43 research outputs found
Action diffusion and lifetimes of quasistationary states in the Hamiltonian Mean Field model
Out-of-equilibrium quasistationary states (QSSs) are one of the signatures of
a broken ergodicity in long-range interacting systems. For the widely studied
Hamiltonian Mean-Field model, the lifetime of some QSSs has been shown to
diverge with the number N of degrees of freedom with a puzzling N^1.7 scaling
law, contradicting the otherwise widespread N scaling law. It is shown here
that this peculiar scaling arises from the locality properties of the dynamics
captured through the computation of the diffusion coefficient in terms of the
action variable. The use of a mean first passage time approach proves to be
successful in explaining the non-trivial scaling at stake here, and sheds some
light on another case, where lifetimes diverging as e^N above some critical
energy have been reported
Microtearing turbulence: magnetic braiding and disruption limit
International audienceA realistic reduced model involving a large poloidal spectrum of microtearing modes is used to probe the existence of some stochasticity of magnetic field lines. Stochasticity is shown to occur even for the low values of the magnetic perturbation δB/B devoted to magnetic turbulence that have been experimentally measured. Because the diffusion coefficient may strongly depend on the radial (or magnetic-flux) coordinate, being very low near some resonant surfaces, and because its evaluation implicitly makes a normal diffusion hypothesis, one turns to another indicator appropriate to diagnose the confinement: the mean residence time of magnetic field lines. Their computation in the microturbulence frame points to the existence of a disruption limit, namely of a critical order of magnitude of δB/B above which stochasticity is no longer benign yet leads to a macroscopic loss of confinement in some tens to hundred of electron toroidal excursions. Since the level of magnetic turbulence δB/B has been measured to grow with the plasma electron density this would also be a density limit
Phase transition in the collisionless regime for wave-particle interaction
Gibbs statistical mechanics is derived for the Hamiltonian system coupling
self-consistently a wave to N particles. This identifies Landau damping with a
regime where a second order phase transition occurs. For nonequilibrium initial
data with warm particles, a critical initial wave intensity is found: above it,
thermodynamics predicts a finite wave amplitude in the limit of infinite N;
below it, the equilibrium amplitude vanishes. Simulations support these
predictions providing new insight on the long-time nonlinear fate of the wave
due to Landau damping in plasmas.Comment: 12 pages (RevTeX), 2 figures (PostScript
Occurrence and impact of the spatial chaos of magnetic field lines
International audienceMagnetic field lines are spatially chaotic at a given time when the space Hamiltonian from which they derive is non integrable. As the minimal number of degrees of freedom required for the possible emergence of chaos is three, situations or models involving only two effective space dimensions cannot develop a spatial chaos of magnetic field lines. The question behind this presentation will be: What is the impact of the spatial chaos of magnetic field lines in hot magnetized plasmas? Two situations will be addressed: i) in tokamak sawteeth, that can be viewed as a laboratory prototype of magnetic reconnection, evidence will be given that magnetic field lines are spatially chaotic during the fast crash (reconnection) phase. ii) the spatial chaos of magnetic field lines will be shown to occur even for the low values of the magnetic perturbation δB/B devoted to magnetic turbulence that have been experimentally measured in toroidal magnetic devices
Interplay of the magnetic and current density field topologies in axisymmetric devices for magnetic confinement fusion
In magnetic confinement fusion devices close to axisymmetry, such as tokamaks, a key element is the winding profile of the magnetic field lines, or its inverse, the safety profile . A corresponding profile, , can be defined for the current density field lines. Amp\`{e}re's law relates any mode of current perturbation with a mode of magnetic perturbation . It is shown that the knowledge of the pair allows then to characterize the resonant, or non-resonant, nature of the modes for both the magnetic and current density field lines. The expression of in flux coordinate is derived. Including this calculation in the real-time Grad-Shafranov equilibrium reconstruction codes would yield a comprehensive view of the magnetics. The monitoring of the pair would then allow investigating the role played by the resonant modes for the current density, that are current filamentary modes, in the plasma small-scale turbulence. By driving the magnetic and current density profiles apart so that the images of and are disjoint, these filamentary modes would not impact the magnetic field topology, being not associated to magnetic islands but to non-resonant magnetic modes. It remains to be explored to which extent such a configuration, where the spectrum of tiny current density filaments produces a spectrum of magnetic modes that has practically no effect on heat transport, is beneficial
Interplay of the magnetic and current density field topologies in axisymmetric devices for magnetic confinement fusion
In magnetic confinement fusion devices close to axisymmetry, such as tokamaks, a key element is the winding profile of the magnetic field lines, or its inverse, the safety profile . A corresponding profile, , can be defined for the current density field lines. Amp\`{e}re's law relates any mode of current perturbation with a mode of magnetic perturbation . It is shown that the knowledge of the pair allows then to characterize the resonant, or non-resonant, nature of the modes for both the magnetic and current density field lines. The expression of in flux coordinate is derived. Including this calculation in the real-time Grad-Shafranov equilibrium reconstruction codes would yield a comprehensive view of the magnetics. The monitoring of the pair would then allow investigating the role played by the resonant modes for the current density, that are current filamentary modes, in the plasma small-scale turbulence. By driving the magnetic and current density profiles apart so that the images of and are disjoint, these filamentary modes would not impact the magnetic field topology, being not associated to magnetic islands but to non-resonant magnetic modes. It remains to be explored to which extent such a configuration, where the spectrum of tiny current density filaments produces a spectrum of magnetic modes that has practically no effect on heat transport, is beneficial
Axisymmetric steady-state flows in tokamak plasmas under the visco-resistive MHD setting
International audienc
Transient fields produced by a cylindrical electron beam flowing through a plasma
To appear in Laser and Particle Beams.International audienceThe out-of-equilibrium situation in which an initially sharp-edged cylindrical electron beam, that could e.g. model electrons flowing within a wire, is injected into a plasma is considered. A detailed computation of the subsequently produced magnetic field is presented. The control parameter of the problem is shown to be the ratio of the beam radius to the electron skin depth. Two alternative ways to address analytically the problem are considered: one uses the usual Laplace transform approach, the other one involves Riemann's method in which causality conditions manifest through some integrals of triple products of Bessel functions