dorsal/arxiv
View SchemaSuccessive approximations for charged particle motion
| Authors | Georg H. Hoffstaetter |
|---|---|
| Categories | |
| ArXiv ID | physics/0006008 |
| URL | https://arxiv.org/abs/physics/0006008 |
| Journal | Ultramicroscopy 81 (2000) 111-121 |
Abstract
Single particle dynamics in electron microscopes, ion or electron lithographic instruments, particle accelerators, and particle spectrographs is described by weakly nonlinear ordinary differential equations. Therefore, the linear part of the equation of motion is usually solved and the nonlinear effects are then found in successive order by iteration methods. A Hamiltonian nature of these equations can lead to simplified computations of particle transport through an optical device when a suitable computational method is used. Many ingenious microscopic and lithographic devices were found by H. Rose and his group due to the simple structure of the eikonal method. In the area of accelerator physics the eikonal method has never become popular. Here I will therefore generalize the eikonal method and derive it from a Hamiltonian quite familiar to the accelerator physics community. With the event of high energy polarized electron beams and plans for high energy proton beams, nonlinear effects in spin motion have become important in high energy accelerators. I will introduce a successive approximation for the nonlinear effects in the coupled spin and orbit motion of charged particles which resembles some of the simplifications resulting from the eikonal method for the pure orbit motion.
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"abstract": "Single particle dynamics in electron microscopes, ion or electron\nlithographic instruments, particle accelerators, and particle spectrographs is\ndescribed by weakly nonlinear ordinary differential equations. Therefore, the\nlinear part of the equation of motion is usually solved and the nonlinear\neffects are then found in successive order by iteration methods. A Hamiltonian\nnature of these equations can lead to simplified computations of particle\ntransport through an optical device when a suitable computational method is\nused. Many ingenious microscopic and lithographic devices were found by H. Rose\nand his group due to the simple structure of the eikonal method. In the area of\naccelerator physics the eikonal method has never become popular. Here I will\ntherefore generalize the eikonal method and derive it from a Hamiltonian quite\nfamiliar to the accelerator physics community. With the event of high energy\npolarized electron beams and plans for high energy proton beams, nonlinear\neffects in spin motion have become important in high energy accelerators. I\nwill introduce a successive approximation for the nonlinear effects in the\ncoupled spin and orbit motion of charged particles which resembles some of the\nsimplifications resulting from the eikonal method for the pure orbit motion.",
"arxiv_id": "physics/0006008",
"authors": [
"Georg H. Hoffstaetter"
],
"categories": [
"physics.acc-ph"
],
"journal_ref": "Ultramicroscopy 81 (2000) 111-121",
"title": "Successive approximations for charged particle motion",
"url": "https://arxiv.org/abs/physics/0006008"
},
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