Global energy confinement degradation due to macroscopic phenomena in tokamaks

Abstract

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.

Numerical modeling of diffusive heat transport across magnetic islands and local stochastic field

“…For w/w c >7.2, the degradation is determined by w, T e0 ′ (r=r s ) and r s as found in the infinite χ || /χ ⊥ limit [15]. As for the radial gradient of the fundamental harmonic, it takes its maximal value in the island region in the middle range of w/w c , and the "large island" limit of NTM discussed in Ref.…”

“…It has been shown by analytical theory that, T 0/0 is approximately the same as T e0 as long as the island width w is much smaller than the critical island width w c =a(χ ⊥ /χ || ) 1/4 (εan/8L q ) -1/2 , where L q =q/q′ and ε=a/R [16]. For infinite ratio of χ || /χ ⊥ , the T e profile becomes flattened inside the island, and the decrease of T 0/0 for r<r -is ∆T e =T e0 -T 0/0 ≈T e0 ′ (r=r s )w/2 1/2 [15]. With our input parameters one finds w c =0.63×10 -2 a, 2.0×10 -2 a and 6.3×10 -2 a for χ || /χ ⊥ =10 10 , 10 8 and 10 6 , respectively.…”

“…In Fig χ || /χ ⊥ , the ∆β/β 0 due to the 4/3 island is larger than that due to the 3/2 island, since the temperature flattening inside the 4/3 island occurs at a smaller χ || /χ ⊥ due to its smaller w c . For large χ || /χ ⊥ , the ∆β/β 0 due to the 3/2 island is larger because r 3/2 >r 4/3 and w>>w c [15].…”

“…The resulting degradation of plasma energy confinement due to the fast parallel transport along the field lines is found to be determined by the island width, the minor radius of the rational surface and the local equilibrium plasma pressure gradient [15].…”

Tomography of (2, 1) and (3, 2) magnetic island structures on Tokamak Fusion Test Reactor

“…It is seen that the heat conduction at the ͑3, 2͒ island is three times higher than that without ͑3, 2͒ mode, as is assumed by Chang and Callen in their model for the confinement degradation due to the island. 23 This result shows that the large amplitude MHD mode enhances the heat conduction. In this case, however, the confinement time degradation is greater than the theoretical model.…”