Millimeter Wave Scattering of 2-D Frequency Selective Surface by Efficient Method of Lines with Preconditioned CG Technique

In this paper, both banded and symmetric successive overrelaxation (SSOR) preconditioned conjugate gradient (PCG) techniques are combined with method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. The electromagnetic wave scattering of 2-D frequency-selective surface is used as the examples to describe its implementation, whose analysis usually needs fast algorithms because of electrically large dimension. For arbitrary incident wave, helmholtz equation and boundary condition are used to calculate the impedance matrix and then to obtain reduced current-voltage linear matrix equation in spatial domain. Both banded and effective symmetric successive overrelaxation preconditioned conjugate gradient iterative method are chosen to solve this matrix equation. Our numerical results show that PCG methods can converge to accurate solution in much fewer iteration steps for analysis of the electromagnetic wave scattering from 2-D frequency-selective surface.     

An Effective Multigrid Preconditioned CG Algorithm for Millimeter Wave Scattering by an Infinite Plane Metallic Grating

An effective multigrid based preconditioned conjugate gradient method is developed to solve electromagnetic large matrix problem for millimeter wave scattering application. By using multigrid technique we restrict the large matrix equation to a relative smaller matrix and which can be solved rapidly. The solution is prolonged as the initial guess for the conjugate gradient (CG) method. Numerical results show that our developed method can reach five times improvement of computational complexity.     

Analysis of Millimeter Wave Scattering by an Electrically Large Metallic Grating Using Wavelet-Based Algebraic Multigrid Preconditioned CG Method

An effective wavelet based multigrid preconditioned conjugate gradient method is developed to solve electromagnetic large matrix problem for millimeter wave scattering application. By using wavelet transformation we restrict the large matrix equation to a relative smaller matrix and which can be solved rapidly. The solution is prolonged as the new improvement for the conjugate gradient (CG) method. Numerical results show that our developed wavelet based multigrid preconditioned CG method can reach large improvement of computational complexity. Due to the automaticity of wavelet transformation, this method is potential to be a block box solver without physical background.     

Analysis of Millimeter Wave Scattering by the Infinite Plane Metallic Grating Using PCG-FFT Technique

In this paper, both fast Fourier transformation (FFT) and preconditioned CG technique are introduced into method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. Electromagnetic wave scattering by an infinite plane metallic grating is used as the examples to describe its implementation. For arbitrary incident wave, Helmholz equation and boundary condition are first transformed into new ones so that the impedance matrix elements are calculated by FFT technique. As a result, this Topelitz impedance matrix only requires O(N) memory storage for the conjugate gradient FFT method to solve the current distribution with the computational complexity O(N log N) . Our numerical results show that circulate matrix preconditioner can speed up CG-FFT method to converge in much smaller CPU time than the banded matrix preconditioner.     

Application of Robust Incomplete Cholesky Factorizations Preconditioned CG Algorithms for FEM Analysis of Millimeter Wave Filters

The Incomplete Cholesky factorizations preconditioning scheme is applied to the conjugate gradient (CG) method for solving a large system of linear equations resulting from finite element method (FEM) analysis of millimeter wave filters. As is well known, the convergence of CG method deteriorates with increasing EM wave number and in millimeter wave band the eigen-values of A are more and more scattered between both the right and the left half-plane. The efficient implementation of this preconditioned CG (PCG) algorithm is described in details for Complex coefficient matrix. With incomplete factorization preconditioning scheme in the conjugate gradient algorithm, this PCG approach can reach convergence in 20 times CPU time shorter than CG for several typical millimeter wave structures.     

Multiple Scattering Solution of Millimeter Wave Propagation in Strong Sandstorm

As the operating frequencies of communication systems more higher into the millimeter wave range, and the density of particles in medium is more denser, the effects of multiple scattering in sandstorm become more significant. This paper treats the problems of electromagnetic multiple scattering in strong sandstorm by the Monte Carlo method. Based on the analytical theory of multiple scattering, the millimeter wave propagation and scattering in discrete random media are investigated by means of the particle-tracking technique. The millimeter wave is regarded as a Markov chain of wave particle collisions in a medium in which it is scattered and absorbed. Considering the effect of multiple scattering, millimeter wave attenuation induced by strong sandstorm is simulated numerically. The values of theoretical calculation are in good agreement with the measured results of simulated experiment at 34 and 93 GHz.     

