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