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Confinement & Transport

Confinement & Transport. 29-11-2010. Plan. Classical theory of confinement and transport. Diffusion equation Particle diffusion in a magnetic field Diffusion as a random walk Collisions in a fully magnetized plasmas Heat diffusion What happens in a real tokamak?. Bibliography.

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Confinement & Transport

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  1. Confinement & Transport 29-11-2010

  2. Plan • Classical theory of confinement and transport. • Diffusion equation • Particle diffusion in a magnetic field • Diffusion as a random walk • Collisions in a fully magnetized plasmas • Heat diffusion • What happens in a real tokamak?

  3. Bibliography • F. Chen: Introduction to plasma physics, pages 165 to 181 • Freidberg: Plasma physics and fusion energy Chapter 14

  4. Energy confinement in magnetically confined plasma • L and H modes in tokamak • H modes exist also in stellarator

  5. ITER Plasma Scenario - ELMy H-mode From D. Campbell-ITER • Conventionally, plasma confinement regimes denoted L-mode and H-mode • The difference between these modes is caused by the formation of an edge pedestal in which transport is significantly reduced - edge transport barrier • edge localized modes maintain plasma in quasi-stationary state JET

  6. ELM= Edge localized modes

  7. Same view of MAST but without ELM

  8. H mode (1) • Excerpt from Wesson -Tokamaks

  9. Again from Wesson

  10. Spectre hn= 13.6 eV = Energie d’ionisation Extrait de Spectroscopy; Edité par B.P. Straughna et S. Walker; Science Paperbacks

  11. Fluctuation

  12. Scaling law for energy confinement time

  13. Degradation of confinement with density Nuclear Fusion, Vol 47, Number 6 June 2007

  14. ITER Baseline Scenario - ELMy H-mode From D. Campbell-ITER • The ELMy H-mode is a robust mode of tokamak operation - ITER baseline scenario • H-mode confinement time is approximately double that in L-mode • multi-machine database provides scaling prediction for ITER energy confinement time th IpR2P-2/3 JET

  15. Scaling laws for energy confinement time

  16. L-H transition: power

  17. Internal barrier From D. Campbell-ITER

  18. Discovery of internal transport barriers “advanced scenarios” From D. Campbell -ITER Steady-State Operation plasma with reversed central shear +sufficient rotational shear internal transport barrier  enhanced confinement reduced current operation +large bootstrap current fraction active mhd control reduced external current drive +current well aligned for mhd stability and confinement enhancement Steady-state operation +High fusion power density • But development of an integrated plasma scenario satisfying all reactor-relevant requirements remains challenging

  19. Quiz to summarize a few important points • Is the diffusion equation symmetric with respect to time? According to you, what is the meaning of this non symmetry? • What is the dependency of the classical diffusion coefficient with respect to the magnetic field? • What are the two main confinement modes in a magnetically confined plasma? • How does one get the H mode?

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