Geometrical effects of the magnetic field on the neoclassical flow, current and rotation in general toroidal systems

In order to clarify geometrical effects of the magnetic field on neoclassical theory, the neoclassical parallel particle flow, heat flux, current and plasma rotation of a multispecies plasma in general toroidal systems are examined in several collisionality regimes. The quantitative and qualitative differences between axisymmetric (tokamaks) and non-axisymmetric toroidal systems (stellarator, heliotron/torsatron) appear mainly through a geometrical factor which prescribes the parallel flow due to the gradients of the density, temperature, and electrostatic potential. In axisymmetric toroidal systems the geometrical factor reduces to the same expression in all collisionality regimes due to axisymmetry. By contrast, in non-axisymmetric toroidal systems, it changes drastically depending on the magnetic fieled structure and the collisionality regime. Thus, the poloidal flow has the radial electric field dependence. When the geometrical factor is very small, the ion parallel flow almost vanishes and the ion rotation consists of the diamagnetic and E vector x B vector flows (perpendicular flows). (author)