Heavy Particle Mode as the Signature of the I-Regime*

Key features [1] of the I-Regime investigated by the Alcator C-Mod can be explained by the excitation of a new heavy particle (e.g. impurity) mode [2] at the plasma edge. This mode involves both density and magnetic fluctuations. The impurity is treated as collisional. Considering a plane geometry, the dispersion relation has a unstable root for $\eta_i\equiv (dT_i/dr) n_i/(T_i dn_i/dr)>2/3$ and $dn_I/dr>0$. The marginal stability point is reached for a maximum $d n_I/dr$ such that $\omega^I_{**}=\omega_{IA}=\omega$, where $\omega^I_{**}\equiv c k_y T_I (dn_I/dr)/(Ze B n_I)$ and $\omega_{IA}\equiv(5/3) k^2 T_I/m_I$. The instability condition is $\omega^I_{**}<\omega_{IA}$. $\rm{Re}\, \omega/\omega^I_{**}>0$ indicates that the mode phase velocity($v_{ph}$)is in the electron diamagnetic direction, a feature consistent[3]with the observation that the plasma spontaneous rotation is in the ion diamagnetic direction. This predicted direction of $v_{ph}$ has been confirmed by the experiments. The impurity flux evaluated from the quasi-linear theory is $\langle\hat{n}_I \hat{v}_{Ex}\rangle=n_i\langle\widehat{T}_i \hat{v}_{Ex}\rangle/(Z T_i) \simeq -n_i (dT_i/dr)/(Z T_i k^2 v_{th i} \lambda_i) \left[1-2/(3\eta_i)\right] \cdot\langle |\hat{v}_{Ex}|^2\rangle >0$ for $\eta_i>2/3$, where $\lambda_i$ is the effective main ion mean free path. This shows that both the main ion thermal energy and the impurity are transported outwards. These features are consistent with a mode with frequency $\sim 200\, kHz$ observed in the I- Regime and with the fact that impurities are confined at the edge in this regime. *Sponsored by the DOE. [1] E. Marmar, B. Lipschultz, A. Dominguez, et al., Bull. Am. Phys. Soc. {\bf 54} (2009) 97 [2] B. Coppi, H. Furth, M. Rosenbluth and R. Sagdeev, Phys. Rev. Lett. {\bf{17}} (1966) 377-379 [3] B. Coppi, Nucl. Fusion {\bf{42}} (2002) 1-4