Particle‐in‐cell simulation of an optimized high‐efficiency multistage plasma thruster

Electric propulsion attracts increasing attention in contemporary space missions as an interesting alternative to chemical propulsion because of the high efficiency it offers. The High‐Efficiency Multistage Plasma thruster, a class of cusped field thruster, is able to operate at different anode voltages and operation points and thereby generate different levels of thrust in a stable and efficient way. Since experiments of such thrusters are inherently expensive, multi‐objective design optimization (MDO) is of great interest. Several optimized thruster designs have resulted from a MDO model based on a zero‐dimensional (0D) power balance model. However, the MDO solutions do not warrant self‐consistency due to their dependency on estimation from empirical modelling based on former experimental studies. In this study, one of the optimized thruster designs is investigated by means of particle‐in‐cell (PIC) analysis to examine the predicted performance characteristics with self‐consistent simulations. The 0D power balance model is used to develop additional diagnostics for the PIC simulations to improve the physics analysis. Using input parameters for the 0D power balance model from the PIC simulations allows further improvement for the design optimization.     

Particle‐in‐Cell Simulations for Ion Thrusters

The Particle‐in‐Cell (PIC) method was used to study two different ion thruster concepts: Hall Effect Thrusters (HETs) and High Efficiency Multistage Plasma Thrusters (HEMPs), in particular the plasma properties in the discharge chamber due to the different magnetic field configurations. Special attention was paid to the simulation of plasma particles fluxes on the thrusters inner surfaces. In both cases PIC proved itself as a powerful tool, delivering important insight into the basic physics of the different thruster concepts.The simulations demonstrated that the new HEMP thruster concept allows for a high thermal efficiency due to both minimal energy dissipation and high acceleration efficiency. In the HEMP thruster the plasma contact to the wall is limited only to very small areas of the magnetic field cusps, which results in much smaller ion flux to the thruster channel surface as compared to HET. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Power-law behaviour evaluation from foreign exchange market data using a wavelet transform method

Numerous studies in the literature have shown that the dynamics of many time series including observations in foreign exchange markets exhibit scaling behaviours. A simple new statistical approach, derived from the concept of the continuous wavelet transform correlation function (WTCF), is proposed for the evaluation of power-law properties from observed data. The new method reveals that foreign exchange rates obey power-laws and thus belong to the class of self-similarity processes.     

Electron temperature scaling in laser interaction with solids

A precise knowledge of the temperature and number of hot electrons generated in the interaction of short-pulse high-intensity lasers with solids is crucial for harnessing the energy of a laser pulse in applications such as laser-driven ion acceleration or fast ignition. Nevertheless, present scaling laws tend to overestimate the hot electron temperature when compared to experiment and simulations. We present a novel approach that is based on a weighted average of the kinetic energy of an ensemble of electrons. We find that the scaling of electron energy with laser intensity can be derived from a general Lorentz invariant electron distribution ansatz that does not rely on a specific model of energy absorption. The scaling derived is in perfect agreement with simulation results and clearly follows the trend seen in recent experiments, especially at high laser intensities where other scalings fail to describe the simulations accurately.     

Nanoporous gold: 3D structural analyses of representative volumes and their implications on scaling relations of mechanical behaviour

We present a quantitative study of the salient structural parameters identified from so-called ‘representative volumes’ of the bicontinuous nanoporous gold (NPG) network, and examine the validity of self-similarity in describing its evolution. The approach is based on 3D-focused ion beam tomography applied to as-dealloyed and isothermally annealed NPG samples. After identifying sufficiently large representative volumes, we show that the ligament width distributions coarsen in a sufficiently self-similar, time-invariant manner, while the scaled connectivity density shows a self-similar ligament network topology. Using these critical parameters, namely mean ligament diameter and connectivity density, the Gibson–Ashby scaling laws for the mechanical response of cellular materials are revisited. The inappropriateness of directly applying the Gibson–Ashby model to NPG is demonstrated by comparing finite element method compression simulations of both the NPG reconstruction and that of the Gibson–Ashby solid model; rather than the solid volume fraction, we show that an effective load-bearing ring structure governs mechanical behaviour.     

Elastic properties of a disordered continuum of regular fractal structure: Self-consistent approach and finite-element method simulations

Macromolecular structures, as well as aggregation of filler in polymer-based composites, often may be described properly as fractals. Scaling behavior of the elastic moduli of a modeled fractal, the Sierpinski carpet, was the subject of this study. Sheng and Tao [1] and Patlazhan [2] found that, in the case of voids in on elastic host, axial and shear moduli exhibit distinct scaling dependencies on the size of the system. Nevertheless, it is widely accepted that moduli of random isotropic fractals (percolation clusters) scale with the same exponents. Explanation of the discrepancy is one of the main targets of the paper. The self-consistent approach and position space renormalization group technique (PSRG) have been applied for this goal. The mapping, corresponding to PSRG, was constructed numerically using the finite-element method (FEM) in the cases of voids and rigid inclusions. The self-consistent approach gives scaling behavior with exponents of values of about 0.11, independent of the modulus and type of inclusion, at developed stages of the fractal. It has been shown that mappings of PSRG on the plane, for two ratios of three independent moduli, have stable fixed points. This means that different elastic moduli exhibit scaling behavior with the same exponents (0.29 for voids and 0.17 for rigid squares) for developed fractal structure. The discrepancy in the exponent values obtained in the previous simulations is caused by the analysis of the initial stages of the structure. We believe that analogous results are valid for the wide class of self-similar fractals, and the dimension is the main parameter that governs the exponents and fixed point values.     

