The radial transport of particles in tokamaks is one of the most stringent issues faced by the magnetic confinement fusion community, because the fusion power is proportional to the square of the pressure, and also because accumulation of heavy impurities in the core leads to important power losses which can lead to a "radiative collapse". Sawteeth and the associated periodic redistribution of the core quantities can significantly impact the radial transport of electrons and impurities. In this thesis, we perform numerical simulations of sawteeth using a nonlinear tridimensional magnetohydrodynamic code called XTOR-2F to study the particle transport induced by sawtooth crashes. We show that the code recovers, after the crash, the fine structures of electron density that are observed with fast-sweeping reflectometry on the JET and TS tokamaks. The presence of these structure may indicate a low efficiency of the sawtooth in expelling the impurities from the core. However, applying the same code to impurity profiles, we show that the redistribution is quantitatively similar to that predicted by Kadomtsev's model, which could not be predicted a priori. Hence finally the sawtooth flushing is efficient in expelling impurities from the core.
Authors
- Bibliographic Reference
- Timothée Nicolas. Transport de particules induit par les Dents-de-Scie dans les palsmas de tokamak. Physique des plasmas [physics.plasm-ph]. Ecole Polytechnique X, 2013. Français. ⟨NNT : ⟩. ⟨pastel-00926428⟩
- HAL Collection
- ["CEA - Commissariat à l'énergie atomique", 'PASTEL - ParisTech', 'ParisTech', 'IRFM', 'Direction de Recherche Fondamentale', 'CEA Cadarache']
- HAL Identifier
- 926428
- Institution
- Commissariat à l'énergie atomique et aux énergies alternatives
- Laboratory
- Institut de Recherche sur la Fusion par confinement Magnétique
- Published in
- France
Table of Contents
- Introduction 12
- The challenge of nuclear fusion as an energy source 12
- The stakes 13
- The principle and the means 14
- The issues 25
- Introduction to the sawtooth phenomenon 30
- Outline of the thesis 32
- The sawtooth instability: fundamentals 34
- Magnetohydrodynamics 35
- Magnetic configuration in a tokamak 35
- The Grad-Shafranov Equation 38
- Kinetic description of a plasma 38
- Derivation of fluid equations 39
- Single fluid ideal MHD 43
- Braginskii equations 46
- The MHD model 48
- Bifluid modification of the MHD equations 50
- The internal kink mode 52
- The ideal MHD energy principle 52
- The ideal mode structure and growth rate 57
- Resistive modification of the growth rate 60
- Bifluid effects on the internal kink mode 64
- Stabilization by the toroidal curvature 67
- Stabilization by trapped fast particles and sawtooth triggering 67
- Sawtooth control with ICRH 70
- Magnetic reconnection 74
- Formal reconnection criterion 74
- Application to special cases of Ohm's law 75
- Biskamp's criterion 75
- Sweet-Parker scaling of reconnection 76
- Summary: Basic features of the sawtooth cycle 79
- Numerical methods 80
- The CHEASE code 80
- The Grad-Shafranov equation 80
- Resolution of the Grad-Shafranov equation 81
- Scaling of the equilibrium 81
- Shafranov shift 82
- The XTOR-2F code 83
- The Newton-Krylov solver 83
- Poincaré plots 89
- Simulation of sawteeth: influence of p, , and 91
- A 2D advection-diffusion code 95
- Summary 95
- Non-linear evolution of the magnetic island 96
- The Kadomtsev model 96
- The model's hypotheses 96
- Magnetic flux reconnection and profile relaxation 97
- Resistive evolution of the island 103
- Discussion 105
- Wesson's model 105
- Refined Kadomtsev-like evolution 106
- Waelbroeck's model 106
- Comparison with XTOR-2F 107
- The bifluid case: asymmetric island with 1 X-point 110
- Wang's model 111
- Comparison with XTOR-2F 112
- Summary 118
- Experimental observations of Sawteeth on the Tore Supra and JET tokamaks 120
- Diagnostics 121
- Fast-sweeping reflectometry for density measurements 121
- ECE radiometry for temperature measurements 126
- Soft X-Ray diagnostic 127
- Phenomenology 129
- Period and shape 129
- Precursor/Postcursor behaviour 130
- Crash time 134
- Compound sawteeth and partial crash 137
- Monster sawteeth, NTMs and mode locking 140
- Incomplete reconnection 143
- Possible explanations for incomplete reconnection 149
- Interaction between sawteeth and impurities in JET 152
- Two specific structures observed on Tore Supra 156
- Summary 158
- Numerical and physical analysis of Tore Supra and JET density measurements 160
- The Mexican hat 160
- Detail of experimental observations 160
- Conditions for Te and ne to be flux functions 165
- Flattening by the postcursor mode 167
- The crescent-shaped structure 172
- Summary 184
- Impurity transport by the sawtooth crash 186
- Introduction 186
- Impurity modelling with XTOR-2F 187
- Results 193
- Case 1 (Peaked Impurity) 193
- Case 2 (W-like) 196
- Case 3 (He-like) 197
- Comparison with Kadomtsev model 200
- Discussion 204
- Summary 205
- Conclusion 208
- Vector operators in covariant formulation 212
- The frozen-in-law 216
- Simplification of the expression for W 218
- Derivation of the bifluid layer equations 220
- The Ware pinch 224
- Waelbroeck's current sheet 228
- The equilibrium electric field in the bifluid model 232
- Diamagnetic asymmetry of an impurity 236
- Bibliography 238
