Chaotic jets with multifractal space-time random walk

Abstract

The problem of normal and anomalous diffusion is examined for the four‐dimensional (4‐D) map that arises from the problem of particle motion in a constant magnetic field and electrostatic wave packet. This 4‐D map consists of two coupled 2‐D maps: a standard map and a web map. The case of a weak chaos is considered. It is shown that due to the finite observation time, the particle diffusion possesses strong nonhomogeneous properties. Existence of long‐living bundles of orbits with coherent propagation property is checked. These bundles are named ‘‘chaotic jets.’’ The same name is used for a part of the trajectory if this part corresponds to long‐living trapping or flight. The existence of chaotic jets depends on the topological properties of the phase space and influences the asymptotic law of transport. The particle transport can be considered as a random walk in the multifractal space‐time that is produced by flights and trappings of a test particle in some area of its phase space. Lévy random walk theory and its generalization for the multifractal space‐time situation is considered and asymptotic laws for displacements are derived. Different intermediate asymptotics are discussed.