{"title":"Green function for the Grad-Shafranov operator","authors":"Julio Herrera Velázquez","doi":"10.31349/revmexfise.19.010211","DOIUrl":null,"url":null,"abstract":"The Grad-Shafranov equation, often written in cylindrical coordinates, is an elliptic partial differential equation in two dimensions. It describes magnetohydrodynamic equilibria in axisymmetric toroidal plasmas, such as tokamaks, and yields the poloidal magnetic flux function, which is related to the azimuthal component of the vector potential for the magnetic field produced by a circular (toroidal) current density. The Green function for the differential operator can be obtained from the vector potential for the magnetic field of a circular current loop, which is a typical problem in magnetostatics. The purpose of the paper is to collect results scattered in electrodynamics and plasma physics textbooks for the benefit of students in the field, as well as attracting the attention of a wider audience, in the context of electrodynamics and partial differential equations.","PeriodicalId":49600,"journal":{"name":"Revista Mexicana De Fisica E","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Mexicana De Fisica E","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31349/revmexfise.19.010211","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Social Sciences","Score":null,"Total":0}
引用次数: 0
Abstract
The Grad-Shafranov equation, often written in cylindrical coordinates, is an elliptic partial differential equation in two dimensions. It describes magnetohydrodynamic equilibria in axisymmetric toroidal plasmas, such as tokamaks, and yields the poloidal magnetic flux function, which is related to the azimuthal component of the vector potential for the magnetic field produced by a circular (toroidal) current density. The Green function for the differential operator can be obtained from the vector potential for the magnetic field of a circular current loop, which is a typical problem in magnetostatics. The purpose of the paper is to collect results scattered in electrodynamics and plasma physics textbooks for the benefit of students in the field, as well as attracting the attention of a wider audience, in the context of electrodynamics and partial differential equations.
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The Revista Mexicana de Física (Rev. Mex. Fis.) publishes original papers of interest to our readers from the physical science com unity. Language may be English or Spanish, however, given the nature of our readers, English is recommended. Articles are classified as follows:
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