Tokamaks 读书报告 叶 磊

4.17 Fluctuations anomalous transport ： turbulent diffusion caused by fluctuations. 1. electrostatic ： E X B drift velocity + Particle flux : heat flux: 2. Electromagnetic : +

edge Langmuir probes Mirnov coils interior MS,FIR,HIBP,BES, MR HIBPCorss polarization scattering Observations K spectrum: Mixing-length estimate: Characteristic frequency:100kHZ Boltzmann relation

Correlations with transport increase with r electrostatic fluctuations provide the dominant transport mechanism.

4.18 Turbulence-induced transport

given turbulence spectra to calculate transport. [random walk model, quasi-linear theory] attempt to calculate nonlinear saturated state. [scale invariance, strong turbulence theory, weak turbulence theory, nonlinear scattering] two kinds of theoretical approach

Why random walk?

Expected value & Variance the expected value E(X) of a random variable X is a weighted average of all possible values. e.g. Let random variable X represent the outcome of a roll. The expectation of X is: Variance measures how far a random variable deviate from its excpected value. e.g.

Drunkun sailor D random walk and diffusion After N steps t= Nτ, what is the probability distribution of the man? D: diffusion coeffcient

turbulent diffusion coeffcient turbulence spectra: correlation time is determined by : and in a strong turbulence by

Quasi-linear theory

Saturation levels and transport fluxes scale invariance If the turbulence is on a microscopic scale, and the fluctuations have a scale then mixing-length estimate

Boltzmann relation quasi linear diffusion coeffcient mixing-length estimate The linear growth balanced by a stabilization from turbulent diffusion

Radial electric field and transport Velocity shear may increase the effective

Orbit squeezing effect It is shown that ion thermal conductivity is reduced by a factor of reflecting an increase of the fraction of trapped particles by a factor of, and the reduction of the orbit size in cby a factor of Shaing, Hazeltine 1997

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