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dc.contributor.authorLucas, Julio
dc.contributor.authorEchevarría Ecenarro, Víctor ORCID
dc.date.accessioned2021-04-23T07:39:37Z
dc.date.available2021-04-23T07:39:37Z
dc.date.issued2021-03
dc.identifier.citationIEEE Transactions On Nuclear Science 68(3) : 270-278 (2021)es_ES
dc.identifier.issn0018-9499
dc.identifier.issn1558-1578
dc.identifier.urihttp://hdl.handle.net/10810/51157
dc.description.abstractIt has long been known that the ellipse normally used to model the phase space extension of a beam in linear dynamics may be represented by a complex number which can be interpreted similar to a complex impedance in electrical circuits, so that classical electrical methods might be used for the design of such beam transport lines. However, this method has never been fully developed, and only the transport transformation of single particular elements, like drift spaces or quadrupoles, has been presented in the past. In this article, we complete the complex formalism of linear beam dynamics by obtaining a general differential equation and solving it, to show that the general transformation of a linear beam line is a complex Moebius transformation. This result opens the possibility of studying the effect of the beam line on complete regions of the complex plane and not only on a single point. Taking advantage of this capability of the formalism, we also obtain an important result in the theory of the transport through a periodic line, proving that the invariant points of the transformation are only a special case of a more general structure of the solution, which are the invariant circles of the one-period transformation. Among other advantages, this provides a new description of the betatron functions beating in case of a mismatched injection in a circular acceleratores_ES
dc.description.sponsorshipThis work was supported in part by the Ministerio de Asuntos Economicos y Transformacion Digital (MINECO) under Grant DPI2017-82373-R and in part by Universidad del Pais Vasco/Euskal Herriko Univertsitatea (UPV/EHU) under Grant GIU18/196es_ES
dc.language.isoenges_ES
dc.publisherIEEE-Institute of Electrical and Electronics Engineerses_ES
dc.relationinfo:eu-repo/grantAgreement/MINECO/DPI2017-82373-Res_ES
dc.rightsinfo:eu-repo/semantics/openAccesses_ES
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/es/*
dc.subjectparticle beamses_ES
dc.subjectlenseses_ES
dc.subjecttransformses_ES
dc.subjectshapees_ES
dc.subjectRiccati equationses_ES
dc.subjectlicenseses_ES
dc.subjectelectromagneticses_ES
dc.subjectlinear beam dynamicses_ES
dc.subjectMoebius transformationes_ES
dc.subjectparticle acceleratorses_ES
dc.subjectTwiss parameterses_ES
dc.titleComplex Formalism of the Linear Beam Dynamicses_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 License (CC BY 4.0)es_ES
dc.rights.holderAtribución 3.0 España*
dc.relation.publisherversionhttps://ieeexplore-ieee-org.ehu.idm.oclc.org/document/9354829es_ES
dc.identifier.doi10.1109/TNS.2021.3059802
dc.departamentoesElectricidad y electrónicaes_ES
dc.departamentoeuElektrizitatea eta elektronikaes_ES


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This work is licensed under a Creative Commons Attribution 4.0 License (CC BY 4.0)
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