On symmetric sandpiles

A symmetric version of the well-known SPM model for sandpiles is introduced. We prove that the new model has fixed point dynamics. Although there might be several fixed points, a precise description of the fixed points is given. Moreover, we provide a simple closed formula for counting the number of fixed points originated by initial conditions made of a single column of grains.Comment: Will be presented at ACRI2006 conferenc

A self-organized criticality model for ion temperature gradient (ITG) mode driven turbulence in confined plasma

A new Self-Organized Criticality (SOC) model is introduced in the form of a Cellular Automaton (CA) for ion temperature gradient (ITG) mode driven turbulence in fusion plasmas. Main characteristics of the model are that it is constructed in terms of the actual physical variable, the ion temperature, and that the temporal evolution of the CA, which necessarily is in the form of rules, mimics actual physical processes as they are considered to be active in the system, i.e. a heating process and a local diffusive process that sets on if a threshold in the normalized ion temperature gradient R/L_T is exceeded. The model reaches the SOC state and yields ion temperature profiles of exponential shape, which exhibit very high stiffness, in that they basically are independent of the loading pattern applied. This implies that there is anomalous heat transport present in the system, despite the fact that diffusion at the local level is imposed to be of a normal kind. The distributions of the heat fluxes in the system and of the heat out-fluxes are of power-law shape. The basic properties of the model are in good qualitative agreement with experimental results.Comment: In press at Physics of Plasmas, July 2010; 11 pages, 5 figure

Advances in symmetric sandpiles

International audienceA symmetric version of the well-known SPM model for sandpiles is introduced. We prove that the new model has fixed-point dynamics. Although there might be several fixed points, a precise description of the fixed points is given. Moreover, we provide a simple closed formula for counting the number of fixed points originated by initial conditions made of a single column of grains. Bounds for the transient length are also given

Diffusive Shock Acceleration and Turbulent Reconnection

International audienceDiffusive shock acceleration (DSA) cannot efficiently accelerate particles without the presence of self-consistently generated or pre-existing strong turbulence (δB/B∼ 1) in the vicinity of the shock. The problem we address in this article is: if large-amplitude magnetic disturbances are present upstream and downstream of a shock then Turbulent Reconnection (TR) will set in and will participate not only in the elastic scattering of particles but also in their heating and acceleration. We demonstrate that large-amplitude magnetic disturbances and Unstable Current Sheets (UCS), spontaneously formed in the strong turbulence in the vicinity of a shock, can accelerate particles as efficiently as DSA in large-scale systems and on long time scales. We start our analysis with ‘elastic’ scatterers upstream and downstream and estimate the energy distribution of particles escaping from the shock, recovering the well-known results from the DSA theory. Next we analyse the additional interaction of the particles with active scatterers (magnetic disturbances and UCS) upstream and downstream of the shock. We show that the asymptotic energy distribution of the particles accelerated by DSA/TR has very similar characteristics with the one due to DSA alone, but the synergy of DSA with TR is much more efficient: The acceleration time is an order of magnitude shorter and the maximum energy reached two orders of magnitude higher. We claim that DSA is the dominant acceleration mechanism in a short period before TR is established, and then strong turbulence will dominate the heating and acceleration of the particles. In other words, the shock serves as the mechanism to set up a strongly turbulent environment, in which the acceleration mechanism will ultimately be the synergy of DSA and TR