Short wavelength ion temperature gradient instability in toroidal plasmas

Abstract

Series of ion temperature gradient (ITG or ηi) driven modes in the short wavelength region, ∣k⊥ρi∣>1, are investigated with a gyrokinetic integral equation code in toroidal plasmas. These instabilities exist even if electrons are assumed adiabatic. However, nonadiabatic electron response can influence these short wavelength ITG (SWITG) modes, especially the fundamental l=0 mode. At typical parameters, excitation of the l=0 mode requires that both ηi and ηe exceed thresholds, while the l=1 and l=2 modes with higher harmonic eigenfunctions persist unstable even at ηe=0. Dependence of the SWITG modes on other parameters is also investigated. The l=1 mode with an odd potential eigenfunction grows faster than the l=0 mode and may be dominant in low ηe, high β, weak positive magnetic shear, and/or weak toroidicity regions.

Gyrokinetic Simulations of Short-Wavelength ITG Instability in the Presence of a Static Magnetic Island

“…Follow up investigation by Gao et al confirmed that the sw-ITG mode exists in sheared slab geometry [2], as well as in toroidal geometry [3]. They found that the linear growth rate of the sw-ITG mode is comparable to the usual long-wavelength standard ITG (std-ITG) mode.…”

Short wavelength ion temperature gradient turbulence

“…However, if the scale length of inhomogeneity is such that x Ãi , the ion diamagnetic drift frequency, becomes larger than the mode frequency x, there can be an instability related to the pressure inhomogeneity of the ions even in this shorter wavelength limit. [12][13][14][15][16] Initially, the mode was thought to be of hybrid type, 13,14 requiring both g i and g e (ratio of the density to temperature scale length of the ions and electrons, respectively) to be above a threshold. Later a parametric study by Gao et al 15 demonstrated that the electron non-adiabaticity is not an essential ingredient for the mode to develop.…”

“…q s > 1, where k ? and q s are the perpendicular wave number and ion Larmor radius evaluated at the sound speed, respectively, has been identified [12][13][14][15][16] linearly. This mode is found to be driven by the temperature gradient of ions in the presence of the Landau resonance/ inverse resonance in a slab geometry and by the toroidal drift resonance in a toroidal geometry, in combination with the non-monotonic behavior of the mode frequency with respect to the perpendicular wave number.…”

“…19 It is to be noted that the typical double hump behavior of growth rate (first hump corresponding to the standard ITG mode and second hump corresponding to the SWITG mode) was pointed out a long way back by Pu et al 20 while studying the ion mixing mode. Thus, it is inherently an ion mode and exists even if the electrons are adiabatic; 15 toroidicity has a strong stabilizing effect on the mode; magnetic shear has a destabilizing effect and the growth rate is approximately proportional to ffiffiffiffiffi jŝj p , 13 whereŝ stands for magnetic shear; similar to the standard ITG, it is also stabilized by a modest a, the ballooning parameter; non-adiabatic circulating electron dynamics provide destabilization; E Â B flow shear has a strong stabilizing effect on the mode. 18 With adiabatic electrons, in the limit…”

Comment on “The universal instability in general geometry” [Phys. Plasmas 22, 090706 (2015)]

“…This analysis was further confirmed and extended within the nonlocal integral equation solutions in sheared slab 5 and tokamak geometry. 6,7 These works presented detailed analysis of the eigen-mode structure of the short wavelength instabilities in the k ? q i !…”