A Study of Self-Sustaining Thin-Films As a Means of Fusion Plasma
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A STUDY OF SELF-SUSTAINING THIN-FILMS AS A MEANS OF FUSION PLASMA IMPURITY AND WALL EROSION CONTROL A THESIS Presented to The Faculty of the Division of Graduate Studies By A. Bruce DeWald, Jr. In Partial Fullfillment of the Requirements for the Degree of Doctor of Philosophy in the School of Nuclear Engineering Georgia Institute of Technology November 12, 1984 Copyright (c) 1984 by A. Bruce DeWald, Jr. Thesis 'A Study of Secondary Ion-Emitting, Self-Sustaining Thin Films as a Means of Fusion Plasma Impurity and Wall Erosion Control" Approved: U I \l/\ 9^ //htf£+\ (At 7^^, y Dr. Weston M. Stacey, Jr., Chairman CJ sjjuvki J<5'tfifyfyitlii Dr. R. Glenn Bateman CIS*** Si'• (I)L\^LL^\ Dr. Alan R. Kraus Josejfn D. Clement 1 TABLE OF CONTENTS Page ACKNOWLEDGEMENTS iv LIST OF ILLUSTRATIONS v SUMMARY xi Chapter I. INTRODUCTION 1.1 Impurity/Erosion Mechanism/Control Review 1.2 Thesis Proposal and Scope 1.3 Relevant Mechanics/Kinetics Review II. THE SHEATH MODEL 23 2. 1 Introduction 2.2 Plasma Sheath Geometry 2.3 Particle Trajectory Model 2.4 Particle Density Calculation 2.5 Initial Conditions 2.6 Electric-Field Solution 2.7 Secondary Electron Emission 2.8 Reflected Ions 2.9 Secondary-Ion Emission 2.10 Summarization of Sheath Model Development 2.11 Sheath Model Verification 2.12 Wal1 Impact Angle 2.13 Secondary/Reflective Particle Effects III. THE SPUTTERING MECHANICS 86 3.1 Introduction 3.2 Geometrical Considerations 3.3 Scattering Mechanics 3.4 Interatomic Potential 3.5 Inelastic Energy Loss 3.6 Cascade Atom Energy Requirements Ill 3.7 Planar Potential 3.8 Displacements 3.9 Summarization of Sputtering Mechanics Development 3.10 Verification of the Sputtering Mechanics IV. THE SURFACE KINETICS MODEL 159 4.1 Introduction 4.2 Partial Diffusion Coefficients 4.3 Kinetic Equations 4.4 Vacancies 4.5 Vacancy Formation Entropy 4.6 Vacancy-Solute Interactions 4.7 Interstitials 4.8 Interstitial-Solute Complexes 4.9 Recombination of Irradiation-Induced Interstitials and Vacancies 4.10 Surface Segregation 4.11 Preferential Sputtering 4.12 Sinks 4.13 Summarization of Surface Kinetics Development 4.14 Preliminary Application of the Kinetics Model V. MODEL APPLICATIONS to the Cu-Li, V-Al, and 209 W-Be ALLOY SYSTEMS 5.1 Introduction 5.2 Cu-Li Sputtering Behaviour 5.3 Evaluation of the Lithium Activation Energy 5.4 DPA Profile Effects 5.5 Cascade Mixing Effects 5.6 Projectile Mass/Energy Effects 5.7 V-Al Sputtering Behaviour 5.8 W-Be Sputtering Behaviour VI. CONCLUSIONS and RECOMMENDATIONS 262 APPENDICES 271 A. Plasma-Edge Primary-Ion Velocity Coordinates B. Electronic Excitation Integral C. Atom and Defect Fluxes D. Substitutional Lithium (in Copper) Geometry Dependences REFERENCES 285 IV ACKNOWLEDGEMENTS I would like to thank Alan Krauss and Dieter Gruen of Argonne National Laboratory for suggesting the thesis topic and for providing the motivation for tackling the varied aspects of the thesis research. Thanks goes to Bill Stacey of Georgia Tech as my thesis advisor for providing the directional support and the political clout necessary to accomplish certain aspects of the thesis research. I am indebted to Al Bailey of Georgia Tech and to the rest of the "guys" at Argonne, especially Mike Pell in, Charlie Young, Manfred Kaminsky, Jeff Brooks, and Nghi Lam, all of whom provided technical insight and guidance. I would further like to thank John Carden, Joseph Clement, and Glenn Bateman for being a part of my thesis reading committee along with Alan Krauss and Bill Stacey. On a more personal note, I am not sure if my "working" sanity would have been maintained without my office buddies: Bob Morris (a pro at filling garters -- oh yes those teeth!) and Mike Valentine (the up and coming protege). Of course without the emotional support of my wife (Dolores), my parents, and my sister, the inner drive to forge ahead would have been lacking. Finally, I would like to thank my wife for playing the role of editor, graphics specialist, and data "reducer" all of which sped the thesis project to its ultimate finality. V LIST OF ILLUSTRATIONS Figures Title Page 1.1 Minimum Tokamak Ignition Temperature Versus 3 Plasma Impurity Concentration 1.2 Impurity Control Based on a Self-Sustaining 11 Thin-Film with a High Secondary-Ion Fraction Emission 1.3 Relative Potassium to Molydenum Surface 12 Concentration as a Function of Fluence While Under 1 keV He+ Bombardment (Sputtering) 2.1 Magnetized Sheath Model Geometry 25 2.2 Particle Motion Geometry 31 2.3 Translated Helical Phase Density and Velocity 36 Along the x'-Axis Within the Sheath Region 2.4 First-Order Cloud-In-Cel1 Weighting Scheme 38 2.5 Grid Spacing of the Least-Squares Spline