Research On Finite-difference Time-Domain Algorithm For Plasmas And Its Applications

This dissertation mainly deals with the research on the Finite-Difference Time-Domain (FDTD) method, which is one of the most important methods in computational electromagnetics. After the comprehensive study of the previous work by people, some high effective and accurate FDTD methods are presented. The FDTD method is applied to study the scattering characteristics of typical target coated by isotropic, anisotropic, inhomogeneous and time-varying plasma and to study the photonic band gaps (PBGs) and the filter properties of plasma photonic crystals.The main innovations of this dissertation are as follows:1. The trapezoidal recursive convolution (TRC) technique requires single convolution integral in the formulation as in the recursive convolution technique, while maintaining the accuracy comparable to the piecewise linear recursive convolution technique with two convolution integrals.The FDTD method for plasma media is derived based on the TRC technique. The complex permittivity tensor of the magnetized plasma in the frequency domain is transformed into the time domain through the inverse fast Fourier transform (IFFT). By introducing the susceptibility tensor and the dielectric displacement in time domain, the FDTD iterative formulae with the convolution summation are presented in the discretised time domain based on the convolution integration principle. In order to calculate the convolution summation, we introduce the auxiliary variable and use the recursive convolution technique to derive the TRC-FDTD formulae for magnetized plasma. The high efficiency and accuracy of the method are confirmed by numerical results.2. This dissertation presents a new kind of plasma FDTD method named the Runge-Kutta exponential time differencing (RKETD) FDTD method. The RKETD-FDTD method is extended to anisotropic magnetized plasma. Based on the Yee's cell theory, averaging value and interpolation principle, the RKETD-FDTD iterative equations for three-domain electromagnetic scattering are derived. The stability, the numerical dispersion error and dissipation error caused by the method are investigated. The RKETD-FDTD formulae for magnetized plasma with perpendicular magnetic declination are derived. The high efficiency and accuracy of the method are confirmed by numerical examples.3. This dissertation presents a new kind of plasma medium FDTD method named the matrix exponential (ME) FDTD method. The Maxwell's curl equations and the constitutive relations between the flux density and the electric field can be looked as a first order differential matrix system. The fundamental solution to such a system is derived in terms of matrix exponential and the update equations can be extracted conveniently from the solution. The numerical dispersion relation of the method is derived and the numerical dispersion and dissipation error caused by the method are investigated using Newton-Raphson iterative method.4. This dissertation presents a kind of plasma medium alternating direction implicit (ADI) unconditionally-stable FDTD method named the higher-order ADI-FDTD method. Such ADI-FDTD method is based on a second-order in time and fourth-order in space and it is proved that the method is unconditionally. In comparison with that of the conventional ADI-FDTD method, the numerical dispersion of the present method is lowered.5. The FDTD method is applied to study the scattering characteristics of typical target coated by plasma. To analyze the bistatic scattering and backscattering of perfectly conducting cylinder coated with inhomogeneous and time-varying unmagnetized plasma. To analyze the bistatic scattering of perfectly conducting cylinder coated with inhomogeneous time-varying magnetized plasma. The effects of the plasma parameters on the Radar Cross Section (RCS) are investigated. To analyze the RCS of conducting sphere coated with inhomogeneous unmagnetized plasma. The FDTD method is also applied to study the RCS of in the horizontal plane for horizontal (HH) polarization and in the vertical plane for vertical (VV) polarization of sphere-cone and Von Karman conductor model coated with magnetized plasma.6. The FDTD method is applied to study the photonic band gaps (PBGs) and the filter properties of plasma photonic crystals. Firstly, the photonic band properties of homogeneous, non homogeneous unmagnetized plasma photonic crystals (PPCs) are simulated. The effects of the plasma parameters such as the plasma density, plasma temperature, and dielectric constant ratios on the PBGs are investigated. Secondly, the FDTD is applied to analyze the PBGs properties of Magnetized Plasma Photonic Crystals on the Basis of the magneto-optical effects. Electromagnetic wave transmission below the plasma frequency can be realized. Finally, to form a new kind of PPCs filters, a plasma defect layer was filled in the PPCs. The effective refractive index can be changed by alternating the electrical parameters of the defect instead of changing the dimension of PPCs, which makes the resonant frequency in plasma defect layer to offset. Then the filter frequency can be tuned.