Collisionless electron-temperature-gradient-driven (ETG) turbulence in toroidal geometry is studied via nonlinear numerical simulations. To this aim, two massively parallel, fully gyrokinetic Vlasov codes are used, both including electromagnetic effects. Somewhat surprisingly, and unlike in the analogous case of ion-temperature-gradient-driven (ITG) turbulence, we find that the turbulent electron heat flux is significantly underpredicted by simple mixing length estimates in a certain parameter regime (ŝ∼1, low α). This observation is directly linked to the presence of radially highly elongated vortices (“streamers”) which lead to very effective cross-field transport. The simulations therefore indicate that ETG turbulence is likely to be relevant to magnetic confinement fusion experiments.

Electron-temperature-gradient-driven turbulence

The solitary structure solution of the radial electric field Er in the tokamak plasmas is obtained. It is shown to be stable under an external power supply, like a biased electrode at the edge. The radial gradient is governed by the ion viscosity and the nonlinearlity of the perpendicular conductivity. The radial structure of Er and reduction of turbulent transport, which belong to key issues of the high confinement mode (H-Mode) [F. Wagner et al., Phys. Rev. Lett. 49, 1408 (1982)], are self-consistently determined. A bifurcation from a radially-uniform one to a solitary one occurs at a certain applied voltage, and a hysteresis is associated.

Solitary Radial Electric Field Structure in Tokamak Plasmas

Electron temperature gradient (ETG) driven instability in toroidal plasmas is studied with gyrokinetic theory. The full electron kinetics including finite Larmor radius effects, toroidal (curvature and magnetic gradient) drift motion ωD, and transit k∥v∥, is considered. The upgraded numerical scheme for solving the integral eigenvalue equations allows the study of both growing and damping modes, and thus direct calculation of critical gradient. A systematic parameter study is carried out for low β(=plasma pressure/magnetic pressure) circular flux surface equilibria. The basic characteristics of the modes are discussed. The scaling of the critical gradient with respect to toroidicity and to the ratio of electron temperature over ion temperature is obtained. Estimation for the transport induced by the modes is given.

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Electron temperature gradient instability in toroidal plasmas

The temperature gradient (ηi and ηe) driven instability in the short wavelength regime, |kyρi|>1, is studied in a sheared slab. An analytical analysis is performed first to clarify the physics mechanisms for the modes in a shearless slab. The correlation between the growth rate and the real frequency of the modes is discussed in detail. The electron temperature gradient is found to have strong influences on the modes in short wavelength regions. Several series of the short wavelength modes are then identified with a kinetic integral equation code in a sheared slab. The radial widths of the modes are found to be comparable with the conventional ηi modes and not short, although the poloidal wavelengths are short. The lowest odd mode usually dominates in the weak magnetic shear and low β regime. However, the fundamental mode seems to be important in tokamak plasmas because the higher order modes are easily stabilized by finite β and/or by magnetic shear. The fundamental short wavelength mode cannot be stabil...

Temperature gradient driven short wavelength modes in sheared slab plasmas

Kinetic shear Alfven modes in tokamak plasmas (with or without temperature gradient) are numerically investigated in the full gyrokinetic limit. It is shown that, in the presence of ion temperature gradient (ITG), the threshold value of plasma pressure gradient is well below that for ideal magnetohydrodynamic ballooning instability. It is also demonstrated in a more general sense that, without ITG, the former is identical with the latter. The electromagnetic instability is also found to exist in the second stable region of the ideal modes when a finite ITG is present. The results are compared with previous similar analyses for kinetic collisionless ballooning modes. Possible correlation of the instability with tokamak experiments is discussed.

https://www.afs.enea.it/zonca/references/journal/dong_pop04.pdf

Study of kinetic shear Alfvén instability in tokamak plasmas

The electron temperature gradient driven instabilities in plasmas with slightly hollow density profiles are studied. The gyrokinetic integral eigenvalue equation valid for a sheared slab configuration is employed. The Debye shielding effect on the modes is investigated. The effects of a sheared E×B flow on the modes are considered. Six modes with even or odd parities are found to be simultaneously unstable. The mixing length estimate for the transport is calculated. The flow shear suppression on the modes, as well as on the transport, is demonstrated. The correlations of the results with helical system Heliotron/Torsotron and tokamak experiments are discussed.

K. Itoh

Papers

Gyrokinetic study of the electron temperature gradient instability in plasmas with slightly hollow density profiles