{"title":"随机速度矩展开中朗道碰撞算子的精确不可约矩","authors":"J. Ji, J. Spencer, E. Held","doi":"10.1088/2516-1067/ab7d0f","DOIUrl":null,"url":null,"abstract":"Exact moments of the Landau collision operator are calculated for the irreducible Hermite polynomials written in terms of the random-velocity variable. We present closed, algebraic formulas which can be implemented in computer algebra systems. The formulas reproduce the results for the total-velocity moment expansion (J-Y Ji and E D Held, 2006 Phys. Plasmas 13 102 103) and for the random-velocity moment expansion with the small mass-ratio approximation (J-Y Ji and E D Held, 2008 Phys. Plasmas 15 102 101). For verification of the formulas, example calculations for several lowest order moments are presented. The collisional moments can be applied in the derivations of Braginskii and integral (nonlocal) closures for arbitrary relative flow velocity between electrons and ions.","PeriodicalId":36295,"journal":{"name":"Plasma Research Express","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Exact irreducible moments of the Landau collision operator in the random-velocity moment expansion\",\"authors\":\"J. Ji, J. Spencer, E. Held\",\"doi\":\"10.1088/2516-1067/ab7d0f\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Exact moments of the Landau collision operator are calculated for the irreducible Hermite polynomials written in terms of the random-velocity variable. We present closed, algebraic formulas which can be implemented in computer algebra systems. The formulas reproduce the results for the total-velocity moment expansion (J-Y Ji and E D Held, 2006 Phys. Plasmas 13 102 103) and for the random-velocity moment expansion with the small mass-ratio approximation (J-Y Ji and E D Held, 2008 Phys. Plasmas 15 102 101). For verification of the formulas, example calculations for several lowest order moments are presented. The collisional moments can be applied in the derivations of Braginskii and integral (nonlocal) closures for arbitrary relative flow velocity between electrons and ions.\",\"PeriodicalId\":36295,\"journal\":{\"name\":\"Plasma Research Express\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2020-03-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Plasma Research Express\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/2516-1067/ab7d0f\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ORTHOPEDICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Plasma Research Express","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/2516-1067/ab7d0f","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ORTHOPEDICS","Score":null,"Total":0}
引用次数: 1
摘要
对于用随机速度变量表示的不可约埃尔米特多项式，计算了朗道碰撞算子的精确矩。我们提出了可以在计算机代数系统中实现的封闭代数公式。这些公式再现了总速度矩展开的结果(J-Y Ji and E D Held, 2006 Phys.)。等离子体13 102 103)和小质量比近似下的随机速度矩膨胀(J-Y Ji, E D Held, 2008)。等离子体15 102 101)。为了验证公式的正确性，给出了几种最低阶矩的算例。碰撞矩可以应用于任意电子和离子之间相对流动速度的Braginskii和积分(非局部)闭包的推导。
Exact irreducible moments of the Landau collision operator in the random-velocity moment expansion
Exact moments of the Landau collision operator are calculated for the irreducible Hermite polynomials written in terms of the random-velocity variable. We present closed, algebraic formulas which can be implemented in computer algebra systems. The formulas reproduce the results for the total-velocity moment expansion (J-Y Ji and E D Held, 2006 Phys. Plasmas 13 102 103) and for the random-velocity moment expansion with the small mass-ratio approximation (J-Y Ji and E D Held, 2008 Phys. Plasmas 15 102 101). For verification of the formulas, example calculations for several lowest order moments are presented. The collisional moments can be applied in the derivations of Braginskii and integral (nonlocal) closures for arbitrary relative flow velocity between electrons and ions.
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