Velocity-space loss regions in toroidal helical systems

Velocity-space loss regions are studied systematically on the basis of the adiabatic invariants J and in a large-aspect-ratio toroidal helical system with an ℓ = 2 helical winding. The adiabatic invariant J is related to bounce motions in a helical ripple and used to study drift surfaces of localized particles, while the adiabatic invariant is related to bounce motions in a toroidal ripple and used to find drift surfaces of blocked particles or transit particles. The velocity-space loss region is determined from the condition whether the drift surfaces cross a limiter radius or not. The transition probability between localized particles and blocked particles is assumed to be unity. – For a configuration with large rotational transform and high shear, or a helical system with a short-pitch helical winding such as Heliotron E, localized particles trapped in helical ripples and with small parallel velocities, v|| ≅ 0, are confined in a plasma column by a drift motion due to a strong magnetic-field inhomogeneity. Velocity-space loss regions appear for both v|| > 0 and v|| < 0. On the other hand, for a configuration with weak shear such as the W VII A stellarator, localized particles are lost from the confinement region completely. Then the velocity-space loss region appears in the neighbourhood of v|| ≅ 0. – Velocity-space los is strongly dependent on the type of helical system.