Alfv\'{e}n Eigenmodes in Enhanced D-alpha H-mode in Alcator C-Mod

Unstable Alfv\'{e}n eigenmodes are observed in Enhanced D-alpha (EDA) H-mode in Alcator C-Mod at least up to densities of $\bar {n}_e \sim 2.5\times 10^{20}\mbox{m}^{-3}$ with strong H-minority ICRF heating. The mode frequencies are typically in the range 400 - 800 kHz. The largest amplitude modes ($\tilde {B}_\theta /B_\theta \sim 5\times 10^{-5}$ at the wall) often agree in frequency with the expected Toroidal Alfv\'{e}n Eigenmode (TAE) frequency ($\omega _{TAE} =\mbox{v}_A /2qR)$ for q=1, indicating that these are core modes. The calculated effective fast ion tail energy $\sim $ 50 keV corresponds to $\mbox{v}_F /\mbox{v}_A \sim 0.4$. These modes are observed to rotate in the electron diamagnetic drift direction, which is opposite to the rotation direction expected for TAEs with a peaked fast ion distribution. Recent calculations with the AORSA and CQL3D codes [1] indicate that the fast ion distribution in C-Mod may be hollow because of poor wave focussing and preferential heating of trapped particles along the resonance. The opposite sign of the gradient of a hollow profile of the fast ion $\beta $ would then explain the opposite direction of rotation. NOVA-K modelling will be used to compare the stability of L and H-mode conditions and determine the radial structure of these modes. \newline [1] E. F. Jaeger, et al, to be published in Plasma Physics and Cont. Fus.