{"title":"具有能量损失和散列的铅笔束方程的解析解","authors":"Tobias Gebäck, M. Asadzadeh","doi":"10.1080/00411450.2012.671207","DOIUrl":null,"url":null,"abstract":"In this article, we derive equations approximating the Boltzmann equation for charged particle transport under the continuous slowing down assumption. The objective is to obtain analytical expressions that approximate the solution to the Boltzmann equation. The analytical expressions found are based on the Fermi-Eyges solution, but include correction factors to account for energy loss and spread. Numerical tests are also performed to investigate the validity of the approximations.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"41 1","pages":"325 - 336"},"PeriodicalIF":0.0000,"publicationDate":"2012-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2012.671207","citationCount":"4","resultStr":"{\"title\":\"Analytical Solutions for the Pencil-Beam Equation with Energy Loss and Straggling\",\"authors\":\"Tobias Gebäck, M. Asadzadeh\",\"doi\":\"10.1080/00411450.2012.671207\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we derive equations approximating the Boltzmann equation for charged particle transport under the continuous slowing down assumption. The objective is to obtain analytical expressions that approximate the solution to the Boltzmann equation. The analytical expressions found are based on the Fermi-Eyges solution, but include correction factors to account for energy loss and spread. Numerical tests are also performed to investigate the validity of the approximations.\",\"PeriodicalId\":49420,\"journal\":{\"name\":\"Transport Theory and Statistical Physics\",\"volume\":\"41 1\",\"pages\":\"325 - 336\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/00411450.2012.671207\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transport Theory and Statistical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/00411450.2012.671207\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transport Theory and Statistical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00411450.2012.671207","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Analytical Solutions for the Pencil-Beam Equation with Energy Loss and Straggling
In this article, we derive equations approximating the Boltzmann equation for charged particle transport under the continuous slowing down assumption. The objective is to obtain analytical expressions that approximate the solution to the Boltzmann equation. The analytical expressions found are based on the Fermi-Eyges solution, but include correction factors to account for energy loss and spread. Numerical tests are also performed to investigate the validity of the approximations.
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