玻璃表面层光学参数分布的研究

利用并改进平板玻璃两面Ｐ偏振光反射光强比的测量来确定玻璃表面光学参数的方法，测量了平板玻璃两面Ｐ偏振光反射光强比γ与入射角θｉ的关系曲线，运用新的表面层模型进行数据模拟，获得了表面层的光学参数分布。     

Parameters Extraction of Millimeter Wave Circuits by Hybrid Vector Finite Element and Moment Method Combined with SOC Technique

This paper presents a hybrid method, which couples the vector finite element method (FEM) and method of moment (MOM) for analyzing the field and current distribution of the millimeter wave circuits. The FEM is applied to handle the interior region of dielectric bodies and MOM is used to solve surface integral equations. Then, These integral expressions are coupled into the FEM equations through the continuity of the tangential fields across the connection boundaries. Simultaneously, the short-open calibration (SOC) technique is used for predicting accurately the scattering parameters of the circuits. Numerical results are well compared with those published in the previous literatures.     

Scattering of Millimeter Waves from Acid Rain

A theoretical investigation of scattering characteristics of millimeter waves from acid rain is conducted using the method of vector spherical function expansion. The particles of acid rain are considered as the double-layered spheroid. The method is used to derive an analytical solution to the problem of scattering of millimeter waves by a coated dielectric spheroid. The normalized bistatic cross section versus scattering angle for the acid raindrop is calculated at frequencies of 35 GHz and 94 GHz. This is the first part of our study scattering characteristics of millimeter waves from acid rain.     

Analysis of Millimeter Wave Power Density Received by Cell Monolayers Inside Culture Dishes

One sort of experiment concerning biological effects of millimeter waves (MMWs) at the cellular level is performed using a culture dish containing a cell monolayer with MMW irradiated from the underneath. For culture dishes with diameters much larger than the wavelength, analysis is carried out with respect to the relationship between the portion of the incident MMW power density (PD) received by the cell monolayer and influencing factors such as the culture dish bottom thickness, MMW wavelength, and the electromagnetic properties of the dish and culture solution. Another analysis is conducted by the FDTD method to reveal the effect of culture dish configuration on MMW PD received by the cell monolayer in a typical culture dish with a diameter not much longer than the wavelength. With the illustrated results, the conclusion is reached that rigorous analysis, precise measurement and accurate calculation of MMW PD should accompany such experiments, and large-diameter culture dishes are more preferred in experiments to small-caliber dishes.     

Analysis of the H-Plane T-Junction Millimeter Wave Waveguide Circulator with a Ferrite Sphere

This paper presents an approximate but efficient field treatment of the new easy-to-fabricate ferrite sphere based H-plane waveguide circulator for potentially low-cost millimeter wave communication systems. A new three-dimension modeling strategy using a self-inconsistent mixed coordinates based mode matching technique is developed, i.e. the solutions of the Helmholz wave equations in the ferrite sphere and in the surrounding areas are deduced in the form of infinite summation of spherical, cylindrical and general Cartesian modes respectively. The point matching method is then used on the interface to numerically obtain the coefficients of different orders basis functions of the field. Therefore, the field distributions as well as the characteristics of the circulator are numerically calculated and the good agreement is observed between the numerical results and the measured data.     

Thermo-Mechanical Analysis of Single-Disc Edge-Cooled Silicon Nitride Millimeter Wave Window for 200 kW CW Gyrotrons

This paper investigates the possibility of using Silicon Nitride Composite (Kyocera SN-287) as single-disc, edge-cooled window for gyrotrons operating below 200 kW CW in the frequency range 28-42 GHz. Rotationally symmetric TE_0n, and TEM₀₀ Gaussian modes of rf transmission through the window have been considered. Analysis performed using a one dimensional (1D) finite difference (FD) code reveals that thermal stresses developed due to non-uniform temperature distribution on the disc surface are well within manageable limits for a 200 kW 42 GHz gyrotron proposed for some ECRH applications. For industrial gyrotrons, for microwave material processing and operating at a maximum power level of 100 kW CW, Si₃N₄ windows may be a cost effective replacement for sapphire windows. It is found that a TE₀₂ profile results in lower peak temperature at the window disc in comparison to a Gaussian beam profile and allows the use of smaller discs.     

A Future Millimeter/Sub–Millimeter Radiometer for Satellite Observation of Ice Clouds

The instrument concept of a future spaceborne millimeter/sub-millimeter radiometer is proposed in this paper for the remote sensing of ice clouds from satellite. The proposed radiometer is expected to operate at a series of frequencies within the millimeter and sub-millimeter wave range from 150 to about 900 GHz. Five frequencies are selected in the atmospheric windows, i.e., 150, 220, 463, 683, 874 GHz, and at each frequency there are two orthogonally polarized channels. Three water vapor channels located close to 183.31 GHz are also included in this instrument, since they can provide water vapor information, which is needed for ice cloud parameter retrieval. To simplify system design and test, a modular design philosophy is followed in the receiver frontend design and two antennas are used separately for the millimeter and sub-millimeter channels. Overall, the instrument requirements can be met with today's technology, except for the channels at the highest frequencies, where the radiometric sensitivity can be larger than the required 1.0 K for the 10 km spatial resolution (2.5 ms integration time). However, this situation can be improved by averaging neighboring pixels in data processing if certain compromise in the spatial resolution can be made at these frequencies.     

