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UCLA Electronic Theses and Dissertations UCLA UCLA Electronic Theses and Dissertations Title Computational Modeling of Plasma-induced Secondary Electron Emission from Micro- architected Surfaces Permalink https://escholarship.org/uc/item/5n50s2wj Author Chang, Hsing-Yin Publication Date 2019 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA Los Angeles Computational Modeling of Plasma-induced Secondary Electron Emission from Micro-architected Surfaces A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Materials Science and Engineering by Hsing-Yin Chang 2019 c Copyright by Hsing-Yin Chang 2019 ABSTRACT OF THE DISSERTATION Computational Modeling of Plasma-induced Secondary Electron Emission from Micro-architected Surfaces by Hsing-Yin Chang Doctor of Philosophy in Materials Science and Engineering University of California, Los Angeles, 2019 Professor Jaime Marian, Chair Advances in electrode, chamber, and structural materials will enable breakthroughs in future gen- erations of electric propulsion and pulsed power (EP & PP) technologies. Although wide ranges of EP & PP technologies have witnessed rapid advances during the past few decades, much of the progress was based on empirical development of materials through experimentation and trial-and- error approaches. To enable future technologies and to furnish the foundations for quantum leaps in performance metrics of these systems, a science-based materials development effort is required. The present study aims to develop computational models to simulate, analyze, and predict the sec- ondary electron emission of plasma devices in order to aid the design of materials architectures for EP & PP technologies through an integrated research approach that combines multi-scale modeling of plasma-material interactions, experimental validation, and material characterization. The range of materials of interest in EP & PP technologies include refractory metals, such as tungsten (W) and its alloys (W-Re) and molybdenum (Mo), ceramic composites, such as boron nitride (BN) and alumina (Al2O3), high-strength copper alloys, and carbon-carbon composites. These classes of ma- terials serve various design functions; primarily in cathode and anode applications, in accelerator grids, and in beam dumps of high power ( a few GW) microwave (HPM) sources. We first give ∼ an overview of our fundamental understanding for the limits of using these materials in EP & PP technologies, and the opportunity to design material architectures that may dramatically improve ii their performance. Next, we introduce the computational framework to model secondary electron emission from micro-architected surfaces. A detailed description of the underlying physics, com- putational models and methods are then provided, followed by simulation results, respectively. Finally, discussions and conclusions of our major findings as well as suggested future work are given. iii The dissertation of Hsing-Yin Chang is approved. Jenn-Ming Yang Nasr M. Ghoniem Richard E. Wirz Jaime Marian, Committee Chair University of California, Los Angeles 2019 iv To my parents and family, for their love, endless support and encouragement v TABLE OF CONTENTS List of Figures ......................................... x List of Tables .......................................... xiv Acknowledgments ....................................... xv Vita ............................................... xvi 1 Introduction ........................................ 4 1.1 Motivation . .4 1.1.1 Electric Propulsion . .4 1.1.2 Magnetic Confinement Fusion . .7 1.1.3 Other Applications . .9 1.2 Problem Statement . .9 1.2.1 Secondary Electron Emission . .9 1.2.2 Concept of Potential Solutions . 11 1.3 Thesis Outline . 12 2 Computational Approach ................................. 14 2.1 Computational Framework . 14 2.2 Molecular Dynamics Simulation . 16 2.2.1 Ab Initio Molecular Dynamics Simulation . 16 2.2.2 Classical Molecular Dynamics Coupled With Electronic Subsystem Dy- namics Simulation . 17 2.3 Monte Carlo Simulation . 20 vi 3 Calculation of Secondary Electron Emission Yields from Low-energy Electron Depo- sition in Tungsten Surfaces .................................. 24 3.1 Introduction . 24 3.2 Theory and Methods . 26 3.2.1 Electron Scattering Theory . 26 3.2.2 Elastic Scattering . 26 3.2.3 Inelastic Scattering . 28 3.3 Monte Carlo Calculations . 33 3.4 Results . 35 3.5 Discussion and Conclusions . 39 4 Monte Carlo Raytracing Method for Calculating Secondary Electron Emission from Micro-architected Surfaces .................................. 43 4.1 Introduction . 43 4.2 Computational Model . 45 4.2.1 Intersection Detection Algorithm . 45 4.2.2 Generation of Secondary Rays . 