1. Tokamaks 读书报告 4.17-4.19 叶 磊 2013.10.24

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

3. 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

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

5. 4.18 Turbulence-induced transport

6. 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

7. Why random walk?

8. 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.

9. Drunkun sailor ---- 1D random walk and diffusion After N steps t= Nτ, what is the probability distribution of the man? D: diffusion coeffcient

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

11. Quasi-linear theory

12. 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

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

14. Radial electric field and transport Velocity shear may increase the effective

15. 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

16. Thank you!