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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We study the interplay between a deterministic process of weak chaos, responsible for the anomalous diffusion of a variable x, and a white noise of intensity =. The deterministic process of anomalous diffusion results from the correlated Quctuations of a statistical variable ( between two distinct values +1 and -1, each of them characterized by the same waiting time distribution @(t), given by @(t) t " with 2 ( p, ( 3, in the long-time limit. We prove that under the influence of a weak white noise of intensity =, the process of anomalous diffusion becomes normal at a time t, given by t, 1/:-~t"l. Here P(p) is a function of p, which depends on the dynamical generator of the waiting-time distribution vtr(t) We der. ive an explicit expression for P(p) in the case of two dynamical systems, a one-dimensional superdifFusive map and the standard map in the accelerating state.The theoretical prediction is supported by numerical calculations. PACS number(s): 05.40. +j, 05.60.+w