等离子体的SO-FDTD算法和对电磁波反射系数的计算分析

将一类色散介质的介电常数写成有理分式函数形式，进而导出FDTD中电位移矢量D和电场强度E之间的关系，形成SO-FDTD方法. 应用该方法计算了冷等离子体平板对电磁波的反射系数，通过与解析结果的比较，验证了该算法的高效性和高精度，同时，应用SO-FDTD方法，计算了等离子体层对垂直入射电磁波的反射系数，结果表明：等离子体厚度、电子密度、电子密度的分布形式和入射波频率是影响反射系数的重要因素. 关键词： 等离子体 电磁波 FDTD方法     

Calculation of the Effect on the Reflection of the Plane Electromagnetic Wave for Non-Magnetized Plasma with Different Electron Density Distributions

In this paper, shift operator finite-difference time-domain (SO-FDTD) method is applied for the calculation of the dispersive medium. The high efficiency and accuracy of this method is verified by calculating the reflection of the plane electromagnetic wave impinging on a non-magnetized plasma slab with different electron density distributions. The results show that the average electron density only determines overall trends of the reflection, and different distributions affect the oscillating process of the reflection. If the average electron density maintains the same, the distribution of electron density with homogenous or inhomogeneous alternation will sharply take effects on the reflection. And magnitude of alternation of electron density affects the incident frequency directly when the reflection tends to uniform.     

Analysis of the temperature influence on the plasma reflectance by a new FDTD method

We apply the shift-operator FDTD (SO-FDTD) method for calculating dispersive media plasmas. We write the dielectric constant of a dispersive medium as a rational fractional function and derive the relation between D and E in the time domain. For a uniform, approximately isothermic, isotropic, warm-collision-plasma slab, the reflection coefficient of electromagnetic waves can be calculated using the SO-FDTD method. We study the influence of temperature on the collisions and absorption of electromagnetic waves in the plasma and discuss the regularity of the relationships obtained.     

弱电离尘埃等离子体层反射与透射的SO-FDTD方法分析

将弱电离尘埃等离子体复介电常数表示以jω 为自变量的分式多项式形式, 利用移位算子时域有限差分(SO-FDTD)方法, 给出了弱电离尘埃等离子体频域本构关系的时域形式. 推导了弱电离尘埃等离子体电磁特性的时域递推关系式. 用SO-FDTD方法计算了弱电离尘埃等离子体层的反射和透射系数, 分析了尘埃粒子浓度和尘埃粒子半径的变化对反射系数和透射系数的影响. 结果表明: 有尘埃粒子时的反射系数比没有尘埃粒子时反射系数小, 而透射系数要比没有尘埃粒子时的透射系数大; 当尘埃粒子浓度或尘埃粒子半径增大时, 其反射系数均减小.     

SO-FDTD Analysis on Magnetized Plasma

In this paper, a novel finite-difference time-domain (FDTD) method with recursive relationships among operators is developed for magnetized dispersive medium, named as the shift operator FDTD(SO-FDTD). The dielectric property of magnetized dispersive medium is written as rational polynomial function, the relationship between D and E is deduced in time-domain. And its high accuracy and efficiency are verified by calculating the reflection and transmission coefficients of electromagnetic waves through a collision plasma slab.     

Shift operator method and Runge-Kutta exponential time differencing method for plasma

In this paper, the shift operator finite difference time domain (SO-FDTD) method and Runge-Kutta exponential time differencing (RKETD) method are introduced. The high accuracy and efficiency of the two methods are verified by calculating the reflection and transmission coefficients of electromagnetic waves through a collisional plasma slab. A comparison of computational efficiency of the two methods is presented by simulating the electromagnetic wave propagation in homogeneous non-magnetized plasma. The numerical results indicate that the calculation time using SO-FDTD method is less than that using RKETD method with almost the same accuracy.     

各向异性磁化等离子体的SO-FDTD算法

给出了一种新的计算各向异性磁化色散介质的有限差分(FDTD)算法，称为移位算子FDTD(SO-FDTD)算法，它利用算子之间的移位递推关系，将一类色散介质的包含介电常数的表达式写成有理分式函数形式，进而导出FDTD中一系列相关量之间的关系.通过计算各向异性等离子体平板对电磁波的反射系数和透射系数，验证了该算法的高效性和高精度，与JEC算法相比，可使计算效率提高数倍. 关键词： 磁化等离子体 电磁波 FDTD方法 各向异性     

