Instability and Transport driven by ITG mode

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Presentation transcript:

Instability and Transport driven by ITG mode 2013-05-23 Ma Jun

Outlines Low frequency drifts Eigenvalue Problem for toroidal drift waves Particle and Heat Transport Other modes and effects

The low frequency drifts We can now write the low frequency drifts as: Where: Here vE vp and vg are both particle and fluid drifts while v* and vл are pure fluid drifts.

The low frequency drifts For further analysis we first look at relations below: 1) 2) 3) 4) 5) “gyro cancellation”

The low frequency drifts Density response: Temperature response: These will give the local response

Eigenvalue Problem for Toroidal Drift Waves The nonlocal response of ion density including parallel ion motion: Boltzman electrons will be used in this analysis

Eigenvalue Problem for Toroidal Drift Waves Using ballooning formalism: , So we obtain: ,

Eigenvalue Problem for Toroidal Drift Waves The general eigenvalue equation for electrostatic ITG modes: , , , , , , , ,

Eigenvalue Problem for Toroidal Drift Waves Analytical solution: Strong ballooning limit: The eigenfunction has solutions of the Gaussian form: Inspired by the strong ballooning limit, introduce an asymptotic eigen function as above, by matching boundary condition we get And dispersion relation

Eigenvalue Problem for Toroidal Drift Waves Comparing with numerical solution from ”Shooting code”:

Eigenvalue Problem for Toroidal Drift Waves Comparing with numerical solution from ”Shooting code”:

Particle and Heat Transport Quasilinear diffusion: For eletron density flux: Assuming Boltzman electrons but with a small imaginary correction: Then particle flux: Diffusivity by Fick’s law: The diffusion is due to the imaginary part of the deviation from the Boltzman distribution. Here for Boltzman electrons So ITG will not contribute to particle transport!

Particle and Heat Transport Saturation level by balancing linear growth with nonlinearity: Temperature response Heat diffusivity

Other modes and effects Trapped electron mode: Trapped electrons act like ions without parallel motion(bounce averaged) Electromagnetic effects(low beta limit) Free electron dynamics including kink term Resistive edge modes