Anomalous electron thermal diffusivity due to the electron temperature gradient mode in Tokamaks

Summary form only given. The electron temperature gradient (ETG) mode is often thought to be dual of the ion temperature gradient (ITG) mode with the roles of ions and electrons interchanged, namely, in the ITG mode, electrons are adiabatic, while in the ETG mode, ions are. The growth rate of the long wavelength (thus charge neutral) ITG mode peaks at k/spl rho//sub i//spl ap/0.3 and if complete duality holds, the growth rate of the ETG mode would peak at k/spl rho//sub e//spl ap/0.3 where /spl rho//sub i/(/spl rho//sub e/) is the ion (electron) Larmor radius. A resultant anomalous electron thermal diffusivity would be smaller than the ITG driven ion thermal diffusivity by a factor (M/m)/sup 1/2/, too small to be relevant. Here M/m is the ion/electron mass ratio. In Tokamaks, the electron Larmor radius is normally smaller than the Debye length, and charge neutrality does not hold in the ETG mode. The duality between the ITG mode and ETG thus breaks down completely, and the ETG mode may cause large enough anomalous electron thermal transport. A kinetic, electromagnetic integral equation code has recently been developed by M. Elia in the Laboratory for stability analyses of drift and ballooning type modes in Tokamaks. The toroidal ETG mode has been analyzed without imposing charge neutrality. Main findings are as follows: (a) Because of charge non-neutrality, the growth rate of the ETG model increases with the plasma beta even though the ETG mode is predominantly electrostatic, (b) The maximum growth rate occurs at k/k/sub De//spl ap/0.7 when the plasma density and temperature are varied. k/spl rho//sub e/ at the maximum growth rate is not constant but varies widely, (c) The electron thermal diffusivity based on a simple mixing length estimation is /spl chi//sub e/ /spl square/ q/spl nu//sub Te//L/sub t/ (c//spl omega//sub pe/)/sup 2/ /spl radic//spl beta//sub e/ /spl prop/ qT/sub e//B/spl radic/n, where q is the safety factor. The diffusivity falls in the range 1 to 10 m/sup 2//sec (relevant to Tokamaks). Also, the diffusivity above increases with the minor radius as seen in experiments.