Theoretical Investigations of Particle Channeling in Crystals

当高能带电粒子束与主要晶体轴或平面对齐时，就会发生粒子通道。通道对于我们理解固体中的粒子运动在基础层面上做出了重要的贡献，同样重要的是，它在物理和技术领域也有许多应用。此外，通道是动力系统和随机过程中有趣和具有挑战性的数学问题的新来源。一个完整的理解通道需要详细的知识通道粒子运动和空间和动量密度的粒子，因为他们穿透晶体。埃利森研究通道的数学方法将继续包括：应变层超晶格和其他扭曲晶体中的通道效应，通道辐射和相关的量子电动力学过程；随机介质中粒子运动的多重散射效应在动力系统的背景下观察完美晶体的通灵。这项研究将加深我们对通道的认识，扩展其用途并导致新的应用。此外，为解决这些问题而开发的动力系统和概率方法将具有普遍的适用性，并将在数学科学的其他领域具有重要意义。

Particle channeling occurs when an energetic charged particle beam is aligned with a major crystal axis or plane. Channeling has contributed in important ways to our understanding of particle motion in solids at the fundamental level and just as significantly has led to numerous applications in physics and technology. Furthermore, channeling is a new source of interesting and challenging mathematical problems in dynamical systems and stochastic processes. A complete understanding of channeling requires detailed knowledge of the channeling particle motion and the spatial and momentum densities of the particles as they penetrate the crystal. Ellison's mathematical approach to the study of channeling will continue including: channeling effects in strain-layer superlattices and other distorted crystals, channeling radiation and related quantum electrodynamical processes; multiple scattering effects viewed as particle motion in a random media; and channeling in perfect crystals viewed within the context of dynamical systems. This research will deepen our knowledge of channeling, extend its usefulness and lead to new applications. Furthermore, the dynamical systems and probabilistic methods developed to solve these problems will be of general applicability and will have importance in other areas of mathematical science.