dorsal/arxiv
View SchemaParaxial Green's functions in Synchrotron Radiation theory
| Authors | Gianluca Geloni, Evgeni Saldin, Evgeni Schneidmiller, Mikhail Yurkov |
|---|---|
| Categories | |
| ArXiv ID | physics/0502120 |
| URL | https://arxiv.org/abs/physics/0502120 |
Abstract
This work contains a systematic treatment of single particle Synchrotron Radiation and some application to realistic beams with given cross section area, divergence and energy spread. Standard theory relies on several approximations whose applicability limits and accuracy are often forgotten. We begin remarking that on the one hand, a paraxial approximation can always be applied without loss of generality and with ultra relativistic accuracy. On the other hand, dominance of the acceleration field over the velocity part in the Lienard-Wiechert expressions is not always granted and constitutes a separate assumption, whose applicability is discussed. Treating Synchrotron Radiation in paraxial approximation we derive the equation for the slow varying envelope function of the Fourier components of the electric field vector. Calculations of Synchrotron Radiation properties performed by others showed that the phase of the Fourier components of the electric field vector differs from the phase of a virtual point source. In this paper we present a systematic, analytical description of this phase shift, calculating amplitude and phase of electric field from bending magnets, short magnets, two bending magnet system separated by a straight section (edge radiation) and undulator devices. We pay particular attention to region of applicability and accuracy of approximations used. Finally, taking advantage of results of analytical calculation presented in reduced form we analyze various features of radiation from a complex insertion device (set of two undulators with a focusing triplet in between) accounting for the influence of energy spread and electron beam emittance.
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"abstract": "This work contains a systematic treatment of single particle Synchrotron\nRadiation and some application to realistic beams with given cross section\narea, divergence and energy spread. Standard theory relies on several\napproximations whose applicability limits and accuracy are often forgotten. We\nbegin remarking that on the one hand, a paraxial approximation can always be\napplied without loss of generality and with ultra relativistic accuracy. On the\nother hand, dominance of the acceleration field over the velocity part in the\nLienard-Wiechert expressions is not always granted and constitutes a separate\nassumption, whose applicability is discussed. Treating Synchrotron Radiation in\nparaxial approximation we derive the equation for the slow varying envelope\nfunction of the Fourier components of the electric field vector. Calculations\nof Synchrotron Radiation properties performed by others showed that the phase\nof the Fourier components of the electric field vector differs from the phase\nof a virtual point source. In this paper we present a systematic, analytical\ndescription of this phase shift, calculating amplitude and phase of electric\nfield from bending magnets, short magnets, two bending magnet system separated\nby a straight section (edge radiation) and undulator devices. We pay particular\nattention to region of applicability and accuracy of approximations used.\nFinally, taking advantage of results of analytical calculation presented in\nreduced form we analyze various features of radiation from a complex insertion\ndevice (set of two undulators with a focusing triplet in between) accounting\nfor the influence of energy spread and electron beam emittance.",
"arxiv_id": "physics/0502120",
"authors": [
"Gianluca Geloni",
"Evgeni Saldin",
"Evgeni Schneidmiller",
"Mikhail Yurkov"
],
"categories": [
"physics.acc-ph"
],
"title": "Paraxial Green\u0027s functions in Synchrotron Radiation theory",
"url": "https://arxiv.org/abs/physics/0502120"
},
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