寻找踢Hamilton的稳定域和逃逸率
Finding stability domains and escape rates in kicked Hamiltonians
摘要：
我们使用一个有效的哈密尔顿粒子动力学的特点，并找到逃逸率在一个周期性踢哈密尔顿。我们研究了一个由混沌辛映射描述的储存环中的粒子模型。忽略共振，动力学通常在相空间中具有其稳定的有限区域。系统中的固有噪声导致粒子从该稳定区域损失。这种噪声与增加稳定性的辐射阻尼的竞争决定了逃逸率。因此，确定这一“孔径”并找到逃逸率是一个重要的物理问题。我们比较了两种不同的微扰理论和变分方法来估计这个稳定区域的结果。包括噪声，我们推导出分析估计的稳态人口（和由此产生的束流发射度），逃逸率在小阻尼制度，并比较它们与数值模拟。
英文摘要：
We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the resonances, the dynamics typically has a finite region in phase space where it is stable. Inherent noise in the system leads to particle loss from this stable region. The competition of this noise with radiation damping, which increases stability, determines the escape rate. Determining this `aperture' and finding escape rates is therefore an important physical problem. We compare the results of two different perturbation theories and a variational method to estimate this stable region. Including noise, we derive analytical estimates for the steady-state populations (and the resulting beam emittance), for the escape rate in the small damping regime, and compare them with numerical simulations.
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