Rotation Velocities and Radial Electric Field in the Plasma Edge

Abstract

A set of equations for the calculation of plasma rotation and the radial electric field in the edge plasma is presented. The equations are based on particle and momentum balance and explicitly incorporate neoclassical viscosity and atomic physics effects, and allow for the inclusion of anomalous effects.

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…”

“…In order to investigate this, it will be necessary to extend the solution procedure [12][13][14] for the Fourier moments of the poloidal momentum balance equation to be based on the Miller equilibrium model, and that will be the subject of a future paper. ͑30͒ and ͑31͒ reduce identically to the first of Eqs.…”

Extension and comparison of neoclassical models for poloidal rotation in tokamaks

“…There are a number of theoretical models for the calculation of poloidal rotation that are referred to as "neoclassical," ranging from the early prediction by Hazeltine 1 of an ion poloidal rotation velocity proportional to the ion radial temperature gradient through the several variants of the Hirshman-Sigmar fluid model 2 ͑in which the ion poloidal rotation is calculated from a balance between parallel frictional and viscous forces͒ to the StaceySigmar model 3 ͑in which the poloidal rotation is calculated from the poloidal momentum balance using a rate-of-strain tensor formulation for the viscous force͒.…”

Reevaluation of the Braginskii viscous force for toroidal plasma

“…For both models we will use the concentric, circular flux surface approximation; however, the treatments of the radial derivative will be distinct. Restricting consideration to flux surfaces with constant density yet allowing for vertical asymmetry to the ion toroidal velocity profile yields a radial shear viscous force which should be accounted for when interpreting experimental measurements [13,14]. An evaluation from data collected at DIII-D [15] indicates qualitative agreement between theory and measurement for impure plasma discharges with significant toroidal rotation.…”