跑道型微子加速器中相位运动的稳定性
Stability of the phase motion in race-track microtons
AI总结：
本文利用保面积映射模拟跑道型微子加速器中电子的相位振荡，研究了原点非线性稳定性及其随同步相位变化的稳定域演化，并阐明了双曲点不变曲线的作用。
摘要：
我们利用一个在原点具有不动点的保面积映射来模拟跑道型微子加速器中电子的相位振荡，该原点代表束流中参考粒子的同步轨迹。我们根据同步相位（即注入时同步粒子的相位）研究原点的非线性稳定性。我们估计了原点周围稳定域的大小和形状，其主要连通分量由最后一条旋转不变曲线包围。我们描述了随着同步相位变化时稳定域的演化。此外，我们用某些哈密顿量的等值集来近似一些旋转不变曲线。最后，我们阐明了某些双曲（不动或周期）点的稳定与不稳定不变曲线的作用。
英文摘要：
We model the phase oscillations of electrons in race-track microtrons by means of an area preserving map with a fixed point at the origin, which represents the synchronous trajectory of a reference particle in the beam. We study the nonlinear stability of the origin in terms of the synchronous phase -- the phase of the synchronous particle at the injection. We estimate the size and shape of the stability domain around the origin, whose main connected component is enclosed by the last rotational invariant curve. We describe the evolution of the stability domain as the synchronous phase varies. Besides, we approximate some rotational invariant curves by level sets of certain Hamiltonians. Finally, we clarify the role of the stable and unstable invariant curves of some hyperbolic (fixed or periodic) points.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
