Short wavelength ion temperature gradient driven instability in toroidal plasmas

1. Short wavelength ion temperature gradient driven instability in toroidal plasmas Zhe Gao,a) H. Sanuki,b) K. Itohb) and J. Q. Dongc) a) Department of Engineering Physics, Tsinghua University, Beijing 100084, China b) National Institute for Fusion Science, Toki, Gifu 509-5292, Japan c) Southwestern Institute of Physics, Chengdu 610041, China Electronic mail: gaozhe@mail.tsinghua.edu.cn 1st Plasma Theory and Simulation (PTS) Workshop Chengdu Sep.13-15 2004

2. Background Model Local slab limit Parameter dependences Critical temperature gradient Conclusions OUTLINE

3. Background (I) • microinstabilitiesmicro-turbulenceanomalous transport ion transport － reduced to NC level; electron transport － still anomalous / ETB • Experimental observations: Turbulent diagnostics  anomalous electron transport is possibly attributable to short wavelength modes Profile stiffness  a threshold in temperature gradient • Two kinds of well-known microinstabilities: ETG modes e.g. F. Jenko et al, PoP 8, 4096 (2000),J. Q. Dong et al, NF 43, 1 (2003) TE modes e.g.J. Weiland et al NF 29, 1810 (1989)

4. Background (II) • comparisons with experimental results e.g F Ryter et al, PPCF 43, A323 (2001) some on ETG: s/q dependence in Tore Supra some on TEM: modulated Te evolution in ASDEX-U • other remarkable experiment results Not all tokamaks observed “stiffness” in Te; e.g. JC DeBooEPS conf. 2002 Clear link between long and short wavelength fluctuation; e.g. GD Conway PRL 84,1463 (2002) Measured high k fluctuation in the ion diamagnetic direction; e.g. KL Wong PLA 236, 339 (1997) • electron transport might be controlled by multi-source instabilities simultaneously, or by different instability depending on different discharge condition.

5. Background (III) Short wavelength ITG modes ( , ) Local mode in a shearless slab AI Smolyakov et al, PRL 89, 125005 (2002). A new TG driven short wavelength mode or “ double-humped behavior” in Pu et al, PF 28,1722 (1985) ? Nonlocal mode in a toroidal geometry A. Hirose et al, PoP 9, 1659 (2002). “electron transit effect driving”, “ essentially a slab mode” , “shear is destabilizing”

6. Model • Gyro-kinetic equation ( ballooning representation in s-a equlibrium ) • Poisson’s Equ. & Ampere’s law Both ions and electrons are nonadiabatic: the transit effect, the finite Larmor radius effects and the curvature and magnetic gradient drift

7. Local slab limit: • The local short wavelength mode is attributable to the Landau damping stabilization/destabilization mechanism and the nonmonotonic behaviors of the real frequency with wavelength variation. • Some explanations in Smolyakov et al are not correct

8. Local slab limit : influences of electron kinetics and k//Ln

9. Toroidal modes : analytical discussion ion response and it integral (under the condition ) If electron is adiabatic Noted: , as Local slab limit: Landau mechanism Toroidal: magnetic drift resonance

10. Toroidal modes : wave spectrums • Parameters: , , , , , • The SWITG mode still exists even with adiabatic electrons assumption.

11. Toroidal modes: toroidicity • more easily stabilized by toroidicity than the conventional ITG mode • condition broken

12. Toroidal modes : eigenfunctions Broaden structures along the magnetic field line and have oscillatory tails when nonadiabatic electron response are considered

13. Toroidal modes : temperature gradients dependence Each of the three modes has a eta_i threshold and the threshold of the fundamental mode is lower that those of higher order modes. The fundamental SWITG mode is unstable when both eta_i and eta_e exceed thresholds. But the higher order modes persist unstable even eta_e decreases to zero

14. Toroidal modes: Te/Ti dependence The SWITG mode can be stabilized by hot ions (small Te/Ti) ITG driven modes

15. Toroidal modes : isotope effects Maximum growth rate • The normalized growth rate and frequency is insensitive to isotope mass 

16. Toroidal modes : magnetic shear • The stabilizing effect of shear is confirmed although the shear needed to stabilize the fundamental mode is rather strong • The grow rate of the fundamental mode at negative shear is almost same as that at positive shear, while obvious low growth rate exists at negative shear for higher order modes • The high order mode may grows faster than the fundamental mode in the weak shear regime

17. Toroidal modes : beta effect • The fundamental mode is easily stabilized by finite beta, mainly due to the coupling effect to shear Alfven waves (SAWs), not the ballooning parameter • The higher order modes are more hardly stabilized, which might be explained by the fact that the higher order modes have lower frequencies.

18. Critical temperature gradient vs. Ln/R R/LTi: saturation in the large enough εn region R/LTe : cannot cross the εn barrier

19. Critical temperature gradient Vs. Te/Ti R/LTi deceases as Te/Ti increase

20. Critical temperature gradient Vs. kθ • “sub-steady-state” region for ITG • critical electron temperature gradient varies with wavelength

21. Coupling between l=0 and l=2 modes

22. Critical temperature gradient for the l=1 mode

23. ηi- ηediagramfor l=0 and l=1 modes • electron kinetics strongly influences the l=0 mode butonly slightly influences the l=1 mode • in the region where ηe is relative smaller, the l=1 mode is dominant

24. Conclusions • The SWITG instability occurs due to the toroidal drift resonance mechanism in the short wavelength region and exist even if adiabatic electrons are assumed • Parameter dependences of the SWITG mode is similar as those of the conventional ITG mode • Nonadiabatic electron response can influence the fundamental SWITG mode. • The SWITG instability has a medium wavelength, so might be more difficult to be suppressed by the E*B flow shear than the ITG instability while could induce higher transport than the ETG mode. • The SWITG mode may be attributed to electron transport, however, it seems the ion kinetic is necessary and basic.

25. ACKNOWLEDGMENTS • Most of this work is performed during Z.G.’s visiting at the National Institute for Fusion Science, Japan.