Confinement & Transport

29-11-2010

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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?

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Bibliography

• F. Chen: Introduction to plasma physics, pages 165 to 181

• Freidberg: Plasma physics and fusion energy Chapter 14

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Energy confinement in magnetically confined plasma

• L and H modes in tokamak• H modes exist also in stellarator

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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

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Same view of MAST but without ELM

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H mode (1)

• Excerpt from Wesson -Tokamaks

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Again from Wesson

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Spectre

h= 13.6 eV = Energie d’ionisation

Extrait de Spectroscopy;

Edité par B.P. Straughna et S. Walker; Science Paperbacks

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Fluctuation

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Scaling law for energy confinement time

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Degradation of confinement with density

Nuclear Fusion, Vol 47, Number 6 June 2007

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ITER Baseline Scenario - ELMy H-mode

th IpR2P-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

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L-H transition: power

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Internal barrierFrom D. Campbell-ITER

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•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 OperationSteady-State OperationFrom 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