PDRK: A General Kinetic Dispersion Relation Solver for Magnetized Plasma

XIE Huasheng (谢华生); XIAO Yong (肖湧)

doi:10.1088/1009-0630/18/2/01

Plasma Science and Technology > 2016 > 18(2): 97-107. > DOI: 10.1088/1009-0630/18/2/01

XIE Huasheng (谢华生), XIAO Yong (肖湧). PDRK: A General Kinetic Dispersion Relation Solver for Magnetized Plasma[J]. Plasma Science and Technology, 2016, 18(2): 97-107. DOI: 10.1088/1009-0630/18/2/01

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PDRK: A General Kinetic Dispersion Relation Solver for Magnetized Plasma

Institute for Fusion Theory and Simulation and the Department of Physics, Zhejiang University, Hangzhou 310027, China

Funds: supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2015GB110003, 2011GB105001, 2013GB111000), National Natural Science Foundation of China (No. 91130031), the Recruitment Program of Global Youth Experts

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Received Date: April 21, 2015

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Abstract

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 two-dimensional wavevectors, and for electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with relative parallel velocity flows between species.
- plasma physics,
- dispersion relation,
- kinetic,
- waves,
- instabilities,
- linear system,
- matrix eigenvalue

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References

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