Edge Plasma Mode as the Signature of the EDA H-Regime

A deep $E_r$-well observed in the EDA H-Regime produced by the Alcator C-Mod machine is considered as inducing a sharp localization of the Quasi-Coherent Mode proposed as the signature of this regime. This has a phase velocity in the ion diamagnetic velocity direction, in the plasma reference frame [1], and is a ``viscous-ballooning-mode'' driven by the combined effects of the plasma pressure gradient and the magnetic field curvature that would be stable due to FLR effects in the absence of a finite viscosity $\mu^i_\bot$. The frequency is near $\omega_{di}\equiv k_\phi v_{di}$ where $v_{di}\equiv-[c/(e nB_\theta)]d p_i/dr$ and $k_\phi = n^0/R$. The relevant model dispersion relation [2] obtained for a plane geometry in which the magnetic field curvature is simulated by an effective gravity is $(\omega+i\gamma_\mu)(\omega-\omega_{di})=-\gamma^2_{IC}+ k^2_\parallel v_A^2/[1+i k^2_\bot D_m/(\omega-\overline{\omega}_{*e})]$, where $\gamma_\mu\propto\mu^i_\bot$, $\gamma_{IC}$ is the interchange growth rate, $D_m\equiv c^2\eta_\parallel/(4\pi)$, $\eta_\parallel$ is the longitudinal resistivity and $\overline{\omega}_{*e}\equiv[ck_\phi T_e/(enB_\theta)](dn/dr)(1+1.71d\ln T_e/d\ln n_e)$.\\[4pt] [1] I. Cziegler (2010).\\[0pt] [2] B. Coppi, et al., Ann. Phys. 121,1 (1979)