Tokamak Physics Jan Mlyn 6 Neoclassical particle and

Tokamak Physics Jan Mlynář 6. Neoclassical particle and heat transport Random walk model, diffusion coefficient, particle confinement time, heat transport, high and low collisionality regimes, thermal diffusion, relaxation times Fyzika tokamaků 1: Úvod, opakování

Random walk model average step between collisions average time between collisions (1 dim case) [m 2/s] Fick’s Ist law + transport eq. Tokamak Physics Fick’s IInd law 6: Neoclassical particle and heat transport

Particle confinement time Fick’s IInd law Cylindrical geometry: Bessel functions J 0 , J 1 , J 2 Coulomb collisions: This estimate is wrong by 5 orders of magnitude !! Tokamak Physics 6: Neoclassical particle and heat transport

Particle confinement time Tokamak Physics 6: Neoclassical particle and heat transport

Heat transport convective loss conductive loss work done by pressure viscous heating heat generation conductive loss: heat flux no convection, no heat sources: à c is thermal diffusion coefficient [ m 2 s-1 ] cylindrical geometry Tokamak Physics 6: Neoclassical particle and heat transport

Ion and electron temperatures thermal equilibrium: the slowest relaxation process Typical tokamaks: Tokamak Physics wrong by 3 orders of magnitude, in fact 6: Neoclassical particle and heat transport

Neoclassical transport mean free path hydrodynamic length (~ banana, field line) Larmor radius ~ correlation length collisional regime collisionless regime also notice: O. K. drift approximation classical diffusion coefficient: Tokamak Physics 6: Neoclassical particle and heat transport

High collisionality regime Particles do not close full poloidal rotation i. e. cold and dense plasmas (e. g. the plasma egde) (freq. of poloidal rotation) Pfirsch –Schlüter diffusion: Ohm’s law: Due to the Pfirsch-Schlüter current “correction” factor of ~ 10 Tokamak Physics O. K. 6: Neoclassical particle and heat transport

Low collisionality regime Galeev-Sagdeev (banana) transport Banana orbits: Banana width: Banana period: Effective collision frequency: physics behind the effective collision frequency Condition: i. e. most particles close full banana orbit before collision Galeev – Sagdeev diffusion: ratio of trapped particles Tokamak Physics increase by factor ~5 compared to high collisionality 6: Neoclassical particle and heat transport

Neoclassical diffusion coefficient summary: high collisionality low collisionality In between np and nb : plateau In the plateau, diffusion coeff. D is independent of nei Tokamak Physics 6: Neoclassical particle and heat transport

Neoclassical thermal diffusion high collisionality : Pfirsch-Schlüter low collisionality : Galeev-Sagdeev main loss channel: thermonuclear core plasma: i. e. it is in the low collisionality regime Tokamak Physics 6: Neoclassical particle and heat transport

Thermal diffusion in experiments however in special regions (transport barriers) i. e. it indeed sets theoretical limit for tokamak confinement !! but in theory it should be and lower!! are anomalous. Notice: Functional dependencies are wrong, too. e. g. Instead of plasmas follow rather Tokamak Physics the externally heated (see also the next talk) 6: Neoclassical particle and heat transport

Summary: Relaxation times (~ Maxwellisation, thermalisation) Te , Ti equilibration notice that : also notice : Tokamak Physics ( OK sound reasonable ) 6: Neoclassical particle and heat transport

Neoclassical thermal diffusion Tokamak Physics 6: Neoclassical particle and heat transport