Gyrokinetic theory of slab electron temperature gradient mode in negative shear tokamaks

With a gyrokinetic integral eigenvalue code, it is shown that both the slab ion temperature gradient (ITG) mode and the slab electron temperature gradient (ETG) mode have three types of branches in the negative shear configuration: a single mode-rational surface mode, a double mode-rational surface mode, and a nonresonant mode. For typical fusion plasma parameters satisfying ${\lambda }_{\mathrm{De}}^2{\mathrm{\gg \rho }}_{\mathrm{te}}^2,$ a Weber-type differential eigenmode equation of the ETG mode becomes essentially different from that of the ITG mode, because of the Debye shielding effect, where ${\lambda }_{\mathrm{De}}$ is the Debye length and ${\rho }_{\mathrm{te}}$ is the electron Larmor radius. A scale length of the ETG modes is characterized by ${\lambda }_{\mathrm{De}},$ and different types of analytic solutions are obtained for the ETG modes. From a comparison of the transport coefficient based on the mixing length theory, it is shown that in the negative shear configuration, the slab ETG mode gives an order of magnitude larger transport coefficient compared with an estimate for the conventional normal-sheared slab ETG mode.