Confinement & Transport

Plan Classical theory of confinement and transport. o 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? 2

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

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

5 ITER Plasma Scenario - ELMy H-mode 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 From D. Campbell-ITER

ELM= Edge localized modes 6

Same view of MAST but without ELM 7

H mode (1) Excerpt from Wesson -Tokamaks 8

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Again from Wesson 10

Spectre h = 13.6 eV = Energie d’ionisation Extrait de Spectroscopy; Edité par B.P. Straughna et S. Walker; Science Paperbacks 11

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Fluctuation 13

Scaling law for energy confinement time 14

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

16 ITER Baseline Scenario - ELMy H-mode  th  I p R 2 P -2/3 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 JET From D. Campbell-ITER

Scaling laws for energy confinement time 17

L-H transition: power 18

Internal barrier From D. Campbell-ITER 19

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

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? 21