Short wavelength ion temperature gradient driven instability in toroidal plasmas Zhe Gao, a) H. Sanuki, b) K. Itoh b) and J. Q. Dong c) a) Department of Engineering Physics, Tsinghua University, Beijing , China b) National Institute for Fusion Science, Toki, Gifu , Japan c) Southwestern Institute of Physics, Chengdu , China Electronic mail: 1 st Plasma Theory and Simulation (PTS) Workshop Chengdu Sep

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

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)

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 DeBoo EPS conf C lear 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.

Background (III) Short wavelength ITG modes (, ) Local mode in a shearless slabAI Smolyakov et al, PRL 89, (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 geometryA. Hirose et al, PoP 9, 1659 (2002). “ electron transit effect driving ”, “ essentially a slab mode ”, “ shear is destabilizing ”

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

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

Local slab limit : influences of electron kinetics and k // L n

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

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

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

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

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

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

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

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

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.

Critical temperature gradient vs. Ln/R R/L Ti : saturation in the large enough ε n region R/L Te : cannot cross the ε n barrier

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

Critical temperature gradient Vs. k θ “ sub-steady-state ” region for ITG critical electron temperature gradient varies with wavelength

Coupling between l=0 and l=2 modes

Critical temperature gradient for the l=1 mode

η i - η e diagram for l=0 and l=1 modes electron kinetics strongly influences the l=0 mode but only slightly influences the l=1 mode in the region where η e is relative smaller, the l=1 mode is dominant

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.

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