Topological Torus Bifurcations and Applications to Ion Traps

拓扑环面分叉及其在离子阱中的应用

• 批准号: 0407521
• 负责人: Andrew Szeri
• 金额: --
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-06-15 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0407521&HistoricalAwards=false
• 关键词: Topological; Torus; Bifurcations; Applications; Ion

Proposal: DMS-0407521PI: Andrew J SzeriInstitution: University of California BerkeleyTitle: Topological Torus Bifurcations and Applications to Ion TrapsABSTRACTIon traps are devices used to contain charged particles, and for highly selective mass spectroscopy. For a nonlinear trap subjected to secondary end-cap excitation and including a buffer gas, the equations of motion are coupled, damped, nonlinear, quasiperiodic Mathieu equations. The attractors for this system are non-trivially "knotted" in the 4-D phase space. The investigator and his colleagues have developed tools to characterize them topologically and geometrically, and have identified new bifurcations associated with their changes of type. Important outstanding problems include: how topological equivalence of attractors through torus braids and through surfaces is related; whether chaos is associated with transverse intersections of stable and unstable manifolds of saddle-type knotted tori.A sequence of the newly identified bifurcations leads to chaotic dynamics through a route observed, but not yet characterized. In some cases, two bifurcations bound extremely sharp resonances which are useful in applications.The new knowledge being developed about this system can be used to suggest new operating regimes for ion traps used in discrimination of species in mass spectroscopy. The sharp resonances already observed suggest the use of an ion trap as a tunable electromechanical filter. Two similar ion trap systems may be used for the purpose of masking and unmasking signals for secure communication. Finally, the results suggest that a trapped charged particle or ion can be used as an accelerometer and gyroscope. These technological innovations or improvements flow directly from a detailed understanding of the underlying mathematics.This award is co-funded by the Applied Mathematics and Topology programs of the Division of Mathematical Sciences and the Analytical and Surface Chemistry program of the Chemistry Division under the umbrella of the NSF-wide Mathematical Sciences Priority Area.

提案：DMS-0407521 PI：Andrew J Szeri机构：加州伯克利大学标题：拓扑环面分叉和应用于离子阱摘要离子阱是用来包含带电粒子的设备，并用于高选择性质谱。 对于二次端盖激励和缓冲气体的非线性陷阱，运动方程是耦合的、阻尼的、非线性的、准周期的Mathieu方程。该系统的吸引子在4-D相空间中是非平凡的“打结”。研究人员和他的同事们已经开发出工具来描述它们的拓扑和几何特征，并确定了与它们的类型变化相关的新分叉。重要的悬而未决的问题包括：通过环辫和通过表面的吸引子的拓扑等价性如何相关;混乱是否与鞍型打结环的稳定和不稳定流形的横向交叉有关。新发现的分叉序列通过一条路径导致混乱动力学观察到，但尚未表征。在某些情况下，两个分叉约束非常尖锐的共振，这是有用的应用。新的知识正在开发的关于这个系统可以用来建议新的操作制度的离子阱用于在质谱中的物种的歧视。 已经观察到的尖锐共振表明使用离子阱作为可调谐机电滤波器。两个类似的离子阱系统可以用于屏蔽和暴露信号以进行安全通信的目的。最后，结果表明，被捕获的带电粒子或离子可以用作加速度计和陀螺仪。 这些技术创新或改进直接源于对基础数学的详细理解。该奖项由数学科学部的应用数学和拓扑学计划以及化学部的分析和表面化学计划共同资助，该计划隶属于NSF范围内的数学科学优先领域。