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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Bibliographic Details
Published inPlasma science & technology Vol. 18; no. 2; pp. 97 - 107
Main Author 谢华生 肖湧
Format Journal Article
LanguageEnglish
Published 01.02.2016
Subjects
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
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Summary: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.
Bibliography: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
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SourceType-Scholarly Journals-1
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ISSN:1009-0630
DOI:10.1088/1009-0630/18/2/01