Application of Preconditioned GMRES Algorithm for Analysis of Millimeter Wave Ferrite Sphere Circulators

The generalized minimal residual (GMRES) iterative method is applied to solve such sparse large non-symmetric system of linear equations resulting from the use of edge-based finite element method. In order to speed up the convergence of GMRES, the symmetric successive overrelaxation (SSOR) preconditioning scheme is applied for the analysis of millimeter wave ferrite circulator. Consequently, this preconditioned GMRES (PGMRES) approach can reach convergence 19 times faster than GMRES. The isolation and insertion losses of millimeter wave waveguide circulator are compared with those obtained from literature.     

Application of Preconditioned GMRES Algorithm for Analysis of Millimeter Wave Ferrite Sphere Circulators

The generalized minimal residual (GMRES) iterative method is applied to solve such sparse large non-symmetric system of linear equations resulting from the use of edge-based finite element method. In order to speed up the convergence of GMRES, the symmetric successive overrelaxation (SSOR) preconditioning scheme is applied for the analysis of millimeter wave ferrite circulator. Consequently, this preconditioned GMRES (PGMRES) approach can reach convergence ten times faster than GMRES. The reflection and insertion losses of millimeter wave waveguide circulator are compared with those obtained from literature.     

Method of Lines Based on Finite Element Discrete Technique to Analyze Eigenvalues of Waveguides

In this paper, a novel numerical technique to solve electromagnetic boundary value problem is described. This finite element based method of lines is developed by combining finite element method and the method of lines, so that it not only has high flexibility to treat geometrically and compositionally complex problems but also maintains high accuracy of semi-analytical technique. The geometry discretization, element mapping, element trial function and standard ordinary differential equation construction are discussed in details. Our numerical result demonstrates that this method can successfully solve the complex problems with fewer mesh lines when compared with conventional method of lines.     

Analysis for a Novel Cocoon-Shaped Groove Guide with Method of Lines

An arbitrarily cross-sectional groove guide is analyzed by using the method of lines and its characteristic equations are gives for TE and TM modes. Some numerical results show that correctness of the method of lines compared with the relevant results in the references is verified, and it is convenient to solve groove guide with arbitrary shape in practical application problems. A novel cocoon-shaped groove guide is firstly presented and its transmission characteristics are analyzed and discussed. The new type of cocoon-shaped groove guide has the good performances. The obtained results are of important application values in theoretical studies and practical applications of groove guides for millimeter waves.     

Production of an Intense, Well-Collimated Submillimeter Wave Beam and Its Application to Plasma Scattering Measurements

Intense submillimeter wavelength radiation (f=354 GHz, P=110 W) from Gyrotron FU II is converted into a well-collimated, linearly-polarized beam by a quasi-optical transmission line consisting of a quasi-optical antenna and several mirrors. The observed focusing of the beam agrees with calculations based on the Huygens equation. We have used this intense beam to study low frequency density fluctuations by plasma scattering in Compact Helical System (CHS) plasmas at the National Institute for Fusion Science.     

Algebraic Multigrid Preconditioning for Finite Element Solution of Inhomogeneous Elastic Inclusion Problems in Articular Cartilage

In studying biomechanical deformation in articular cartilage, the presence of cells (chondrocytes) necessitates the consideration of inhomogeneous elasticity problems in which cells are idealized as soft inclusions within a stiff extracellular matrix. An analytical solution of a soft inclusion problem is derived and used to evaluate iterative numerical solutions of the associated linear algebraic system based on discretization via the finite element method, and use of an iterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG). Accuracy and efficiency of the AMG-PCG algorithm is compared to two other conjugate gradient algorithms with diagonal preconditioning (DS-PCG) or a modified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution. While all three algorithms are shown to be accurate, the AMG-PCG algorithm is demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased. In contrast to the other two algorithms, the AMG-PCG algorithm also exhibits little sensitivity of CPU time and number of iterations to variations in material properties that are known to significantly affect model variables. Results demonstrate the benefits of algebraic multigrid preconditioners for the iterative solution of assembled linear systems based on finite element modeling of soft elastic inclusion problems and may be particularly advantageous for large scale problems with many nodal unknowns.     

Investigation of the Dielectric-Loaded, Ridged Helical Groove Slow-Wave System for the Millimeter Wave TWT

A dielectric-loaded, ridged helical groove slow-wave structure for the millimeter wave traveling wave tube is presented in this paper. The effects of the groove depth, ridge dimensions and the dielectric permitivety on the wave propagating properties and the interaction impedance are investigated in detail. From the analysis, it is indicated that for broader band amplification in a helical groove travelling wave tube, a ridged helical structure with shallow groove and loaded by dielectric with proper relative permitivety may be applied.