PhD and MPhil Thesis Classes - UniversitÃ© Libre de Bruxelles

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$Studies of fractional D-branes in the gauge/gravity correspondence ...$

CONTENTS2 Aims of the project 232.1 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.2 Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Drift Waves 253.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Hamiltonian Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2.1 Principle of Least Action and Equation of Motion . . . . . . . . 263.2.2 Maxwell-Lorentz Equations . . . . . . . . . . . . . . . . . . . . . 273.3 Charged Particle Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.1 Equation of Motion . . . . . . . . . . . . . . . . . . . . . . . . . 303.3.2 Uniform E and B fields . . . . . . . . . . . . . . . . . . . . . . . 303.3.2.1 B = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.3.2.2 E = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.3.2.3 Particle Drift . . . . . . . . . . . . . . . . . . . . . . . . 333.3.2.4 Validity Limit . . . . . . . . . . . . . . . . . . . . . . . 373.3.3 Nonuniform E and B fields . . . . . . . . . . . . . . . . . . . . . 383.3.3.1 ∇B⊥B: Grad−B Drift . . . . . . . . . . . . . . . . . . 383.3.3.2 Curved B: Curvature Drift . . . . . . . . . . . . . . . . 393.3.3.3 Magnetic Mirrors . . . . . . . . . . . . . . . . . . . . . 403.3.4 Nonuniform E Field . . . . . . . . . . . . . . . . . . . . . . . . . 413.3.5 Summary of Guiding Center Drifts . . . . . . . . . . . . . . . . . 443.4 Fluid Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.4.1 Summary of Fluid Equations . . . . . . . . . . . . . . . . . . . . 473.4.2 Closure of Fluid Equations . . . . . . . . . . . . . . . . . . . . . 473.5 Transport Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.5.1 Experimental Aspects . . . . . . . . . . . . . . . . . . . . . . . . 483.6 Fluid Drifts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.6.1 Fluid Drifts ⊥B . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.6.2 Fluid Motion ‖ B . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.7 Drift Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.7.1 Drift Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . 533.7.2 Drift Instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54vi
CONTENTS3.7.3 Drift Wave in Laboratory . . . . . . . . . . . . . . . . . . . . . . 553.8 Anomalous Transport due to Drift Waves . . . . . . . . . . . . . . . . . 553.8.1 Mixing Length Approximation . . . . . . . . . . . . . . . . . . . 574 Drift Instability Analysis: Linear Fluid Model 594.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.2 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.2.0.1 Collisional Effect On Trapped Electrons . . . . . . . . . 614.2.1 Compressibility of The Drift Velocity . . . . . . . . . . . . . . . . 624.2.2 Quasi-Neutrality Condition . . . . . . . . . . . . . . . . . . . . . 644.2.3 Linear Response . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.2.4 Solution of Dispersion Equation . . . . . . . . . . . . . . . . . . . 664.3 Instability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.3.1 ITG Instability Mechanism . . . . . . . . . . . . . . . . . . . . . 684.3.2 TE Instability Mechanism . . . . . . . . . . . . . . . . . . . . . . 694.3.3 ETG Instability Mechanism . . . . . . . . . . . . . . . . . . . . . 694.3.4 Numerical Computations . . . . . . . . . . . . . . . . . . . . . . 694.3.5 Computation of the Solutions of the Dispersion Equation . . . . 724.3.6 Impurity Effect on Drift Instabilities . . . . . . . . . . . . . . . . 785 Anomalous Transport due to Drift Wave Microinstabilities 875.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.2 Transport coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.3 Impurity Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925.3.1 Peaking Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.4 Importance of Collisions on Anomalous Transport of Impurity . . . . . . 965.5 Results of calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1066 Benchmark with a Quasi-linear Gyro-kinetic Model 1096.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096.1.1 Dispersion Equation . . . . . . . . . . . . . . . . . . . . . . . . . 1136.2 QuaLiKiz code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1146.3 Comparison With AFC-FL . . . . . . . . . . . . . . . . . . . . . . . . . 115vii
Page 1 and 2: Transport Analysis in TokamakPlasma
Page 3 and 4: mode (ITG mode) by the impurities.
Page 5 and 6: I dedicate my thesis to maman, baba
Page 7: philosophical debates, exchanges of
Page 12 and 13: CONTENTS7 Transport Modeling of Imp
Page 14 and 15: LIST OF FIGURES3.4 Drift of a gyrat
Page 16 and 17: LIST OF FIGURES5.8 The peaking fact
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Page 22 and 23: 1. INTRODUCTION1.2 Fusion ReactionT
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Page 40 and 41: 1. INTRODUCTIONδV E = δE × BB 2
Page 42 and 43: 1. INTRODUCTIONmagnetic field geome
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Page 46 and 47: 3. DRIFT WAVESOur goal is to study
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3. DRIFT WAVESWe need to compute th
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3. DRIFT WAVESIf the electric field
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3. DRIFT WAVES3.3.5 Summary of Guid
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3. DRIFT WAVESwhere P is the pressu
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3. DRIFT WAVESprescribed as a given
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3. DRIFT WAVESever, in general the
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3. DRIFT WAVESthough the individual
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3. DRIFT WAVESReplacing the eq. (3.
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3. DRIFT WAVES∂n= −∇ · Γ (3
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3. DRIFT WAVES58
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4. DRIFT INSTABILITY ANALYSIS: LINE
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5. ANOMALOUS TRANSPORT DUE TO DRIFT
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6. BENCHMARK WITH A QUASI-LINEAR GY
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7. TRANSPORT MODELING OF IMPURITY S
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8. STUDY OF DRIFT WAVE CHARACTERIST
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9. DISCUSSIONthat the impurity dens
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9. DISCUSSIONsurface and machine wa
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9. DISCUSSIONthe plasma distributio
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REFERENCES[21] Weiland J. Collectiv
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REFERENCES[73] Neuhauser J. et al.
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PhD and MPhil Thesis Classes - UniversitÃ© Libre de Bruxelles

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