{"title":"用于陀螺动力学模拟的线性化福克-普朗克碰撞模型","authors":"A von Boetticher, F I Parra, M Barnes","doi":"10.1088/1361-6587/ad6c7c","DOIUrl":null,"url":null,"abstract":"We introduce a gyrokinetic, linearised Fokker–Planck collision model that satisfies conservation laws and is accurate at arbitrary collisionalities. The differential test-particle component of the operator is exact; the integral field-particle component is approximated using a spherical harmonic and a modified Laguerre polynomial expansion developed by Hirshman and Sigmar (1976 <italic toggle=\"yes\">Phys. Fluids</italic> <bold>19</bold> 1532). The numerical methods of the implementation in the δ<italic toggle=\"yes\">f</italic>-gyrokinetic code <inline-formula>\n<tex-math><?CDATA $\\texttt{stella}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mtext mathvariant=\"monospace\">stella</mml:mtext></mml:mrow></mml:math><inline-graphic xlink:href=\"ppcfad6c7cieqn1.gif\"></inline-graphic></inline-formula> (Barnes <italic toggle=\"yes\">et al</italic> 2019 <italic toggle=\"yes\">J. Comput. Phys.</italic> <bold>391</bold> 365–80) are discussed, and conservation properties of the operator are demonstrated. The collision model is then benchmarked against the collision model of the gyrokinetic solver <monospace>GS2</monospace> in the limiting cases of a reduced test-particle collision operator and energy- and momentum-conserving operator. The accuracy of the full collision model is investigated by solving the parallel Spitzer-Härm problem for the transport coefficients. It is shown that retaining collisional energy flux and higher-order terms in the field-particle operator reduces errors in the transport coefficients from 10%–25% for a simple momentum- and energy-conserving model to under 1%.","PeriodicalId":20239,"journal":{"name":"Plasma Physics and Controlled Fusion","volume":"2 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Linearised Fokker–Planck collision model for gyrokinetic simulations\",\"authors\":\"A von Boetticher, F I Parra, M Barnes\",\"doi\":\"10.1088/1361-6587/ad6c7c\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a gyrokinetic, linearised Fokker–Planck collision model that satisfies conservation laws and is accurate at arbitrary collisionalities. The differential test-particle component of the operator is exact; the integral field-particle component is approximated using a spherical harmonic and a modified Laguerre polynomial expansion developed by Hirshman and Sigmar (1976 <italic toggle=\\\"yes\\\">Phys. Fluids</italic> <bold>19</bold> 1532). The numerical methods of the implementation in the δ<italic toggle=\\\"yes\\\">f</italic>-gyrokinetic code <inline-formula>\\n<tex-math><?CDATA $\\\\texttt{stella}$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mtext mathvariant=\\\"monospace\\\">stella</mml:mtext></mml:mrow></mml:math><inline-graphic xlink:href=\\\"ppcfad6c7cieqn1.gif\\\"></inline-graphic></inline-formula> (Barnes <italic toggle=\\\"yes\\\">et al</italic> 2019 <italic toggle=\\\"yes\\\">J. Comput. Phys.</italic> <bold>391</bold> 365–80) are discussed, and conservation properties of the operator are demonstrated. The collision model is then benchmarked against the collision model of the gyrokinetic solver <monospace>GS2</monospace> in the limiting cases of a reduced test-particle collision operator and energy- and momentum-conserving operator. The accuracy of the full collision model is investigated by solving the parallel Spitzer-Härm problem for the transport coefficients. It is shown that retaining collisional energy flux and higher-order terms in the field-particle operator reduces errors in the transport coefficients from 10%–25% for a simple momentum- and energy-conserving model to under 1%.\",\"PeriodicalId\":20239,\"journal\":{\"name\":\"Plasma Physics and Controlled Fusion\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Plasma Physics and Controlled Fusion\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6587/ad6c7c\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, FLUIDS & PLASMAS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Plasma Physics and Controlled Fusion","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1361-6587/ad6c7c","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, FLUIDS & PLASMAS","Score":null,"Total":0}
Linearised Fokker–Planck collision model for gyrokinetic simulations
We introduce a gyrokinetic, linearised Fokker–Planck collision model that satisfies conservation laws and is accurate at arbitrary collisionalities. The differential test-particle component of the operator is exact; the integral field-particle component is approximated using a spherical harmonic and a modified Laguerre polynomial expansion developed by Hirshman and Sigmar (1976 Phys. Fluids19 1532). The numerical methods of the implementation in the δf-gyrokinetic code stella (Barnes et al 2019 J. Comput. Phys.391 365–80) are discussed, and conservation properties of the operator are demonstrated. The collision model is then benchmarked against the collision model of the gyrokinetic solver GS2 in the limiting cases of a reduced test-particle collision operator and energy- and momentum-conserving operator. The accuracy of the full collision model is investigated by solving the parallel Spitzer-Härm problem for the transport coefficients. It is shown that retaining collisional energy flux and higher-order terms in the field-particle operator reduces errors in the transport coefficients from 10%–25% for a simple momentum- and energy-conserving model to under 1%.
期刊介绍:
Plasma Physics and Controlled Fusion covers all aspects of the physics of hot, highly ionised plasmas. This includes results of current experimental and theoretical research on all aspects of the physics of high-temperature plasmas and of controlled nuclear fusion, including the basic phenomena in highly-ionised gases in the laboratory, in the ionosphere and in space, in magnetic-confinement and inertial-confinement fusion as well as related diagnostic methods.
Papers with a technological emphasis, for example in such topics as plasma control, fusion technology and diagnostics, are welcomed when the plasma physics is an integral part of the paper or when the technology is unique to plasma applications or new to the field of plasma physics. Papers on dusty plasma physics are welcome when there is a clear relevance to fusion.