Extension and comparison of neoclassical models for poloidal rotation in tokamaks

Abstract

Several neoclassical models for the calculation of poloidal rotation in tokamaks were rederived within a common framework, extended to include additional physics and numerically compared. The importance of new physics phenomena not usually included in poloidal rotation calculations (e.g., poloidal electric field, V×B force resulting from enhanced radial particle flow arising from the ionization of recycling neutrals) was examined. Extensions of the Hirshman–Sigmar, Kim–Diamond–Groebner, and Stacey–Sigmar poloidal rotation models are presented.

Interpretation of changes in diffusive and non-diffusive transport in the edge plasma during pedestal buildup following a low-high transition in DIII-D

“…There are other versions of neoclassical theory in which more terms are retained in the poloidal momentum balance and a different evaluation of the viscous term is used, and in which poloidal asymmetries in the density and flow are included, known as Stacey-Sigmar (S-S) theory. 32 Although there have been mixed reports of agreement and disagreement between poloidal rotation measurements and various version of neoclassical theory, the most recent evidence indicates that when all the important terms are retained and poloidal asymmetries in density and flow are taken into account that the neoclassical prediction is in good agreement with experiment. An extended version of this S-S theory, 32 in which the poloidal asymmetries in the flux surface geometry were represented by the Miller model 37 and the poloidal asymmetries in density and flows were calculated, predicted the poloidal velocities measured in two DIII-D shots quite well.…”

“…32 Although there have been mixed reports of agreement and disagreement between poloidal rotation measurements and various version of neoclassical theory, the most recent evidence indicates that when all the important terms are retained and poloidal asymmetries in density and flow are taken into account that the neoclassical prediction is in good agreement with experiment. An extended version of this S-S theory, 32 in which the poloidal asymmetries in the flux surface geometry were represented by the Miller model 37 and the poloidal asymmetries in density and flows were calculated, predicted the poloidal velocities measured in two DIII-D shots quite well. 38 Furthermore, recent measurements 39 of poloidal rotation in "matched" experiments in NSTX and DIII-D were found to be in reasonable agreement with each other and with a version of neoclassical theory.…”

“…Following the discussion of this subject in Ref. 32, the poloidal rotation is governed by the poloidal momentum balance, and the various versions of neoclassical theory depend on just which terms are retained in this equation and the theoretical evaluation of the viscous and friction terms. The best-known theory is the HirshmanSigmar theory, 33 which retains only the viscous and frictional terms and implicitly assumes poloidal symmetry of density and flows-a version of this H-S theory is in the NCLASS code.…”

Applications of the Miller equilibrium to extend tokamak computational models

“…13,14 The radial component of the momentum balance then can be used to relate the toroidal velocity coefficients to the poloidal density coefficients 14 13,14 The radial component of the momentum balance then can be used to relate the toroidal velocity coefficients to the poloidal density coefficients 14…”

The effects of rotation, electric field, and recycling neutrals on determining the edge pedestal density profile

“…15, 0j = n j m j thj qRf j ͑ jj ‫ء‬ ͒, with f j = −3/2 jj ‫ء‬ / ͓͑1+ −3/2 jj ‫ء‬ ͒͑1+ jj ‫ء‬ ͔͒ being an interpolation formula connecting the collisional result f j =1/ jj ‫ء‬ to the strongly rotating banana and plateau regime results, and with jj ‫ء‬ = jj qR / thj .…”