{"title":"球面场阴极二极管系统的数学建模","authors":"Valeriya S. Novikova, E. Vinogradova","doi":"10.1109/VMNEYR.2016.7880414","DOIUrl":null,"url":null,"abstract":"The rotationally symmetric diode system with a field cathode is under investigation. The shape of the field cathode is sphere-on-cone. The anode is a part of a sphere. In this paper two cases are considered, when the interior of system’s domain is filled with two and three different dielectrics. To calculate the electrostatic potential distribution the method of separation of variables is used. The solution of the boundary-value problem for the Laplace’s equation in the spherical coordinates is found an analytical form as the Legendre functions series.","PeriodicalId":407958,"journal":{"name":"2016 Young Researchers in Vacuum Micro/Nano Electronics (VMNE-YR)","volume":"59 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mathematical modeling of a diode system with a spherical field cathode\",\"authors\":\"Valeriya S. Novikova, E. Vinogradova\",\"doi\":\"10.1109/VMNEYR.2016.7880414\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The rotationally symmetric diode system with a field cathode is under investigation. The shape of the field cathode is sphere-on-cone. The anode is a part of a sphere. In this paper two cases are considered, when the interior of system’s domain is filled with two and three different dielectrics. To calculate the electrostatic potential distribution the method of separation of variables is used. The solution of the boundary-value problem for the Laplace’s equation in the spherical coordinates is found an analytical form as the Legendre functions series.\",\"PeriodicalId\":407958,\"journal\":{\"name\":\"2016 Young Researchers in Vacuum Micro/Nano Electronics (VMNE-YR)\",\"volume\":\"59 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2016 Young Researchers in Vacuum Micro/Nano Electronics (VMNE-YR)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/VMNEYR.2016.7880414\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2016 Young Researchers in Vacuum Micro/Nano Electronics (VMNE-YR)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/VMNEYR.2016.7880414","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Mathematical modeling of a diode system with a spherical field cathode
The rotationally symmetric diode system with a field cathode is under investigation. The shape of the field cathode is sphere-on-cone. The anode is a part of a sphere. In this paper two cases are considered, when the interior of system’s domain is filled with two and three different dielectrics. To calculate the electrostatic potential distribution the method of separation of variables is used. The solution of the boundary-value problem for the Laplace’s equation in the spherical coordinates is found an analytical form as the Legendre functions series.
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