CEA-EDF-INRIA school "Numerical Models for Controlled Fusion", Nice (8-12 Sept. 2008)Y. Sarazin 1 Turbulence & Transport in magnetised plasmas Y. Sarazin.

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CEA-EDF-INRIA school "Numerical Models for Controlled Fusion", Nice (8-12 Sept. 2008)Y. Sarazin 3 Confinement ensured by large B field Confinement ensured by large B field (~10 5 B Earth ) Helicoidal field lines generate toroidal flux surfaces MHD equilibrium: Laplace force (j p B) Expansion ( P) n,T are flux functions Particle trajectories ~ magnetic field lines ( Transp. Transp.) Polodal angle Toroidal angle v // vv B i = m i v /eB 10 3 m current j p r Non-circular poloidal cross-section Axi-symmetric X-point Z R Safety factor q r

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CEA-EDF-INRIA school "Numerical Models for Controlled Fusion", Nice (8-12 Sept. 2008)Y. Sarazin 1 Turbulence & Transport in magnetised plasmas Y. Sarazin Institut de Recherche sur la Fusion par confinement Magntique CEA Cadarache, France Association Euratom-Cea Acknowledgements:P. Beyer, G. Dif-Pradalier, X. Garbet, Ph. Ghendrih, V. Grandgirard CEA-EDF-INRIA school "Numerical Models for Controlled Fusion", Nice (8-12 Sept. 2008)Y. Sarazin 2 Confinement governs tokamak performances Economic viability of Fusion governed by E Self-heating (ignition) Upper bound for n i : nT B 2 2 0 E ~ few sec. Amplification Factor Q CEA-EDF-INRIA school "Numerical Models for Controlled Fusion", Nice (8-12 Sept. 2008)Y. Sarazin 3 Confinement ensured by large B field Confinement ensured by large B field (~10 5 B Earth ) Helicoidal field lines generate toroidal flux surfaces MHD equilibrium: Laplace force (j p B) Expansion ( P) n,T are flux functions Particle trajectories ~ magnetic field lines ( Transp. Transp.) Polodal angle Toroidal angle v // vv B i = m i v /eB 10 3 m current j p r Non-circular poloidal cross-section Axi-symmetric X-point Z R Safety factor q r CEA-EDF-INRIA school "Numerical Models for Controlled Fusion", Nice (8-12 Sept. 2008)Y. Sarazin 4 Transport is turbulent Collisional transport negligible: Fusion plasmas weakly collisional Heat losses are mainly convective: Turbulent diffusivity turb governs confinement properties ~ s 1 ~10 5 s 1 CEA-EDF-INRIA school "Numerical Models for Controlled Fusion", Nice (8-12 Sept. 2008)Y. Sarazin 5 Outline Basics of turbulent transport Drift- Wave instabilities in tokamaks Wave-particle resonance k // ~0 Transport models: fluid vs. Gyrokinetic and numerical tools Dimensionless scaling laws: similarity principle, experiments vs theory Large scale structures: Zonal Flows & Avalanche-like events Improved confinement, physics of Transport Barriers CEA-EDF-INRIA school "Numerical Models for Controlled Fusion", Nice (8-12 Sept. 2008)Y. Sarazin 6 Outline Basics of turbulent transport Drift- Wave instabilities in tokamaks Wave-particle resonance k // ~0 Transport models: fluid vs. Gyrokinetic and numerical tools Dimensionless scaling laws: similarity principle, experiments vs theory Large scale structures: Zonal Flows & Avalanche-like events Improved confinement, physics of Transport Barriers CEA-EDF-INRIA school "Numerical Models for Controlled Fusion", Nice (8-12 Sept. 2008)Y. Sarazin 7 Electrostatic turbulence E B drift:. Turbulent field Random walk Diffusion ES Correlation time of Turbulent convection cells Challenge: correl ? Contour lines of iso-potential Test particle trajectory CEA-EDF-INRIA school "Numerical Models for Controlled Fusion", Nice (8-12 Sept. 2008)Y. Sarazin 8 B r fluctuations Radial component of v // : v r ~ ( B/B) v // Random walk Diffusion:. Magnetic turbulence BB B eq v r ( B r /B) v // v // Magnetic field line Fast particles more sensitive to magnetic turbulence CEA-EDF-INRIA school "Numerical Models for Controlled Fusion", Nice (8-12 Sept. 2008)Y. Sarazin 9 Electrostatic vs Magnetic Transport m

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