Extension of the flow-rate-of-strain tensor formulation of plasma rotation theory to non-axisymmetric tokamaks

Abstract

A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Xs-ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric "neoclassical toroidal viscosity" mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation. V

Recent Developments in Plasma Edge Theory

“…6 Viscous damping of toroidal rotation and poloidal asymmetries in the edge plasma [9,10] The viscous damping of toroidal angular momentum is represented by the flux surface average (FSA) of the toroidal component of the viscous torque [9]…”

“…While the calculated poloidal asymmetries are small and the rotation velocities are in reasonable agreement with measured values in the core plasma, the calculated asymmetries become questionable in the edge plasma. Radial magnetic field components would be expected to be strongest in the plasma edge and are at least in part responsible for the rotation velocities in the edge plasma, and we have recently initiated an extension of the theory in this area [9,10]. Various representations of f ψ ≡ B ψ /|B| have been discussed in the literature (e.g.…”

“…upon the flows and their gradients[9,10] , leaving the gyroviscous [η 3 W 3 αβ + η 4 W 4 αβ ] contribution[12] …”

On the physics of the pressure and temperature gradients in the edge of tokamak plasmas

“…[17,19,25,[27][28][29][30]). One reason may be that the replacement R 2 ∇ϕ • ∇ • Π j Rn j m j ν dj V ϕj , which is generally valid for a rate-of-strain type viscosity tensor in an axisymmetric geometry [24], may be invalid in an non-axisymmetric geometry with radial B-field components [31,32], in which case it will be necessary to extend this relatively simple viscosity model to a so-called 'neoclassical toroidal viscosity' form [33]. A similar statement applies to the representation of the viscosity in the poloidal momentum balance equation.…”

Extended fluid transport theory in the tokamak plasma edge

“…x in terms of which the toroidal momentum balance equation for each ion species can be written in the form of equation 4to obtain a coupled set of n equations in n unknowns, where n is the number of ion species. We note that such a representation is strictly valid only for a toroidally axisymmetric system with no radial magnetic field components, and that the presence of non-axisymmetric radial magnetic field components changes the structure of the viscosity representation [21,23], as well as introduces a host of new viscosity mechanisms [24].…”