Global energy confinement degradation due to macroscopic phenomena in tokamaks

Models are developed for estimating the effects of macroscopic phenomena in tokamaks (sawteeth, Mirnov oscillations, edge localized modes (ELMs), etc.) on plasma global energy confinement. The analysis is based on a recently developed formalism for determining the incremental energy confinement time τinc from a local transport model. The macroscopic phenomena are assumed to influence the plasma only in the regions where they occur, without changing the heat diffusivity elsewhere in the plasma. General expressions are presented in terms of a magnetic flux surface label (ρ). Simplified formulas for the effects are also given for a cylindrical geometry. For the Mirnov oscillation case (m/n = 2/1 or 3/1 tearing modes), two models (for 'belt' and island influenced regions) are investigated and compared. When a number of macroscopic phenomena are present simultaneously (but not overlapping) their net effect is shown to be a sum of the individual effects. Finally, for time dependent phenomena such as sawteeth and ELMs, appropriate time averages of their net effects are developed.