论文标题
$ 2 q_x -2 q_y = 0 $非线性耦合共振的hamiltonian交叉理论
Hamiltonian theory of the crossing of the $2 Q_x -2 Q_y=0$ nonlinear coupling resonance
论文作者
论文摘要
在最近的一篇论文中，哈密顿系统的绝热理论成功地用于研究线性耦合共振的穿越，$ q_x-q_y = 0 $。详细解释了在谐振过程中发生的众所周知现象，例如发射交换及其对过程的绝热性的依赖。在本文中，我们考虑使用相同的理论框架的非线性耦合的共振$ 2 q_x -2 q_y = 0 $。我们使用哈密顿模型进行分析，其中非线性耦合共振令人兴奋，并详细研究了相应的动力学，特别是研究了相位空间拓扑及其演变，鉴于表征了发射交换现象。然后使用符号图测试理论结果。得益于这种方法，得出了对应用程序普遍关注的规律定律。
In a recent paper, the adiabatic theory of Hamiltonian systems was successfully applied to study the crossing of the linear coupling resonance, $Q_x-Q_y=0$. A detailed explanation of the well-known phenomena that occur during the resonance-crossing process, such as emittance exchange and its dependence on the adiabaticity of the process was obtained. In this paper, we consider the crossing of the resonance of nonlinear coupling $2 Q_x -2 Q_y = 0$ using the same theoretical framework. We perform the analysis using a Hamiltonian model in which the nonlinear coupling resonance is excited and the corresponding dynamics is studied in detail, in particular looking at the phase-space topology and its evolution, in view of characterizing the emittance exchange phenomena. The theoretical results are then tested using a symplectic map. Thanks to this approach, scaling laws of general interest for applications are derived.
