699 research outputs found
Local control of Hamiltonian chaos
We review a method of control for Hamiltonian systems which is able to create
smooth invariant tori. This method of control is based on an apt modification
of the perturbation which is small and localized in phase space
Perturbation Theory and Control in Classical or Quantum Mechanics by an Inversion Formula
We consider a perturbation of an ``integrable'' Hamiltonian and give an
expression for the canonical or unitary transformation which ``simplifies''
this perturbed system. The problem is to invert a functional defined on the
Lie- algebra of observables. We give a bound for the perturbation in order to
solve this inversion. And apply this result to a particular case of the control
theory, as a first example, and to the ``quantum adiabatic transformation'', as
another example.Comment: Version 8.0. 26 pages, Latex2e, final version published in J. Phys.
Controlling chaotic transport in a Hamiltonian model of interest to magnetized plasmas
We present a technique to control chaos in Hamiltonian systems which are
close to integrable. By adding a small and simple control term to the
perturbation, the system becomes more regular than the original one. We apply
this technique to a model that reproduces turbulent ExB drift and show
numerically that the control is able to drastically reduce chaotic transport
Control of Hamiltonian chaos as a possible tool to control anomalous transport in fusion plasmas
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 cut-off 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.Comment: 17 pages, 21 figure
Solutions of elliptic equations with a level surface parallel to the boundary: stability of the radial configuration
Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of their level surfaces is parallel to the boundary of the domain. Here, for the elliptic case, we prove the stability counterpart of that result. In fact, we show that if the solution is almost constant on a surface at a fixed distance from the boundary, then the domain is almost radially symmetric, in the sense that is contained in and contains two concentric balls Bre and Bri, with the difference re 12ri (linearly) controlled by a suitable norm of the deviation of the solution from a constant. The proof relies on and enhances arguments developed in a paper by Aftalion, Busca and Reichel
Dynamic modelling of local fuel inventory and desorption in the whole tokamak vacuum vessel for auto-consistent plasma-wall interaction simulations
An extension of the SolEdge2D-EIRENE code package, named D-WEE, has been developed to add the dynamics of thermal desorption of hydrogen isotopes from the surface of plasma facing materials. To achieve this purpose, D-WEE models hydrogen isotopes implantation, transport and retention in those materials. Before launching auto-consistent simulation (with feedback of D-WEE on SolEdge2D-EIRENE), D-WEE has to be initialised to ensure a realistic wall behaviour in terms of dynamics (pumping or fuelling areas) and fuel content. A methodology based on modelling is introduced to perform such initialisation. A synthetic plasma pulse is built from consecutive SolEdge2D-EIRENE simulations. This synthetic pulse is used as a plasma background for the D-WEE module. A sequence of plasma pulses is simulated with D-WEE to model a tokamak operation. This simulation enables to extract at a desired time during a pulse the local fuel inventory and the local desorption flux density which could be used as initial condition for coupled plasma-wall simulations. To assess the relevance of the dynamic retention behaviour obtained in the simulation, a confrontation to post-pulse experimental pressure measurement is performed. Such confrontation reveals a qualitative agreement between the temporal pressure drop obtained in the simulation and the one observed experimentally. The simulated dynamic retention during the consecutive pulses is also studied.EURATOM 63305
Implementation of drift velocities and currents in SOLEDGE2D-EIRENE
International audienceIn order to improve cross-field transport description, drifts and currents have been implemented in SOLEDGE2D-EIRENE. The derivation of an equation for the electric potential is recalled. The resolution of current equation is tested in a simple slab case. WEST divertor simulations in forward-B and reverse-B fields are also discussed. A significant increase of ExB shear is observed in the forward-B configuration that could explain a favorable L-H transition in this case
Barriers for the reduction of transport due to the EXB drift in magnetized plasmas
We consider a 1 1/2degrees of freedom Hamiltonian dynamical system, which
models the chaotic dynamics of charged test-particles in a turbulent electric
field, across the confining magnetic field in controlled thermonuclear fusion
devices. The external electric field E = \nabla\bigvee is modeled by a
phenomenological potential V and the magnetic field B is considered uniform. It
is shown that, by introducing a small additive control term to the external
electric field, it is possible to create a transport barrier for this dynamical
system. The robustness of this control method is also investigated. This
theoretical study indicates that alternative transport barriers can be
triggered without requiring a control action on the device scale as in present
Internal Transport Barriers (ITB).Comment: 1
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