Velocity Space Loss Region in a Toroidal System with a Non-Planar Magnetic Axis

Abstract

Velocity space loss regions are analytically estimated in the helical solenoid with low toroidicity by means of the invariants ψ^* and J_⁄⁄. The drift surface integral ψ^* describes the trajectories of passing and blocked particles, while the longitudinal adiabatic invariant J_⁄⁄ expresses the motion of banana center. The loss regions are basically composed of both the tokamak type’s contribution in the case of the helically symmetric system and the stellarator type’s contribution caused by the radial drift of the banana center of localized particles due to the toroidal effect, and appear for both v_⁄⁄>0 and v_⁄⁄<0 in the low particle energy region due to the effect of the latter. Analytical results are checked by the intensive numerical orbit calculation. Both are in good agreement each other except in the v_⁄⁄\simeq0 region.