B.S. in Electrical and Computer Eng., Ajou University, Suwon, Korea July, 2014 . M.S. in Electrical and Computer Eng., Ajou University, Suwon, Korea August, 2014-May, 2017 . Graduate Research Associate, ElectroScience Laboratory, The Ohio State University, USA May, 2017-May, 2018 . Presidential Fellowship Program, The Ohio State University, USA May, 2018-August, 2018 . Graduate Research Associate, ElectroScience Laboratory, The Ohio State University, USA August, 2018-present . Graduate Teaching Associate, Electrical and Computer Eng., The Ohio State University, USA Publications Jounral Publications Dong-Yeop Na, Haksu Moon, Yuri A. Omelchenko, Fernando L. Teixeira, \Local, explicit, and charge-conserving electromagnetic particle-in-cell algorithm on unstruc- tured grids," IEEE Trans. Plasma Sci., 44 (2016) 1353{1362. Dong-Yeop Na, Yuri A. Omelchenko, Haksu Moon, Ben-Hur V. Borges, Fernando L. Teixeira, \Axisymmetric charge-conservative electromagnetic particle simulation algorithm on unstructured grids: Application to microwave vacuum electronic De- vices," J. Comput. Phys., 346 (2017) 295{317. vii Dong-Yeop Na, Haksu Moon, Yuri A. Omelchenko, Fernando L. Teixeira, \Rel- ativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations," Phys. Plasmas, 25 (2018) 013109. Dong-Yeop Na, Ben-Hur V. Borges, Fernando L. Teixeira, \Finite element time- domain body-of-revolution Maxwell solver based on discrete exterior calculus," J. Comput. Phys., 376 (2017) 249{275. Conference publications Dong-Yeop Na, Fernando L. Teixeira, Yuri A. Omelchenko, \Charge-conserving relativistic PIC algorithm on unstructured grids," 2016 USNC-URSI National Radio Science Meeting, Boulder, CO, Jan. 6-9, 2016. Dong-Yeop Na, Fernando L. Teixeira, H. Moon, Yuri A. Omelchenko, \Full-wave FETD-based PIC algorithm with local explicit update," 2016 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, Fajardo, PR, June 26-July 1, 2016. Dong-Yeop Na, Fernando L. Teixeira, Yuri A. Omelchenko, \Unstructured-grid and conservative electromagnetic particle-in-cell: application to micromachined slow- wave structures," 2016 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, Fajardo, PR, June 26-July 1, 2016. Dong-Yeop Na, Yuri A. Omelchenko, Fernando L. Teixeira, \An efficient algorithm for simulation of plasma beam high-power microwave sources," 2017 IEEE MTT-S International Microwave Symposium, Honolulu, HI, June 4-9, 2017. Dong-Yeop Na, Fernando L. Teixeira, Ben-Hur V. Borges, \Finite-element time- domain solver for axisymmetric devices based on discrete exterior calculus and trans- formation optics," 2017 SBMO/IEEE MTT-S International Microwave and Opto- electronics Conference, Aguas de Lindoia, Brazil, Aug. 27-30, 2017. Dong-Yeop Na, Yuri A. Omelchenko, Fernando L. Teixeira, \Irregular-grid-based particle-in-cell simulations of resonant electron discharges with probabilistic secondary electron emission model," 2017 XXXIInd General Assembly and Scientific Sympo- sium of the International Union of Radio Science, Montreal, QC, Canada, August 19-26, 2017. viii Dong-Yeop Na, Yuri A. Omelchenko, Fernando L. Teixeira, \Discretization of Maxwell-vlasov equations based on discrete exterior calculus," 2017 XXXIInd General Assembly and Scientific Symposium of the International Union of Radio Science, Montreal, QC, Canada, August 19-26, 2017. Dong-Yeop Na, Julio L. Nicolini, Robert Lee, Ben-Hur V. Borges, Yuri A. Omelchenko, Fernando L. Teixeira, \Diagnosis of Numerical Cherenkov Instability in Plasma Simu- lations on General Mesh," Computational Aspects of Time Dependent Electromagnetic Wave Problems in Complex Materials, The Institute of Computational and Experi- mental Research in Mathematics (ICERM), Providence, RI, June 24-29, 2018. Dong-Yeop Na, Fernando L. Teixeira, Yuri A. Omelchenko, \Dispersion Analy- sis of Electron Bernstein Waves in Magnetized Warm Plasmas by Finite Element Particle-in-Cell Modeling," 2018 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, Boston, MA, July 8-13, 2018. Dong-Yeop Na, Fernando L. Teixeira, Yuri A. Omelchenko, \Numerical Cherenkov Radiation Effects from Grid Dispersion in Finite Element Particle-in-Cell Simulations of Relativistic Electron Beams," 2018 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, Boston, MA, July 8-13,