Afanasiev Valerii V., Sagdeev Roald Z., Zaslavsky George M.
Space Research Institute, Academy of Science of the USSR, Profsouznaya 84/32, Moscow 117810, USSRSpace Research Institute, Academy of Science of the USSR, Profsouznaya 84/32, Moscow 117810, USSRUniversity of Maryland, College Park, Maryland 20742.
Chaos. 1991 Aug;1(2):143-159. doi: 10.1063/1.165824.
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. Levy 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.
研究了由恒定磁场和静电波包中的粒子运动问题产生的四维（4-D）映射的正常扩散和反常扩散问题。这个4-D映射由两个耦合的二维映射组成：一个标准映射和一个网络映射。考虑了弱混沌的情况。结果表明，由于观测时间有限，粒子扩散具有很强的非均匀特性。检查了具有相干传播特性的长寿命轨道束的存在性。这些束被称为“混沌喷流”。如果轨迹的一部分对应于长寿命的捕获或飞行，则该部分轨迹也使用相同的名称。混沌喷流的存在取决于相空间的拓扑性质，并影响输运的渐近规律。粒子输运可以看作是测试粒子在其相空间的某个区域中的飞行和捕获所产生的多分形时空里的随机游走。考虑了列维随机游走理论及其对多分形时空情况的推广，并推导了位移的渐近规律。讨论了不同的中间渐近性。
