Temperature ratio dependence of ion temperature gradient and trapped electron mode instability thresholds

2008 ◽  
Vol 15 (4) ◽  
pp. 042310 ◽  
Author(s):  
Alessandro Casati ◽  
C. Bourdelle ◽  
X. Garbet ◽  
F. Imbeaux
Keyword(s):  
Temperature Gradient ◽  
Ion Temperature ◽  
Temperature Ratio ◽  
Mode Instability ◽  
Ion Temperature Gradient ◽  
Ratio Dependence ◽  
Electron Mode ◽  
Trapped Electron

scholarly journals Transport through dissipative trapped electron mode and toroidal ion temperature gradient mode in TEXTOR

1988 ◽  
Vol 28 (6) ◽  
pp. 1053-1073 ◽  
Author(s):  
A. Rogister ◽  
G. Hasselberg ◽  
F.G. Waelbroeck ◽  
J. Weiland
Keyword(s):  
Temperature Gradient ◽  
Ion Temperature ◽  
Ion Temperature Gradient ◽  
Electron Mode ◽  
Trapped Electron ◽  
Gradient Mode

scholarly journals Threshold for the destabilisation of the ion-temperature-gradient mode in magnetically confined toroidal plasmas

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
A. Zocco ◽  
P. Xanthopoulos ◽  
H. Doerk ◽  
J. W. Connor ◽  
P. Helander
Keyword(s):  
Temperature Gradient ◽  
Temperature Dependence ◽  
Local Equilibrium ◽  
Acta Math ◽  
Theoretical Interpretation ◽  
Ion Temperature ◽  
Temperature Ratio ◽  
Ion Temperature Gradient ◽  
First Case ◽  
Unstable Solutions

The threshold for the resonant destabilisation of ion-temperature-gradient (ITG) driven instabilities that render the modes ubiquitous in both tokamaks and stellarators is investigated. We discover remarkably similar results for both confinement concepts if care is taken in the analysis of the effect of the global shear ${\hat{s}}$. We revisit, analytically and by means of gyrokinetic simulations, accepted tokamak results and discover inadequacies of some aspects of their theoretical interpretation. In particular, for standard tokamak configurations, we find that global shear effects on the critical gradient cannot be attributed to the wave–particle resonance destabilising mechanism of Hahm & Tang (Phys. Plasmas, vol. 1, 1989, pp. 1185–1192), but are consistent with a stabilising contribution predicted by Biglari et al. (Phys. Plasmas, vol. 1, 1989, pp. 109–118). Extensive analytical and numerical investigations show that virtually no previous tokamak theoretical predictions capture the temperature dependence of the mode frequency at marginality, thus leading to incorrect instability thresholds. In the asymptotic limit ${\hat{s}}\unicode[STIX]{x1D704}\ll 1$, where $\unicode[STIX]{x1D704}$ is the rotational transform, and such a threshold should be solely determined by the resonant toroidal branch of the ITG mode, we discover a family of unstable solutions below the previously known threshold of instability. This is true for a tokamak case described by a local ${\hat{s}}-\unicode[STIX]{x1D6FC}$ local equilibrium, and for the stellarator Wendelstein 7-X, where these unstable solutions are present even for configurations with a small trapped-particle population. We conjecture they are of the Floquet type and derive their properties from the Fourier analysis of toroidal drift modes of Connor & Taylor (Phys. Fluids, vol. 30, 1987, pp. 3180–3185), and to Hill’s theory of the motion of the lunar perigee (Acta Math., vol. 8, 1886, pp. 1–36). The temperature dependence of the newly determined threshold is given for both confinement concepts. In the first case, the new temperature-gradient threshold is found to be rather insensitive to the temperature ratio $T_{i}/T_{e}$, at least for $T_{i}/T_{e}\lesssim 1$, and to be a growing function of the density gradient scale for $T_{i}/T_{e}\gtrsim 1$. For Wendelstein 7-X, the new critical temperature gradient is a growing function of the temperature ratio. The importance of these findings for the assessment of turbulence in stellarators and low-shear tokamak configurations is discussed.

Properties of ion temperature gradient and trapped electron modes in tokamak plasmas with inverted density profiles

2017 ◽  
Vol 24 (12) ◽  
pp. 122501 ◽  
Author(s):  
Huarong Du ◽  
Hogun Jhang ◽  
T. S. Hahm ◽  
J. Q. Dong ◽  
Z. X. Wang
Keyword(s):  
Temperature Gradient ◽  
Tokamak Plasmas ◽  
Ion Temperature ◽  
Ion Temperature Gradient ◽  
Density Profiles ◽  
Trapped Electron

Collisionless trapped electron and ion temperature gradient modes in an advanced tokamak equilibrium

2009 ◽  
Vol 16 (2) ◽  
pp. 022503 ◽  
Author(s):  
M. Ansar Mahmood ◽  
T. Rafiq ◽  
M. Persson ◽  
J. Weiland
Keyword(s):  
Temperature Gradient ◽  
Ion Temperature ◽  
Ion Temperature Gradient ◽  
Trapped Electron
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