Del-Castillo-Negrete D., Firpo Marie-Christine
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-8071.
Chaos. 2002 Jun;12(2):496-507. doi: 10.1063/1.1470203.
A study of coherent structures and self-consistent transport is presented in the context of a Hamiltonian mean field, single wave model. The model describes the weakly nonlinear dynamics of marginally stable plasmas and fluids, and it is related to models of systems with long-range interactions in statistical mechanics. In plasma physics the model applies to the interaction of electron "holes" and electron "clumps," which are depletions and excesses of phase-space electron density with respect to a fixed background. In fluid dynamics the system describes the interaction of vortices with positive and negative circulation in a two-dimensional background shear flow. Numerical simulations in the finite-N and in the N--> infinity kinetic limit (where N is the number of particles) show the existence of coherent, rotating dipole states. We approximate the dipole as two "macroparticles" (one hole and one clump) and consider the N=2 limit of the model. We show that this limit has a family of symmetric, rotating integrable solutions described by a one-degree-of-freedom nontwist Hamiltonian. A perturbative solution of the nontwist Hamiltonian provides an accurate description of the mean field and rotation period of the dipole. The coherence of the dipole is explained in terms of a parametric resonance between the rotation frequency of the macroparticles and the oscillation frequency of the self-consistent mean field. This resonance creates islands of integrability that shield the dipole from regions of chaotic transport. For a class of initial conditions, the mean field exhibits an elliptic-hyperbolic bifurcation that leads to the filamentation, chaotic mixing and eventual destruction of the dipole. (c) 2002 American Institute of Physics.
本文在哈密顿平均场单波模型的背景下，对相干结构和自洽输运进行了研究。该模型描述了临界稳定等离子体和流体的弱非线性动力学，并且与统计力学中具有长程相互作用的系统模型相关。在等离子体物理学中，该模型适用于电子“空穴”和电子“团块”的相互作用，其中电子“空穴”和电子“团块”分别是相空间电子密度相对于固定背景的耗尽和过剩。在流体动力学中，该系统描述了二维背景剪切流中具有正、负环流的涡旋之间的相互作用。有限(N)和(N\to\infty)动力学极限（其中(N)是粒子数）下的数值模拟表明存在相干的旋转偶极子态。我们将偶极子近似为两个“宏观粒子”（一个空穴和一个团块），并考虑模型的(N = 2)极限。我们表明，该极限具有一族由单自由度非扭转哈密顿量描述的对称、旋转可积解。非扭转哈密顿量的微扰解准确地描述了偶极子的平均场和旋转周期。偶极子的相干性是根据宏观粒子的旋转频率与自洽平均场的振荡频率之间的参量共振来解释的。这种共振产生了可积性岛，使偶极子免受混沌输运区域的影响。对于一类初始条件，平均场表现出椭圆 - 双曲分岔，导致偶极子的丝状化、混沌混合并最终破坏。（c）2002美国物理研究所。
