Bootstrap current and parallel ion velocity in imperfectly optimized stellarators

A novel derivation of the parallel ion velocity, and the bootstrap and Pfirsch-Schlüter currents in an imperfectly optimized (that is, almost omnigenous) stellarator magnetic field, \vec B, is presented. It is shown that, when the conventional radially local form of the drift kinetic equation is employed, the flow velocity and the bootstrap current acquire a spurious contribution proportional to ω /ν , where ω denotes the \vec E × \vec B rotation frequency (due to the radial electric field E ) and ν the collision frequency. This contribution is particularly large in the squareroot ν regime and at smaller collisionalities, where ω /ν > 1 , and is presumably present in most numerical calculations, but it disappears if a more accurate drift kinetic equation is used.