1. Excitation of ion temperature gradient and trapped electron modes in HL-2A tokamak The 3 th 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. Song 3 1 School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, China 2 Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 310027, China 3 Southwestern Institute of Physics, Chengdu 610041, China * E-mail: zxwang@dlut.edu.cn zxwang@dlut.edu.cn 1

2. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015  Background  Physics Model and Equations  Numerical Results  Conclusion Outline 2

3. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 Background The 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. 3 W. L. Zhong et al PRL (2013)F Jenko et al PPCF 47 (2005) F. Merz and F. Jenko NF 50 (2010)

4. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 Background 4 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.

5. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015  Background  Physics Model and Equations  Numerical Results  Conclusion Outline 5

6. 6 Model and Equations The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 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 Gyrokinetic integral equation derived for the study of low frequency electrostatic drift (ITG /TEM)……

7. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 Model and Equations  Quasi-neutrality condition --- fraction of trapped electrons --- trapped electron density --- passing electron density  Perturbed densities transit frequency magnetic drift frequency pressure driven diamagnetic drift frequency  The non-adiabatic response is determined by gyro-kinetic equation in the ballooning space FLR effect 7

8. 8 electron term --- the pinch angle variable --- trapped electron bounce frequency --- the bounce-averaged TEs magnetic drift (precession) frequency Guo, S. C., & Romanelli, F. (1993). Dong, J. Q., Mahajan, S. M., & Horton, W. (1997). Model and Equations The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015  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. with

9. 9 Model and Equations The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015  The perturbed density of ions can be represented as  The integral eigenmode equations with trapped electron response can be written as with

10. 10 Model and Equations The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 are normalized to The mode real frequency and growth rate are normalized to

11. 11 Model and Equations The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 Numerical Tool: HD7 code _ a solver of the integral eigenmode equation 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

12. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015  Background  Physics Model and Equations  Numerical Results  Conclusion Outline 12

13. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 Equilibrium profile HL-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. 13

14. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 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. Ohimc phase ECRH phase 14

15. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 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 phaseECRH phase ITG and TEM instabilities clearly coexist  in ITG dominant cases in the Ohimc phase.  in TEM dominant cases in the ECRH phase. 15

16. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 Numerical Results effect  Increasing stabilizes (destabilizes) the pure TEM (ITG) mode.  The ITG mode can be stabilized by increasing with TE effect. Interchange type toroidal ITG instability 16

17. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 Numerical Results effect  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. 17

18. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 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/L Ti (large R/L Te ).  The dominated ITG instabilities induce strong ion heat transport for low R/L Te (large R/L Ti ). 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). FOR 18

19. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015  Background  Physics Model and Equations  Numerical Results  Conclusion Outline 19

20. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 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 20

21. The 3 th Annual Workshop on Fusion Simulation and Theory, Hefei, March 23-25, 2015 Thank you for your attention! 21