Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles

International audienceThe chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddle-node bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gap-filling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed

Ambipolar diffusion in low-mass star formation. I. General comparison with the ideal MHD case

In this paper, we provide a more accurate description of the evolution of the magnetic flux redistribution during prestellar core collapse by including resistive terms in the magnetohydrodynamics (MHD) equations. We focus more particularly on the impact of ambipolar diffusion. We use the adaptive mesh refinement code RAMSES to carry out such calculations. The resistivities required to calculate the ambipolar diffusion terms were computed using a reduced chemical network of charged, neutral and grain species. The inclusion of ambipolar diffusion leads to the formation of a magnetic diffusion barrier in the vicinity of the core, preventing accumulation of magnetic flux in and around the core and amplification of the field above 0.1G. The mass and radius of the first Larson core remain similar between ideal and non-ideal MHD models. This diffusion plateau has crucial consequences on magnetic braking processes, allowing the formation of disk structures. Magnetically supported outflows launched in ideal MHD models are weakened when using non-ideal MHD. Contrary to ideal MHD misalignment between the initial rotation axis and the magnetic field direction does not significantly affect the results for a given mu, showing that the physical dissipation truly dominate over numerical diffusion. We demonstrate severe limits of the ideal MHD formalism, which yield unphysical behaviours in the long-term evolution of the system. This includes counter rotation inside the outflow, interchange instabilities, and flux redistribution triggered by numerical diffusion, none observed in non-ideal MHD. Disks with Keplerian velocity profiles form in all our non-ideal MHD simulations, with final mass and size which depend on the initial magnetisation. This ranges from a few 0.01 solar masses and 20-30 au for the most magnetised case (mu=2) to 0.2 solar masses and 40-80 au for a lower magnetisation (mu=5).Comment: Accepted in A&A section 7 (on Wednesday, september the 16th, year 2015

Non-ideal magnetohydrodynamics on a moving mesh I: Ohmic and ambipolar diffusion

Especially in cold and high-density regions, the assumptions of ideal magnetohydrodynamics (MHD) can break down, making first order non-ideal terms such as Ohmic and ambipolar diffusion as well as the Hall effect important. In this study we present a new numerical scheme for the first two resistive terms, which we implement in the moving-mesh code AREPO using the single-fluid approximation combined with a new gradient estimation technique based on a least-squares fit per interface. Through various test calculations including the diffusion of a magnetic peak, the structure of a magnetic C-shock, and the damping of an Alfv\'en wave, we show that we can achieve an accuracy comparable to the state-of-the-art code ATHENA++. We apply the scheme to the linear growth of the magnetorotational instability and find good agreement with the analytical growth rates. By simulating the collapse of a magnetised cloud with constant magnetic diffusion, we show that the new scheme is stable even for large density contrasts. Thanks to the Lagrangian nature of the moving mesh method the new scheme is thus well suited for intended future applications where a high resolution in the dense cores of collapsing protostellar clouds needs to be achieved. In a forthcoming work we will extend the scheme to the Hall effect.Comment: 17 pages, 18 figure

Crisis dynamics of a class of single-degree-of-freedom piecewise linear oscillators

Peer reviewe

Development of an experiment for investigating the magnetohydrodynamic richtmyer-meshkov instability

Collaboration by some of the world's brightest minds of the 21st Century pinpointed fourteen Grand Engineering Challenges that face humankind today. At the top of this list is "Provide Energy from Fusion"; a requirement deemed crucial for humankind to thrive flourish. Scientists from all over the globe have risen to this challenge in many ways; most recognizably by attempting to succeed at performing inertial confinement fusion (ICF). However, ICF currently remains unsuccessful at providing net-positive energy production, largely due to hydrodynamic instabilities, such as the shock-driven Richtmyer-Meshkov instability (RMI), which occur within the fusion reaction process, creating detrimental mixing. Applying magnetohydrodynamic approaches however, can mitigate these instabilities and reduce fluid mixing. It is precisely this problem that necessitates the research on magnetohydrodynamic instabilities presented in this dissertation to aid in solving the challenge to "Provide Energy from Fusion"; specifically the development of an experiment for investigating the magnetohydrodynamic Richtmyer-Meshkov instability (MHD-RMI). ... By developing and performing the computational and experimental efforts at the Missouri Fluid Mixing and Shock Tube Laboratory (FMSTL), the author has laid the groundwork to observe the suppression of the MHD-RMI in future shock tube experiments.Includes bibliographical reference

Ion cyclotron emission on ASDEX upgrade

This works deals with the Ion Cyclotron Emission (ICE), a plasma instability that takes place both in astrophysical plasmas and in fusion energy facilities like Tokamaks and Stellarators, when a population of high energetic ions is present. These fast ions can interact with the waves which propagate in the background thermal plasma and excite instabilities in the Mega-Hertz range. This emission can be measured in a non-intrusive way with radio-frequency probes and provide information on the characteristics of the fast ions. The hope of a new diagnostic sparked many studies in the years 1992-2002 but, in spite of the theoretical and experimental progresses, no practical instrumentation was achieved. There are indeed two main difficulties: first, the ICE involves many different types of plasma phenomena: waves propagation, resonances, conversion and absorption in complex geometries, core and edge plasma modelling, fast ion creation and trajectories; all these aspects are entangled. Therefore, accurate data both in time and frequency domains and a theory that covers these physics fields are necessary to distinguish the impact of these different phenomena. Second, there are technical difficulties in measuring high-frequency signals with a sufficient Signal-to-Noise Ratio to discriminate it from the background noise. The purpose of this study is to address these issues with the use of the latest acquisition technologies and an improved ICE theory, which can relate in a new light the properties of the fast ions to the characteristics of the emission