Giuseppe Dattoli, Mariano Carpanese, Emanuele Di Palma, Alberto Petralia
{"title":"关于磁多极多项式的说明","authors":"Giuseppe Dattoli, Mariano Carpanese, Emanuele Di Palma, Alberto Petralia","doi":"10.1016/S0034-4877(24)00014-4","DOIUrl":null,"url":null,"abstract":"<div><p>A family of two variable polynomials naturally emerges from the expansion in multipoles of a magnetic field. The order of the expansion fixes the polynomial degree and the multipolar content: dipole, quadrupole, sextupole and so on. The associated polynomials share analogies with Hermite-type families. The relevant properties are studied, within an umbral framework, which simplifies the derivation of the associated mathematical technicalities. We take advantage from this analogy to present a fairly general discussion about the properties of the “magnetic” polynomials. We touch on the possibility of embedding the results of the present study in a dedicated algorithm for the analysis of the transport of a charged beam in a magnetic structure.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0034487724000144/pdfft?md5=e7262f46398b4f88b7e6034a078ff7ac&pid=1-s2.0-S0034487724000144-main.pdf","citationCount":"0","resultStr":"{\"title\":\"A note on the magnetic multipole polynomials\",\"authors\":\"Giuseppe Dattoli, Mariano Carpanese, Emanuele Di Palma, Alberto Petralia\",\"doi\":\"10.1016/S0034-4877(24)00014-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A family of two variable polynomials naturally emerges from the expansion in multipoles of a magnetic field. The order of the expansion fixes the polynomial degree and the multipolar content: dipole, quadrupole, sextupole and so on. The associated polynomials share analogies with Hermite-type families. The relevant properties are studied, within an umbral framework, which simplifies the derivation of the associated mathematical technicalities. We take advantage from this analogy to present a fairly general discussion about the properties of the “magnetic” polynomials. We touch on the possibility of embedding the results of the present study in a dedicated algorithm for the analysis of the transport of a charged beam in a magnetic structure.</p></div>\",\"PeriodicalId\":49630,\"journal\":{\"name\":\"Reports on Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0034487724000144/pdfft?md5=e7262f46398b4f88b7e6034a078ff7ac&pid=1-s2.0-S0034487724000144-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Reports on Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0034487724000144\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000144","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
A family of two variable polynomials naturally emerges from the expansion in multipoles of a magnetic field. The order of the expansion fixes the polynomial degree and the multipolar content: dipole, quadrupole, sextupole and so on. The associated polynomials share analogies with Hermite-type families. The relevant properties are studied, within an umbral framework, which simplifies the derivation of the associated mathematical technicalities. We take advantage from this analogy to present a fairly general discussion about the properties of the “magnetic” polynomials. We touch on the possibility of embedding the results of the present study in a dedicated algorithm for the analysis of the transport of a charged beam in a magnetic structure.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
