Time: 2014-06-04 14:00:00
Speaker: Wei Zhang, Hua-sheng XIE [IFTS]
Place: Rm. 413, Bld. 11#, Yuquan Campus
Abstract: Topic:Magnetohydrodynamics equilibria with toroidal and poloidal flow
Speaker: Wei,Zhang (张威)
Topic: A Full-Matrix Approach to Solve Kinetic Plasma Dispersion Relations
Speaker: Hua-sheng XIE(谢华生)
Abstract:
Due to the richness of waves and instabilities in astrophysical, space, laser, and laboratory plasmas, it is of practical interest to study the corresponding linear dispersion relations. However, the complications of plasma dispersion function Z and n-th order summation of Bessel functions in kinetic plasma dispersion relations are difficult to be solved not only analytically but also numerically, due to time-costly and singularity. A general, fast, and effective approach is developed to numerically solve this problem based on J-pole expansion of Z function, which is still accurate for most modes except the little interesting heavily damped modes. Then, the task is transformed to a matrix eigenvalue problem of an equivalent linear system, which can be solved with no difficulty using standard matrix solver. Contrast to conventional approaches, such as Newton’s iterative method, this approach can give either all solutions in the system or few solutions around the initial guess, and is free from convergent difficulties. The approach is demonstrated from simple electrostatic one-dimension Landau damping and three-dimension Harris dispersion relations to complicated gyro-kinetic and full kinetic electromagnetic magnetized dispersion relations. Besides the usages to practical problems, this approach can also provide a rigorous checking of the validities of simplified models, such as Darwin, gyro-kinetic (e.g., the ongoing radio-frequency waves works in GeFi and GTC), and fluid models.