  In tokamaks, internal transport barriers, produced by modifications of the
plasma current profile, reduce particle transport and improve plasma
confinement. The triggering of the internal transport barriers and their
dependence on the plasma profiles is a key nonlinear dynamics problem still
under investigation. We consider the onset of shearless invariant curves inside
the plasma which create internal transport barriers. A non-integrable
drift-kinetic model is used to describe particle transport driven by drift
waves and to investigate these shearless barriers onset in tokamaks. We show
that for some currently observed plasma profiles shearless particle transport
barriers can be triggered by properly modifying the electric field profile and
the influence of non-resonant modes in the barriers onset. In particular, we
show that a broken barrier can be restored by enhancing non-resonant modes.
