PDRK：A General Kinetic Dispersion Relation Solver for Magnetized Plasma
A general,fast,and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations.The plasma dispersion function is approximated by J-pole expansion.Subsequently,the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent l...
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| Published in | Plasma science & technology Vol. 18; no. 2; pp. 97 - 107 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.02.2016
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1009-0630 |
| DOI | 10.1088/1009-0630/18/2/01 |
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| Abstract | A general,fast,and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations.The plasma dispersion function is approximated by J-pole expansion.Subsequently,the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system.Numerical solutions for the least damped or fastest growing modes using an 8-pole expansion are generally accurate;more strongly damped modes are less accurate,but are less likely to be of physical interest.In contrast to conventional approaches,such as Newton＇s iterative method,this approach can give either all the solutions in the system or a few solutions around the initial guess.It is also free from convergence problems.The approach is demonstrated for electrostatic dispersion equations with one-dimensional and twodimensional wavevectors,and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species. |
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| AbstractList | A general,fast,and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations.The plasma dispersion function is approximated by J-pole expansion.Subsequently,the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system.Numerical solutions for the least damped or fastest growing modes using an 8-pole expansion are generally accurate;more strongly damped modes are less accurate,but are less likely to be of physical interest.In contrast to conventional approaches,such as Newton＇s iterative method,this approach can give either all the solutions in the system or a few solutions around the initial guess.It is also free from convergence problems.The approach is demonstrated for electrostatic dispersion equations with one-dimensional and twodimensional wavevectors,and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species. A general, fast, and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations. The plasma dispersion function is approximated by J-pole expansion. Subsequently, the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system. Numerical solutions for the least damped or fastest growing modes using an 8-pole expansion are generally accurate; more strongly damped modes are less accurate, but are less likely to be of physical interest. In contrast to conventional approaches, such as Newton's iterative method, this approach can give either all the solutions in the system or a few solutions around the initial guess. It is also free from convergence problems. The approach is demonstrated for electrostatic dispersion equations with one-dimensional and two-dimensional wavevectors, and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species. |
| Author | 谢华生 肖湧 |
| AuthorAffiliation | Institute for Fusion Theory and Simulation and the Department of Physics,Zhejiang University, Hangzhou 310027, China |
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| Cites_doi | 10.1017/S0022377800008606 10.1086/506172 10.1063/1.3610378 10.1017/S0022377800013519 10.1887/0750301171 10.1063/1.4823722 10.1063/1.524411 10.1063/1.4812196 10.1063/1.4736848 10.1063/1.1694133 10.1063/1.4822332 10.1017/S0022377800002270 10.1088/0741-3335/47/4/006 10.1103/PhysRevE.81.036402 10.1088/0032-1028/25/6/007 10.1063/1.2769968 10.1063/1.3132628 10.1016/j.cpc.2013.10.012 10.1063/1.874180 10.1063/1.4736980 10.1088/0004-637X/773/1/8 10.1238/Physica.Topical.084a00206 10.1017/CBO9780511551512 10.1017/CBO9780511809125 10.1063/1.4831761 |
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| Notes | plasma physics dispersion relation kinetic waves instabilities linear system matrix eigenvalue XIE Huasheng , XlAO Yong （ Institute for Fusion Theory and Simulation and the Department of Physics Zhejiang University, Hangzhou 310027, China） A general,fast,and effective approach is developed for numerical calculation of kinetic plasma linear dispersion relations.The plasma dispersion function is approximated by J-pole expansion.Subsequently,the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system.Numerical solutions for the least damped or fastest growing modes using an 8-pole expansion are generally accurate;more strongly damped modes are less accurate,but are less likely to be of physical interest.In contrast to conventional approaches,such as Newton＇s iterative method,this approach can give either all the solutions in the system or a few solutions around the initial guess.It is also free from convergence problems.The approach is demonstrated for electrostatic dispersion equations with one-dimensional and twodimensional wavevectors,and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species. 34-1187/TL ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
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| References | 23 24 Ronnmark K (2) 1982 25 26 27 28 Stix T (19) 1992 Lin Y (9) 2005; 47 Howes G G (29) 2006; 651 Cereceda C (11) 2000; 2000 10 Bao J (22) 2014; 56 12 13 14 15 16 17 Verscharen D (4) 2013; 773 18 Ronnmark K (3) 1983; 25 1 Xie H S (20) 2014; 89 5 6 7 8 21 |
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| SubjectTerms | Approximation Convergence Dispersion Equivalence Linear systems Mathematical analysis Mathematical models Solvers 动力学 数值计算 求解 牛顿迭代法 矩阵特征值问题 磁化等离子体 色散关系 麦克斯韦分布 |
| Title | PDRK：A General Kinetic Dispersion Relation Solver for Magnetized Plasma |
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