Shift-Operator FDTD Method for Anisotropic Plasma in KDB Coordinates System

Abstract

Abstract-Electromagnetic (EM) problem model for anisotropic plasma in kDB coordinates system is set up. And the model includes almost all the respects of EM-problems for anisotropic plasma. Based on shift-operator finite difference time-domain (SO-FDTD) method, Maxwell equations and EM-field constitutive equations are solved and discrete difference scheme of each EM-field component is obtained. Then the propagation characteristics of eigen wave are expressed by the two components of electric displacement vector as well. Lastly, three typical examples are calculated by SO-FDTD method, and the results verify the effectiveness and exactness of SO-FDTD method in kDB coordinates system.

Improved Shift-Operator FDTD Method for Anisotropic Magnetized Cold Plasmas With Arbitrary Magnetic Field Declination

“…Subsequently, we employ a memory-minimized algorithm [23] to reduce memory requirement. It is seen from (11) that the order of jω in the rational polynomial function is lower in comparison with the SO-FDTD method introduced in [22] (for example, the order N = 4 and M = 6 in [22], N = 2 and M = 3 in this paper), which is advantageous for reducing the memory storage when adopting the memory-minimized algorithm. Introducing two auxiliary variables J x1 and J x2 , (14a) can be rewritten in the form of the following three equations:…”

“…The number of storage arrays used for each field Total number of the storage arrays 31 FDTD method SO-FDTD method proposed in [22] (based on the kDB coordinates system) Field components…”

“…To illuminate the validity of the proposed new SO-FDTD method in saving memory requirement, we compared the number of storage arrays used to store field quantities between three SO-FDTD methods, i.e., the proposed SO-FDTD method in this paper, the original SO-FDTD method (here, referring to that the implementation scheme is the same as that of the new SO-FDTD method provided in this paper but without a combination of the memory-minimized algorithm) and the SO-FDTD method in kDB coordinates system introduced in [22]. In order to construct the same case as that in kDB coordinates system, we suppose the direction of incident EM-wave parallel to the Table 1.…”

“…During the derivation of the formulations, we see some advantages of this method, such as easy derivation of formulae, clear concept and simplicity. Compared to the SO-FDTD method in kDB coordinates system proposed in [22], the proposed method not only improves the accuracy but also spends less machine time due to the great reduction of storage arrays for the problem space. The high efficiency and accuracy of this method are confirmed by computing the reflection and transmission coefficients of electromagnetic wave through a magnetized plasma layer with the biasing magnetic field at an arbitrary angle θ with respect to the direction of propagation.…”

“…Through a shift operator, the constitutive relations in time-domain are transformed to the discrete time-domain. In [22], the SO-FDTD method is first introduced into the kDB coordinates system and the EM-problem model which covers all the respects of EM-problem for anisotropic plasma is set up, then the reflection and transmission coefficients of magnetized plasma slab are calculated. However, the required storage variables for each cell in the problem space are numerous due to the high order (the order is 4 or 6 in general) of the jω in the rational polynomial function, so the FDTD iteration will take much memory and the computational efficiency is not high.…”