Collisionless Trapped Electron Mode Turbulence

Collisionless Trapped Electron Mode (CTEM) turbulence is a likely canidate for explaining anomolous transport in tokamak discharges that have a strong density gradient relative to the ion temperature gradient\footnote{D. R. Ernst {\it et. al.}, Phys. Plasma 11 (2004) 2637; T.~Dannert and F.~Jenko, Phys. Plasma 12 (2005) 072309; R. Gatto {\it et. al.}, Phys. Plasma 13 (2006) 022306;}. Here, CTEM turbulence is investigated using the Gyrokinetic $\delta f$ GEM code.\footnote{Y.~Chen and S.~E.~Parker, J. Comput. Phys. 189 (2003) 463; Y.~Chen ad S.E.~Parker, accepted, to appear in J. Comput. Phys. (2006)} GEM is electromagnetic, includes full drift-kinetic electrons, generaly axisymmetric equilbria, collisions and minority species. Here, the flux-tube limit is taken and $\beta$ is so small that the simulations are essentially electrostatic. Linear theory\footnote{J. Wesson (1997) {\it Tokamaks}, Oxford Science} predicts that the instability occurs at $\frac{\sqrt{2\varepsilon}R}{L_n}>1$, which agrees very well with the simulation results. With increasing density gradient, it is observed that the most unstable mode transitions from a CTEM to drift wave mode and the short-wavelength modes are most unstable ($ 2 > k_\perp \rho_i > 1$). Nonlinear simulations are underway to address the parametric dependence of particle and energy transport. The importance of zonal flows for CTEM turbulence, is still not well understood and is under investigation.