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Confinement & Transport

This plan explores the classical theory of confinement and transport mechanisms in magnetically confined plasmas. Key topics include the diffusion equation, particle diffusion in magnetic fields, and heat diffusion. It highlights the differences between L-mode and H-mode confinement regimes, the impact of edge transport barriers, and the significance of internal transport barriers in achieving steady-state operation. Through a series of quizzes, it reinforces critical concepts related to diffusion, confinement modes, and the challenges in developing integrated plasma scenarios for nuclear fusion applications.

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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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