excitation of ion temperature gradient and trapped electron modes in hl-2a tokamak the 3 th annual...

1

Excitation of ion temperature gradient and trapped electron modes in HL-2A

tokamak

The 3th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015

Huarong Du,1 Zheng-Xiong Wang,1,*

J. Q. Dong,2,3 and S. D. Song3

1School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China2Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 310027, China3Southwestern Institute of Physics, Chengdu 610041, China* E-mail: [email protected]

mailto:[email protected]

2The 3th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015

Background Physics Model and Equations

Numerical Results

Conclusion

Outline


BackgroundThe dominant source of anomalous transport in fusion plasmas on ion scales is turbulence driven by trapped electron mode (TEM) and ion temperature gradient (ITG) mode.

The application of several auxiliary heating, such as ECRH, NBI, ICRH, and LHCD, leads to the temperature and density perturbations that provide a source of free energy to drive both the TEM and ITG mode instabilities simultaneously.

W. L. Zhong et al PRL (2013)F Jenko et al PPCF 47 (2005)F. Merz and F. Jenko NF 50 (2010)


Background

The theory of particle transport driven by ITG and TEM instabilities is applied to study the density profile under experimental conditions with central electron heating.

Investigations of the coexistence of the two modes and the phenomena of transitions between the TEM and ITG dominant regimes have recently been reported for tokamak experiments, such as DIII-D, ASDEX upgrade, Alcator C-Mod, and Tore Supra.

We carry out the gyrokinetic simulation of the dominant TEM and ITG modes for Ohmic heating and ECRH of the HL-2A tokamak.



Numerical Results

Conclusion

Outline

6

Model and Equations


• model equilibrium with circular flux surface

• Ballooning representation

• gyro-kinetic description (Main ions, trapped electron)

• Transit motion, curvature and magnetic gradient drifts, and finite ion Larmor radius

• Ion magnetic trapping are neglected

• Passing electrons are assumed to be adiabatic

s

Gyrokinetic integral equation derived for the study of low frequency electrostatic drift (ITG /TEM)……


Model and EquationsQuasi-neutrality condition (1 )i ne te pe te ten n f n f n

--- fraction of trapped electrons--- trapped electron density

--- passing electron densityPerturbed densities 3

s sn f d v ,s e i

0 ( )s s Ms s s sf q F T h J 3 22 2 2expMs ts tsF v v v

0* 0

ˆs st s Ds s sT s Ms

s

q ni h h J F

T

2

2* ˆ2 cos sin

2Ds n s

vs v

2

* * 2

31

2sT s sts

v

v

*s s s nsck T q BL

2ts s sv T m

2 2 22 s ts sb k v

transit frequency magnetic drift frequency pressure driven diamagnetic drift frequency

The non-adiabatic response is determined by gyro-kinetic equation in the ballooning space

sh

t v Rq

1/22s sb v

FLR effect

8

electron term

2 2

,sin 2

r

r

dg

3* * 21e

e e t 0sin 2 1 1r B E

be

---the pinch angle variable

---trapped electron bounce frequency

---the bounce-averaged TEs magnetic drift (precession) frequency

edbe

Guo, S. C., & Romanelli, F. (1993).

Dong, J. Q., Mahajan, S. M., & Horton, W. (1997).

2

* *

2ˆ ˆ, 1 4 1e

d e n e n

F FtG s t s

K K

Model and Equations


The passing electrons are assumed adiabatic with The non-adiabatic response of the TEs can be obtained by

expanding Eq. (2) in , and the perturbed density of the TEs can be represented as

pe en en T

.

210

02 2 , , 2 ,

4e

te teje

en dn g j d g j

T F

*

0

2 etoe

te ee d

endt te

T

with

*,be e de effv

9

Model and Equations


30 00 ,

2i i

i i iii i i

en en enn k d vJ h

dkK k kk

T T Tk

The perturbed density of ions can be represented as

The integral eigenmode equations with trapped electron response can be written as

ˆ ˆ1 ,2

i Te i

dkk n K k k k

with 0

*, ,2 ei

i ieK k k i d H k k

210 *

0 0

2

4

2 , , 2

ete

Te ee d

j

en dn dt te

T F

g j d g j

2

0

2 2 21

* 0

exp 4, ,

1

231 1 .

