Topological instability along invariant surfaces and pseudochaotic transport

Abstract

The paper describes the complex topological structure of invariant surfaces that appears in a quasi-stationary regime of the tokamak plasma, and it considers in detail anomalous transport of particles along the invariant surfaces (isosurfaces) that have topological genus greater than 1. Such dynamics is pseudochaotic; i.e. it has a zero Lyapunov exponent. Simulations discover such surfaces in confined plasmas under a fairly low ratio of pressure to the magnetic field energy (beta). The isosurfaces correspond to quasi-coherent structures called "streamers" and the streamers are connected by filaments. We study distribution of time of particle separation, Poincaré; recurrences of trajectories, and first time arrival to the system's edge. A model of a multibar-in-square billiard, introduced by Carreras et al. [Chaos 13, 1175 (2003)] is studied with renormalization group method to obtain a distribution of the first time of particles arrival to the edge as a function of the number of bars, which appears to be power-like. The characteristic exponent of this distribution is discussed with respect to its dependence on the number of filaments that connect adjacent streamers.