Transport barriers for two modes drift wave map

Shearless barrier improves the plasma confinement and can be created by the application of a bias. Previously, they were identified with a 2D map of charged particle motion in one drift mode. Now, we add a second drift mode and derive a 3D map. By fixing the parameters related to the first mode and varying the second mode amplitude, we show that the existence of the barriers depends on the second mode amplitude. Winding number and recurrence times have been used to study the particle transport and the existence of the shearless. We also observe that even after the shearless destruction, the stickiness in its neighborhood continues to have a transport blocking effect to some extent. So, to evaluate the effectiveness of the barriers, we compute the ratio of initial conditions that crossed the barriers and by using the space parameter we highlighted the sensitivity of transport barriers to perturbations.