Control of Hamiltonian chaos as a possible tool to control anomalous transport in fusion plasmas

Abstract

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.

Control of test particle transport in a turbulent electrostatic model of the Scrape-Off-Layer

“…A significant reduction of D ⋆ is observed in the controlled case. These preliminary results obtained for small amplitudes of the electric potential show that the control strategy we propose can be applied to much more turbulent flows than the one considered in [9]. Further investigations on the efficiency domain of the control term and its robustness are required.…”

“…Our strategy is to define a small apt modification of the system which enhances confinement, at low additional cost of energy [9,10,11]. In the present case it consists in reducing the chaotic diffusion of charged test particles advected by the E × B drift motion.…”

Controlling chaos in wave-particle interactions

“…[27] has been used mainly as a way to control chaotic transport in Hamiltonian systems, such as in magnetized plasmas [19,29,30], fusion devices [19], and turbulent electric fields [31]. Indeed, to control chaos in the system, this method creates invariant tori in the whole phase space preventing chaotic transport from taking place.…”

“…[27] and presented in Refs. [28][29][30], which consists of the addition of a small perturbation to the Hamiltonian. For the system under study, we show that this perturbation is simply a second stationary electrostatic wave with wave amplitude much smaller than the amplitude of the original electrostatic wave.…”

Channeling Chaos by Building Barriers

“…Recently a new method of control of hamiltonian chaos has been proposed based on perturbation theory and Lie algebra [18][19]. We consider hamiltonians of the form H H , i.e.…”