时空非均匀等离子体鞘套中太赫兹波的传播特性

高超声速飞行器再入地面的过程中,其周围等离子体的电子密度是非均匀且随时间变化的.对于不同的再入高度,飞行器周围的温度和压强也会发生改变.因此,研究电磁波在时空非均匀等离子体鞘套中的传播特性意义重大.首先建立了时变非均匀的等离子体鞘套模型,然后通过经验公式得到温度、压强与碰撞频率三者的关系.采用时域有限差分方法计算了太赫兹波段中不同电子密度弛豫时间、温度、压强时的反射系数、透射系数和吸收率.研究结果表明:在太赫兹波段中,电子密度的弛豫时间越长,温度越高,压强越大,电磁波越容易穿透等离子体;弛豫时间越短,温度越低,压强越小,等离子体对电磁波吸收率的变化越明显.这些结果为解决"黑障"问题提供了理论依据.     

A general finite difference time domain method for hybrid dispersive media model

The shift operator finite difference time domain (SO-FDTD) method is developed to deal with a hybrid dispersive media model. First, we prove that the complex permittivity of the hybrid dispersive media model can be described by a rational polynomial fraction with respect to jω. Then, the relation between electric displacement D and electric field strength E is derived in the time domain by introducing z_t as a shift operator. The constitutive relation in the discretized time domain and the recursive formulation of D and E available for FDTD computation are obtained. Finally, the reflection of the hybrid dispersive slab is computed. The computed results are in good agreement with that obtained by analytic method. This illustrates the generalization and the feasibility of the presented scheme.     

Propagation characteristics of oblique incidence terahertz wave through non-uniform plasma

The propagation characteristics of oblique incidence terahertz(THz) waves through non-uniform plasma are investigated by the shift-operator finite-difference time-domain(SO-FDTD) method combined with the phase matching condition.The electron density distribution of the non-uniform plasma is assumed to be in a Gaussian profile. Validation of the present method is performed by comparing the results with those obtained by an analytical method for a homogeneous plasma slab.Then the effects of parameters of THz wave and plasma layer on the propagation properties are analyzed. It is found that the transmission coefficients greatly depend on the incident angle as well as on the thickness of the plasma, while the polarization of the incident wave has little influence on the propagation process in the range of frequency considered in this paper. The results confirm that the THz wave can pass through the plasma sheath effectively under certain conditions,which makes it a potential candidate to overcome the ionization blackout problem.     

New FDTD-based method for computing the Lorentz dispersive media

We apply the shift-operator finite-difference time-domain (SO-FDTD) method to the calculation of the Lorentz dispersive media. The Lorentz-medium permittivity is written as a rational fractional function, and the relation between D and E is derived in a time domain. The high efficiency and accuracy of the method is demonstrated by calculating the reflection and transmission of the electromagnetic plane wave impinging on a Lorentz-dispersive-medium slab. The results obtained with the help of the SOFDTD method are compared with analytical results. The SO-FDTD method is proved to have high efficiency and accuracy in computing the Lorentz dispersive media.     

Microwave pulse shortening in plasma relativistic high-current microwave electronics

We describe mechanisms of microwave pulse shortening in radiation sources with the power of about 10⁸ W based on interaction between relativistic electron beams of nanosecond duration and preformed plasma. The shortening is mainly due to the electron return flow through the plasma, which leads to a multiple decrease in the linear gain of the microwave by the relativistic electron beam and in the reflection coefficient of the plasma wave that provides the generator feedback. The ways to eliminate the effect of microwave pulse shortening are proposed.     

Effect of a dust component on the rates of elementary processes in low-temperature plasmas

Elementary processes in dusty, beam-driven plasma discharges are studied experimentally and theoretically for the first time. A theoretical model is constructed for a beam-driven plasma containing macroscopic particles. The effect of macroscopic particles on the electron energy distribution function is estimated assuming a Coulomb field for the particles. The resulting rate of electron-ion recombination on the macroscopic particles is compared with the electron loss constant calculated from the electron energy distribution function with an electron absorption constant in the orbital-motion approximation. This approximation, which is valid in the collisionless case, is found to work satisfactorily beyond its range of applicability. The distributions of the charged particles and electric fields created by macroscopic particles in a helium plasma are determined. The experimental data demonstrate the importance of secondary emission by high-energy electrons. Zh. éksp. Teor. Fiz. 115, 2020–2036 (June 1999)     

