Channeling Chaos by Building Barriers

Abstract

Chaos often represents a severe obstacle for the set-up of many-body experiments, e.g., in fusion plasmas or turbulent flows. We propose a strategy to control chaotic diffusion in conservative systems. The core of our approach is a small apt modification of the system which channels chaos by building barriers to diffusion. It leads to practical prescriptions for an experimental apparatus to operate in a regular regime (drastic enhancement of confinement). The experimental realization of this control on a Travelling Wave Tube opens the possibility to practically achieve the control of a wide range of systems at a low additional cost of energy.

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

“…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.…”

Enhancement of particle trapping in the wave-particle interaction

“…Further, it is planned to apply the above technique to the case of the reduced Hamiltonian of [2,3]. We point out that an experimental test of the control method on a modified Travelling Wave Tube has been done [10] in absence of self-consistency.…”

Controlling chaos in wave-particle interactions

“…The control term can be either a global one and acts in the entire phase space [28][29][30] or a local one that acts only in a specific region of phase space [19,31,33]. However, in this paper, we consider only the case where f is a global control term.…”

“…It is also required that the control term must be as simple as possible in order to be implemented in experiments, such as in Ref. [28] where a control term was used to increase the kinetic coherence of an electron beam in a traveling wave tube.…”

“…[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.…”