Knots 40 Necessary for CIC Density Smoothing 2.6 Primary/Secondary Charged Particle Fluxes for 42 Which"the Potential Sheath is Determined 2.7 Control Surface Defining the Region of Solutions 43 for the Appropiate Boundary Conditions 2.8 Angular Dependence of the Electron Impact Energy 52 a,b for Maximum Secondary Electron Emission 2.9 Sheath Potential Variation as a Function of 63 Presheath Ion Flow Velocity 2.10 Sheath Potential Variation as a Function of 63 Vanadium (Z=3) Impurity Fraction 2.11 Spatial Development of the Sheath Potential 65 for Different Plasma-Edge Densities 2.12 Potential Sheath Spatial Variation as a Function 68 a~c of Magnetic Angle for Different Edge-Densities 2.13 Potential Magnitude Variation as a Function of 72 Magnetic Angle for Constant Edge-Density and Flow Velocity Conditions vi 2.14 Average Deuterium (Ion) Impact Energy as a 72 Function of Magnetic Angle for Constant Edge-Density and Flow Velocity Conditions 2.15 Cold-ion Impact Angle Behaviour Versus Magnetic 74 Angle in the Absence of an Electric Field 2.16 Hot-ion (Deuterium) Impact Angle Behaviour Versus 74 Magnetic Angle in the Presence of an Electric Field 2.17 Impact Angle Dependence Upon the Magnetic Angle 76 a-d of the Impurities Al, V, Be, and W, Respectively for Constant Plasma-Edge Conditions 2.18 The Average Impact Angle Versus Magnetic Angle 80 a,b Behaviour as a Function of Plasma-Edge Density for Deuterium and Vanadium (Z=3) Ions 2.19 Electron and Ion Space-Charge Density Profiles 83 for Light-Ion Reflection and JA = 30° 3.1a General Multilayer Structure of the Target Material 89 3.1b Local Atomic Separation (Mean-Free-Path Distance) 90 Within a Given Atomic Layer 3.1c Surface Layer Geometry Characterization 90 3.2 Trajectories of a Classical Binary Collision in the 93 Presence of a Conservative Central Repulsive Force 3.3 Center of Mass Scattering Triangle 98 3.4 Universal Moliere Correction Factor "Fit" to the 106 Biersack-Ziegler Potential for Ar+-*Cu as a Function of the Reduced Collision Apsis 3.5 TRIM Dependence of the Fraction of First Collisions 107 Upon the Distance of Closest Approach for 3 keV Argon at Normal Incidence Off of Copper 3.6 TRIM Dependence of the Sputtered Fraction as a 114 Function of Cascade Membership for 3 keV Ar+ —*Ti at Normal Incidence 3.7 TRIM Dependence of the Sputtered Fraction Upon 116 the Causal Kinetic Energy for Titanium Causal Sputtering Events Set in Motion by 3 keV Ar+-*Ti at Normal Incidence 3.8 TRIM Dependence of the Sputtering Fraction Upon 117 vii the Causal Reduced Impact Parameter for 3 KeV Ar+—*Ti at Normal Incidence 3.9 Comparison of Local Excitation IVIodels as a Function 118 of the Reduced Collision Impact Parameter for 10 eV and 1 KeV 3.10 Atomic Threshold Displacement Energy as a Function 124 of Atomic Sublimation Energy 3.11 Relative Damage Efficiency Dependence Upon the 126 Average PKA Damage Energy For Several Projectile Species 3.12 Refraction of Atoms Overcoming a Planar Potential 129 3.13 Sputtering Energy Distributions for Isotropic and 130 Planar Surface Potentials 3.14 Energy Dependence of the Sputtering Yield for the 135 a-g Projectile/Target Combinations of D/Cu, He/Cu, Ar/Cu, D/V, Ar/V, Ar/W, and U/<*-U at Normal Incidence 3.15 Angular Dependence of the Sputtering Yield for the 146 a,b Ar/Cu and Ar/W Projectile/Target Combinations at Constant Energy 3.16 Sputtering Yield Ratio as a Function of Energy for 148 a Deuterium on Copper at 60 Degrees Compared to Normal Incidence 3.16 Deuterium Reflection Probability from Copper as a 149 b- Function of Energy for Normal and 60 Degrees Incidence Angles 3.17 Self-Reflection Yield of V, Cu, and W as a 151 Function of Energy for a 60 Degrees Impact Angle 3.18 Sigmund-Thompson Sputtered Energy Distribution for 152 a Copper Assuming a Surface Binding Energy of 3.53 eV 3.18 Copper Self-Sputtered Energy Distributions as a 153 b,c Result of 100 eV and 1000 eV Normal Incidence Copper 3.19 Copper Self-Sputtered Angular Distributions for 156 a,b Normal Incidence Copper at 100 eV and 1000 eV 3.20 Copper and Lithium Sputtered Angular Distributions 158 a,b from a Lithium Monolayer on Pure Copper as a Result of 1000 eV Copper at Normal and 60 Degrees Incident Angles viii 4.1 Defect Lattice Configurational Space for N Atoms 163 Possessing 3N Degrees of Freedom 4.2 Arrhenius Behaviour of Copper Self-Diffusion 169 (Experimental Tracer) Data 4.3 Most Probable fee and bec .Vieta 1 Dumbbell 177 a,b Configurations 4.4 Elementary Dumbbell Jumps in fee and bee Metals 179 a,b Having the Lowest Energy of Migration 4.5 Experimental Correlation of the Solute Capture 182 in Copper Alloys as a Function of Solute Volume Dilatat ion 4.6 Segregant Atom Free Energy Versus Surface Depth 190 for a Homogeneous Binary Alloy at Time, t=0.