47 4.2.3 Finite Element Model and Surface Geometry Development . 50 4.3 Results and Discussion . 51 4.3.1 Verification . 51 4.3.2 Micro-architected Foam Structures . 53 4.4 Discussion and Conclusions . 58 5 Monte Carlo Modeling of Low Electron Energy Induced Secondary Electron Emis- sion Yields in Micro-architectured h-BN Surfaces ..................... 61 5.1 Introduction . 61 vii 5.2 Theory and Methods . 62 5.2.1 Electron-Insulator Interaction Model . 62 5.2.2 Elastic Scattering . 63 5.2.3 Inelastic Scattering . 66 5.2.4 Phonon Excitation . 69 5.2.5 Polaronic Effects . 70 5.3 Monte Carlo Calculation . 71 5.4 Results . 73 5.4.1 Flat Surfaces . 73 5.4.2 Micro-Architectured Foam Structures . 74 5.5 Discussion and Conclusions . 75 5.6 Verification . 78 6 Conclusions ......................................... 81 6.1 Discussion of Results . 81 6.2 Future Work . 83 6.2.1 Charging Effect on Secondary Electron Emission . 83 A List of Symbols ....................................... 84 B Constants & Kinematical Quantities ........................... 87 C Definition of Coordinate System ............................. 88 D Classical Scattering .................................... 90 D.1 Definition of Cross Section . 90 D.2 Rutherford Scattering . 92 viii E Partial Wave Analysis ................................... 94 E.1 Preliminary Scattering Theory . 94 E.2 Partial Wave Expansion . 95 References ........................................... 98 ix LIST OF FIGURES 1.1 Thrust and specific impulse ranges for various forms of propulsion. .8 1.2 Schematic of a tokamak chamber and magnetic profile. Figure reproduced from [1]. .9 1.3 Plasma sheath profile (a) in the absence of secondary electrons (b) in presence of secondary electrons. Figure reproduced from [2]. 10 1.4 Candidates geometries: (a) micro-spears (b) micro-nodules (c) micro-velvets (d) micro- pillars (e) micro-foams (f) self-similar surface structures. 12 2.1 Temporal snapshots of a collision cascade created by a 5 keV Ag atom impinging onto an Ag (111) surface. The excitation energy density is shown as a continuous color map in addition to atoms displaced during the cascade. Figure reproduced from [3]. 21 2.2 Flowchart of the combined Molecular Dynamics approach. Figure reproduced from [4]. 23 3.1 Schematic diagram of the discrete collision model of electron scattering simulated using Monte Carlo. 33 3.2 Normalized distributions for 100-eV primary electrons incident at 0◦: (a) Energy dis- tribution of secondary electrons; (b) Angular distribution of secondary electrons. 36 3.3 (a) Depth distribution of both emitted and thermalized (captured) electrons for a pri- mary electron energy and incident angle of 100 eV and 0◦. (b) Relative occurrence of the main scattering mechanisms as a function of primary energy for normal incidence. 37 x 3.4 (a) Total SEE yield from an ideally-flat W surface as a function of primary electron energy for electrons incident at 0 . = this work; black dashed line = Ahearn (1931) ◦ • [5]; cyan dashed line = Coomes (1939) [6]; = Bronshtein and Fraiman (1969) [7]; N = Ding et al. (2001) using the method where the SE is assumed to come from a distribution of electron energies in the valence band; H = Ding et al. (2001) using the method where the SEs are assumed to originate from the Fermi level [8, 9]; = Patino et al. (2016) [10]. (b) Total SEE yield from smooth W as a function of primary electron energy, for electrons incident at 45 . = this work; = Patino et al. (2016) ◦ • [10]. 38 3.5 Total SEE yield from a flat W surface as a function of primary electron energy and incidence angles. 39 3.6 (a) Total SEE yield from an ideally-flat W as a function of primary electron energy, for electrons incident at 0◦, 30◦, 45◦, 60◦, 75◦ and 89◦. (b) Surface plot of the total SEE yield from an ideally-flat W as a function of primary electron energy and angle of incidence. 40 3.7 Flow chart of the Monte Carlo program . 42 4.1 Flowchart of the raytracing Monte Carlo code. 49 4.2 (a) Finite element model of a real micro-architected foam structure rendered from X- ray tomography images. (b) Histogram of surface element normals. 51 4.3 SEE yield as a function of primary energy for normal incidence on ideally flat W sur- faces obtained using (i) scattering Monte Carlo (raw data from ref. [11]), (ii) sampling functions given in Equation (4.6), and (iii) using the raytracing model described here. 52 4.4 (a) Image of a cubic open cell foam structure with the cage size l and ligament size t indicated. (b) Secondary electron yield versus electron beam energy at 0 degree incidence from the cubic cage. 53 xi 4.5 SEE yield versus electron beam energy initially projected from 0 degree incidence to the foam at varying volume-fraction percentages. The inset shows
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