1. Instability and Transport driven by ITG mode
Ma Jun

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

3. 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.

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

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

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

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

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

9. 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

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

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

12. 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!

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

14. 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