{"title":"纵向束梁失稳阈值的计算","authors":"R. Baartman, M. Dyachkov","doi":"10.1109/PAC.1993.309642","DOIUrl":null,"url":null,"abstract":"An integral equation derived from the linearized Vlasov equation has been used to find the instability thresholds in the case of space-charge impedance alone for various distribution functions. It has been found that the thresholds for the instability which are caused by the coupling between m=/spl plusmn/1 azimuthal modes may be obtained analytically for many practically used distributions. Moreover, the criterion determining these thresholds appears to be the same as that for thresholds beyond which no stationary distribution can be found.<<ETX>>","PeriodicalId":128308,"journal":{"name":"Proceedings of International Conference on Particle Accelerators","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Computation of longitudinal bunched beam instability thresholds\",\"authors\":\"R. Baartman, M. Dyachkov\",\"doi\":\"10.1109/PAC.1993.309642\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An integral equation derived from the linearized Vlasov equation has been used to find the instability thresholds in the case of space-charge impedance alone for various distribution functions. It has been found that the thresholds for the instability which are caused by the coupling between m=/spl plusmn/1 azimuthal modes may be obtained analytically for many practically used distributions. Moreover, the criterion determining these thresholds appears to be the same as that for thresholds beyond which no stationary distribution can be found.<<ETX>>\",\"PeriodicalId\":128308,\"journal\":{\"name\":\"Proceedings of International Conference on Particle Accelerators\",\"volume\":\"9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-05-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of International Conference on Particle Accelerators\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/PAC.1993.309642\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of International Conference on Particle Accelerators","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/PAC.1993.309642","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Computation of longitudinal bunched beam instability thresholds
An integral equation derived from the linearized Vlasov equation has been used to find the instability thresholds in the case of space-charge impedance alone for various distribution functions. It has been found that the thresholds for the instability which are caused by the coupling between m=/spl plusmn/1 azimuthal modes may be obtained analytically for many practically used distributions. Moreover, the criterion determining these thresholds appears to be the same as that for thresholds beyond which no stationary distribution can be found.<>
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