Bootstrap current and neoclassical transport in tokamaks of arbitrary collisionality and aspect ratio

TLDR

A multi‑species fluid model for steady‑state parallel and radial force balance in axisymmetric tokamak plasmas enables inclusion of external momentum and heat sources, allowing general plasma rotation studies while retaining neoclassical effects. The model evaluates bootstrap current, resistivity, and particle/heat fluxes from rotation velocities, friction, and viscosity coefficients, using a recent neoclassical viscosity formulation valid for arbitrary shape, aspect ratio, and collisionality—including orbit squeezing—and incorporates multiple impurity charge states via a reduced ion charge state formalism for computational efficiency. Comparisons with the National Spherical Torus Experiment show that the model’s bootstrap current differs most near the plasma edge due to collisional contributions, and orbit‑squeezing effects on bootstrap current, transport, and poloidal rotation are illustrated in an enhanced reverse‑shear TFTR plasma. Reference: D.

Abstract

A multi-species fluid model is described for the steady state parallel and radial force balance equations in axisymmetric tokamak plasmas. The bootstrap current, electrical resistivity, and particle and heat fluxes are evaluated in terms of the rotation velocities and friction and viscosity coefficients. A recent formulation of the neoclassical plasma viscosity for arbitrary shape and aspect ratio (including the unity aspect ratio limit), arbitrary collisionality, and orbit squeezing from strong radial electric fields is used to illustrate features of the model. The bootstrap current for the very low aspect ratio National Spherical Torus Experiment [J. Spitzer et al., Fusion Technol. 30, 1337 (1996)] is compared with other models; the largest differences occur near the plasma edge from treatment of the collisional contributions. The effects of orbit squeezing on bootstrap current, thermal and particle transport, and poloidal rotation are illustrated for an enhanced reverse shear plasma in the Tokamak Fusion Test Reactor [D. Meade and the TFTR Group, Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. I, p. 9]. Multiple charge states of impurities are incorporated using the reduced ion charge state formalism for computational efficiency. Because the force balance equations allow for inclusion of external momentum and heat sources and sinks they can be used for general plasma rotation studies while retaining the multi-species neoclassical effects.