对已有的 Z 变换时域有限差分法(Z-transformation Finite Difference Time Domain,Z-FDTD)在电磁波与非均匀磁化等离子体中的传输特性分析的计算误差问题进行了研究,并探讨了一种修正计算误差的Z变换时域有限差分方法(Modified Z-transform Finite Difference Time Domain,MZ-FDTD),以提升 Z-FDTD 方法对非均匀磁化等离子体的适用性.对MZ-FDTD和Z-FDTD之间的计算误差问题,通过严格的公式推导求得该误差的计算公式,并引入误差分析因子,对比分析了该误差受空间步长和非均匀磁化等离子体的物理特性的影响特征,在充分的误差分析与网格参数对比后,以电磁波在非均匀磁化等离子体中的传输特性为分析目标,举例说明了 MZ-FDTD的优越性.研究结果表明,相比于经典Z-FDTD,通过MZ-FDTD方法计算得到的数值结果具有更高的计算准确度,较低的运行时间和较少的运行内存占用.此外,对电磁波在非均匀等离子体中传输特性分析的举例说明也证明了相比于Z-FDTD,优化的Z-FDTD方法无论是在较低频段还是较高频段都保持较好的稳定性.在今后的工作中,使用MZ-FDTD方法研究非均匀磁化等离子体问题将会获得更好的计算结果,这项工作中的误差分析方法也将对某些计算电磁学在等离子体中的应用与优化工作起到一定的帮助作用.
A Modified Z-FDTD Based on Inhomogeneous Magnetized Plasma
A problem about the calculation error of the classical Z-transformation finite dif-ference time domain(Z-FDTD)method in the analysis of the transmission characteristics of electromagnetic wave and non-uniformly magnetized plasma is studied.A modified Z-transform finite difference time domain(MZ-FDTD)method is discussed to improve the applicability of the Z-FDTD method for non-uniformly magnetized plasmas.For the calculation error between MZ-FDTD and Z-FDTD,the calculation formula of the error is derived,and error analysis factor is introduced.The characteristics of the error affected by the spatial step size and the physical characteristics of non-uniformly magnetized plasma are compared and analysed.After sufficient error analysis and mesh parameter comparison,the advantages of MZ-FDTD are illus-trated by analysing the propagation characteristics of electromagnetic wave in inhomogeneous magnetized plasma as the objective.The research results show that compared with the clas-sical Z-FDTD,the numerical results obtained by MZ-FDTD method have higher calculation accuracy,lower running time and memory consumption.In addition,the analysis of electro-magnetic wave transmission characteristics in non-uniform plasma also proves that compared with Z-FDTD,the numerical results obtained by MZ-FDTD method are relative stability,no matter whether it's in the low band.In the future,using MZ-FDTD method to study the problem of non-uniformly magnetized plasma will get better calculation results,and the error analysis method in this work will also play a helpful role in the application and optimization of some computational electro-magnetics in plasma.
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维普
