Experimental Evidence for Increased Particle Fluxes Due to a Change in Transport at the Separatrix near Density Limits on Alcator C-Mod

Experimental inferences of cross-field particle flux at the separatrix, $Γ_{\perp}^\mathrm{sep}$, show rapid growth near H-mode and L-mode density limits at high magnetic field on Alcator C-Mod. Increases in $Γ_{\perp}^\mathrm{sep}$ correlate well with proximity to high density operational boundaries as proposed by the separatrix operational space model. $Γ_{\perp}^\mathrm{sep}$ grows as the L-mode density limit and the H-L-mode back transition boundaries are approached, consistent with expectations of plasma instability-driven turbulence suggested by theory, confirming the power dependence of density limits. $Γ_{\perp}^\mathrm{sep}$ is well-organized by the characteristic wavenumber for resistive ballooning mode turbulence, $k_\mathrm{RBM}$, from interchange-drift-Alfvén fluid turbulence theory, with additional dependence on the cylindrical safety factor, $\hat{q}_\mathrm{cyl}$, yielding an empirical limit to plasma operation of $k_\mathrm{RBM}^{2}\hat{q}_\mathrm{cyl} = 1$. This limit corresponds to the point where the perpendicular heat flux, $Q_{\perp}$, reaches the level of the parallel heat flux, $Q_{\parallel}$, i.e. $Q_{\perp} \approx Q_{\parallel}$, beyond which point thermal equilibrium is not satisfied, resulting in a fold catastrophe.