This paper presents the results of three-dimensional fluid global simulations of electrostatic ion turbulence in tokamaks with reversed magnetic shear. It is found that a transport barrier appears at the location of magnetic shear reversal. This is due to a rarefaction of resonant surfaces in this region. For the same reason, the barrier is more pronounced when the minimum of the safety factor is a simple rational number. The barrier is broadened by velocity shear effects. It is also found that large-scale transport events hardly cross a transport barrier. Finally, a significant amount of toroidal rotation is generated by the turbulence. This rotation changes its sign at the position of magnetic shear reversal, as expected from a quasi-linear estimate of the Reynolds stress tensor.

The effect of a sheared toroidal velocity on a transport barrier is studied. This analysis is done by using three-dimensional global fluid simulations of electrostatic ion temperature gradient driven turbulence in tokamaks. The barrier is produced with a reversed magnetic shear. For a flat density profile, and at low collisionality, co-rotation leads to an outward motion of the barrier, whereas counter rotation leads to an inward displacement. However, the barrier displacement saturates when increasing the torque at fixed heat source. This saturation is attributed to the onset of Kelvin–Helmholtz modes. Also the central temperature is larger without external torque because the width of the transport barrier is wider. The consequence is that better confinement is obtained in absence of external torque.

It is shown that a relevant control of Hamiltonian chaos is possible through suitable small perturbations whose form can be explicitly computed. In particular, it is possible to control (reduce) the chaotic diffusion in the phase space of a Hamiltonian system with 1.5 degrees of freedom which models the diffusion of charged test particles in a turbulent electric field across the confining magnetic field in controlled thermonuclear fusion devices. Though still far from practical applications, this result suggests that some strategy to control turbulent transport in magnetized plasmas, in particular, tokamaks, is conceivable. The robustness of the control is investigated in terms of a departure from the optimum magnitude, of a varying cutoff at large wave vectors, and of random errors on the phases of the modes. In all three cases, there is a significant region of maximum efficiency in the vicinity of the optimum control term.

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