垂直入射电磁波在大气压非平衡等离子体层中的传播特性

用数值模拟的方法对大气压非平衡等离子体薄层中，不同的电子密度分布对微波反射、吸收和透射的影响进行了研究。所采用的理论分析方法是分层模型和镶嵌不变原理。计算中考虑了微波在子层间的多次反射和吸收。数值结果表明，对于电磁波的吸收来说，等离子体中具有二次分布的电子密度，其效果要高于线性分布10%左右；而对于反射来说，线性分布效率更高。功率反射系数随波长的增大而增大，功率吸收系数A也不是单调的，当电子密度不变时，A存在一个峰值，随着电磁波波长的增加而增加，达到最大值后，缓慢降低。     

A FDTD formulation for high order dispersive media of muscle-equivalent

In this paper, shift operator finite-difference time-domain (SO-FDTD) method is applied for the calculation of the dispersive medium. The high efficiency and accuracy of this method is verified by calculating the reflection of the plane electromagnetic wave impinging on a muscle slab. For human tissues where multiterm Debye relaxation equations must generally be used. We describe a new differential equation approach, which can be used for general dispersive media. In this method D(t) is expressed in terms of E(t) by means of a differential equation involving D, E, and their time derivatives. The method is illustrated by means of example of media for which relative permittivity is given by a multiterm Debye equation, and for an approximate two-thirds muscle-equivalent model of the human body.     

Effect of an electron beam generated in an X-pinch plasma on the structure of the K spectra of multiply charged ions

The first experimental studies of an electron beam generated in an X pinch on the XP machine (Cornell University, USA) and the BIN machine (P. N. Lebedev Physical Institute, Russian Academy of Sciences) are reported. It is shown that it is possible in an X pinch to isolate the effect of a plasma-generated electron beam on the multiply charged ion radiation. The intensities of the satellite lines corresponding to Li-, Be-, B-, and C-like ions are calculated for the Al spectrum on the basis of a collisional-radiative model with a non-Maxwellian electron distribution in the plasma. The effect of an electron beam on the multiply charged light ion radiation in an X-pinch plasma is demonstrated. Comparing our calculations with the experimental spectra, we conclude that the present model can be used to estimate the electron beam intensity. Zh. éksp. Teor. Fiz. 112, 894–909 (September 1997)     

Attenuation properties of EM wave by magnetized nonuniform plasma slab coated on perfect conductor plane

The total amplitude reflection coefficient of EM wave in a nonuniform plasma slab coated on perfect conductor plane is newly derived by using the scattering matrix method (SMM), and the attenuation is calculated. Three types of plasma electron density profile, that is the hyperbolic, sinusoidal, and linear profiles, are used. The external magnetic field and plasma parameters such as the maximum electron density and collision frequencies are discussed to calculate the attenuation of EM wave. The calculation results show that the plasma electron density profile and maximum electron density exert a large effect to the attenuation of EM wave and the attenuation under the uniform external magnetic field is taken place by the electron cyclotron resonance absorption, the up hybrid resonance absorption and geometric resonances absorption.     

Effect of size quantization of the reflection coefficient of an electron beam incident on a thin heteroepitaxial film

The effect of size quantization of the reflection coefficient of electrons incident on a thin single-crystal film located on a substrate has been theoretically predicted. Two methods for observing this effect experimentally are proposed. In the first method, the variation in the intensity of the beam of specularly reflected electrons can be measured by varying the small glancing angle α of the electron beam with a particle energy on the order of 10 keV. In the second method, intensity oscillations of the diffracted beam as a function of the variation in the reflection angle β are measured in the case of a small fixed glancing angle α (on the order of 1°–3°). Thus, the second variant corresponds to studying the intensity distribution along streaks (reflexes) in the case of electron diffraction on a smooth surface. In the second case, the appearance of elastically scattered electrons along the streaks between diffraction reflexes is predicted. Their number (the beam intensity) varies periodically as a function of the angle β.     

The comparison of the CPU time between SO-FDTD method and PLCDRC method for dispersive media

The precision and computational efficiency of the shift operator finite-difference time-domain (SO-FDTD) method are compared with those of the piecewise linear current density recursive convolution (PLCDRC) method by simulating the electromagnetic wave at different frequency propagation in homogeneous unmagnetized plasma in this paper. The results show that the two methods almost have the same precision, but the CPU time of the SO-FDTD method is less than that of the PLCDRC method, this is because the SO-FDTD method eliminates many convolution operations of the PLCDRC method.     

Influence of boundary conditions on statistical characteristics of the wavefield in a layered randomly inhomogeneous medium

Abstract

We consider the problem of the oblique incidence of a wave on the half-space of a layered randomly inhomogeneous medium without absorption and analyse the influence of boundary conditions on the probability distribution of the reflection coefficient phase, and the statistical behaviour of the wavefield intensity moments inside the medium.