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Tokamaks 读书报告 4.17-4.19

Tokamaks 读书报告 4.17-4.19. 叶 磊 2013.10.24. 4.17 Fluctuations. anomalous transport ： turbulent diffusion caused by fluctuations . 1. electrostatic ： E X B drift velocity + Particle flux : heat flux: 2. Electromagnetic : +. Observations. Boltzmann relation. K spectrum:.

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Tokamaks 读书报告 4.17-4.19

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  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. Observations Boltzmann relation K spectrum: Mixing-length estimate: Characteristic frequency: 100kHZ

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

  5. 4.18 Turbulence-induced transport

  6. two kinds of theoretical approach • 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]

  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 Xis: • Variancemeasures 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. mixing-length estimate Boltzmann relation quasi linear diffusion coeffcient 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 Shaing, Hazeltine 1997 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

  16. Thank you!

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