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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