2 4 1 2 1 1

i

ii i eiei i

e i i

k kH k k k k

a a

k k L k k k k IL

a a a a I

with

10

Model and Equations


k k k are normalized to1 2s i ti e iv eB c T m

The mode real frequency and growth rate are normalized to *e e neck T eBL

11

Model and Equations


Numerical Tool: HD7 code _ a solver of the integral eigenmode equation

ˆ, , , , , , / , /i e s i n neq s k r R L R

• Main ions, trapped electron, impurity ions

• (ITG /TEM, ETG, IM, KSAW)

• Electrostatic, Electromagnetic perturbation

• Tokamak, reversed Field Pinch (RFP)

• model equilibrium with circular flux surfaces

/ Miller’s local equilibrium model with non-circular geometry

• gyro-kinetic description

• Ballooning representation • Input parameters:• Output: real frequency, growth rate, particle flux

s



Numerical Results

Conclusion

Outline


Equilibrium profileHL-2A shot # 22805

The equilibrium profiles of temperature and density for TEM and ITG driven instability.

The electron and ion temperature increase, while the temperature gradient decrease.

The density reduction called ‘particle pump-out’ is well known as a typical behaviour when the ECRH is turned on, which is in consistence with the theoretically predicted outward particle thermal diffusion in case of dominant TEM instabilities.

19 3

1.65

0.4

175

1.33

(1.5 3.5) 10

180

1.6

p

T

e

ohimc

ECRH

R m

r m

I KA

B T

n m

P KW

P MW


Numerical Results

Two independent unstable modes, which propagate in electron and ion diamagnetic drift directions, corresponding to TEM and ITG mode, respectively, are found to coexist in the region considered of HL-2A plasmas.

/e iT T

Ohimc phase

ECRH phase

/e iT T


Numerical Results

The instability changes from predominantly ITG to TEM with the application of ECRH. The dominant ITG-TEM transition also depends on .

In HL-2A ECRH discharge experiments , thus the TEM is the dominate instability in the ECRH phase.

Ohimc phase ECRH phase

/ 4e iT T

/e iT T

ITG and TEM instabilities clearly coexist in ITG dominant cases in the Ohimc phase.in TEM dominant cases in the ECRH phase.


Numerical Results effect/e iT T

Increasing stabilizes (destabilizes) the pure TEM (ITG) mode. The ITG mode can be stabilized by increasing with TE effect.

/e iT T/e iT T

Interchange type toroidal ITG instability

*e

Di Tii

T

T


Numerical Results effect/e iT T

Increasing destabilizes the dominant TEM mode. The TEM can be stabilized by increasing , when the drive of the ITG mode is small and/or the dynamics of the ITG mode is ignored.

/e iT T/e iT T


Numerical Results particle flux

Both the TEM and ITG modes lead to outward particle transport.The dominated TEM induces electron heat transport for low R/LTi (large R/LTe) . The dominated ITG instabilities induce strong ion heat transport for low R/LTe (large R/LTi) .

The quasilinear model is applied to study the particle transport driven by TEM and ITG mode, and the present model has been checked by reproducing the relevant simulation results done by F. Merz and F. Jenko (Nucl. Fusion 50, 2010)

r

iknv n

B

.

B B E E

E

/ /rv E B B

FOR



Numerical Results

Conclusion

Outline


With the gyrokinetic code HD7, the TEM and ITG instabilities in HL-2A tokamak are numerically investigated .

For pure Ohmic heating , the ITG mode is the dominate instability due to large ion temperature gradient.

For Ohmic heating +ECRH, the dominant mode changes from ion temperature gradient (ITG) mode to trapped electron mode (TEM). Increasing destabilizes the TEM, while stabilizes the ITG mode.

The dominated TEM instabilities induce large electron heat transport in the ECRH phase.

Conclusions

/e iT T


Thank you for your attention!

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excitation of ion temperature gradient and trapped electron modes in hl-2a tokamak the 3 th annual...

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