[en] The effect of weak dissipation on drift orbits has been investigated making use of a simple mapping model in a helical magnetic field. It is found that, after many mapping iterations, any orbit tends to an attractor forming a vortex line even with very small dissipation. The convergence is faster for larger dissipation, i.e., the number of iteration N to converge within a certain distance from the attractor is inversely proportional to the amount of the dissipation. Although the behavior of orbits completely change, the basic stability characteristics of the system does not change, i.e, the coordinate of the attractors are determined by the stable fixed points in the area preserving system because the dissipation is very small. Since wide range of orbits are concentrated around the attractors after many toroidal circulations, a pinch effect is created by a small dissipation. Application of this pinch effect to fusion plasmas is discussed. (author)