论文标题
在单波模型中的低维混沌
Low-dimensional chaos in the single wave model for self-consistent wave-particle Hamiltonian
论文作者
论文摘要
我们在单波模型中使用哈密顿动力学分析了自洽的波粒子相互作用的非线性方面，在该模型中，由于粒子动力学，波被修改。这种相互作用在血浆不稳定性和湍流的出现中起着重要作用。最简单的情况，其中一个粒子（n = 1）与一个波（M = 1）耦合，完全可以集成，而非线性效应则减少了波电位脉动，而粒子要么永远被捕获或永远循环。在增加粒子数量（n = 2，m = 1）时，积分性会丢失，并且会发展混乱。我们的分析确定了混乱出现和生长的两种标准方法（从分离物出生的同质缠结，以及椭圆固定点附近的共振重叠）。此外，当能量足够高以使波幅度偶尔消失时，就会发生强烈的混乱形式。
We analyze nonlinear aspects of the self-consistent wave-particle interaction using Hamiltonian dynamics in the single wave model, where the wave is modified due to the particle dynamics. This interaction plays an important role in the emergence of plasma instabilities and turbulence. The simplest case, where one particle (N = 1) is coupled with one wave (M = 1), is completely integrable, and the nonlinear effects reduce to the wave potential pulsating while the particle either remains trapped or circulates forever. On increasing the number of particles (N = 2, M = 1), integrability is lost and chaos develops. Our analyses identify the two standard ways for chaos to appear and grow (the homoclinic tangle born from a separatrix, and the resonance overlap near an elliptic fixed point). Moreover, a strong form of chaos occurs when the energy is high enough for the wave amplitude to vanish occasionally.