Study on Similarity Criteria of Hall Effect Thrusters

The scaling design of Hall effect thrusters is based on similarity criteria. Up to now, few of the similarity criteria proposed concern about the inside physical processes of the thruster except Melikov‐Morozov similarity criterion which embodies the ionization of propellant. As many other significant processes, such as electron conduction, ion acceleration and energy exchange, are out of consideration, it is far from enough to direct the thruster design appropriately at present. Therefore, in this paper, we have deduced out many new similarity criteria by analyzing the neutral continuity equation, the ion/electron momentum equations and the electron energy equation with the equation analysis method. By further comparing the magnitudes of source terms of those equations, we obtain certain similarity criteria which are primary and should be guaranteed for modeling design of thrusters. These dominant similarity criteria are finally verified in experiments (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Scaling Design and Experimental Study on Hall Thrusters with Curved Magnetic Field

The existing scaling theories of Hall thrusters are based on the hypothesis of a one‐dimensional straight magnetic field, which is not suitable for the design of modern thrusters with a two‐dimensional curved magnetic field. In this paper, using the equation analysis method, we derive new similarity criterions in a curved magnetic field by analyzing the momentum equations of charged particles; consequently, we propose a new modeling design method for Hall thrusters with a constant discharge voltage. This method is further validated by experiments. A designed model with a power of 1.5 kW is made based on our proposed method from a prototype model with a power of 1 kW. The experimental results demonstrate that these two thrusters have little differences in performance and physical processes as expected from the scaling. Therefore, our method is well suited for designing a Hall thruster with a curved magnetic field (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

线耦合平板瞬态高频振动响应预报

提出了一种用于线耦合平板瞬态高频振动分析的预报方法.基于瞬态统计能量分析,从子系统能量平衡方程的动力学相似性,推导出了时域尺度变换法则:在时间尺度上进行缩尺变换,而损耗因子相应地成反比变换。在此基础上,针对线耦合平板的能量传递特点,导出了两种不同变换方式:一种对结构的材料参数进行变换,另一种对结构的几何参数进行变换。采用两种连接方式的线耦合平板模型对时域尺度变换方法进行数值验证,结果表明该方法能以较高的计算效率准确获得结构的瞬态高频振动响应。      

Breakdown of Kolmogorov scaling in models of cluster aggregation

We describe a model of cluster aggregation with a source which provides a rare example of an analytically tractable turbulent system. The steady state is characterized by a constant mass flux from small masses to large. Thus it can be studied using a phenomenological theory, inspired by Kolmogorov's 1941 theory, which assumes constant flux and self-similarity. We prove that such self-similarity is violated in dimensions less than or equal to two. We then use dynamical renormalization group techniques to show that the scaling of multipoint correlation functions implies nontrivial multifractality. The analytical results are supported by Monte Carlo simulations.     

一种识别关联维数无标度区间的新方法

在计算关联维数过程中, 为了减少人为因素识别无标度区间带来的误差, 提出一种基于模拟退火遗传模糊C均值聚类识别无标度区间的新方法. 该方法根据无标度区间对应曲线的二阶导数在零附近波动的变化特征, 利用分类算法进行识别. 首先对双对数关联积分的离散数据进行二阶差分; 然后利用模拟退火遗传模糊C均值聚类方法对该数据进行分类, 选出在零附近波动的数据; 再剔除粗大误差保留有效数据; 最后进行统计分析识别出线性度最好的作为无标度区间. 应用新方法对两个著名的混沌系统Lorenz 和Henon 进行了仿真, 计算结果与理论值非常符合. 实验表明, 所提出的新方法与主观识别、K-means和2-means方法比较, 可以有效自动识别无标度区间, 减少误差, 计算结果更加精确.     

Scaling of the acoustic emission characteristics during plastic deformation and fracture

The scaling of the amplitude and time distributions of acoustic emission pulses, which reflects the self-similarity of defect structures, is revealed. The possibility of separation of independent contributions to the flow of acoustic emission events, which have substantially different scaling exponents, is shown for porous materials. The differences in the scaling exponents are related to the development of plastic deformation and fracture of the materials. The developed approach to an analysis of acoustic emission can be used to describe its predominant mechanisms during deformation.     

离子推力器工作性能参数控制模型

为了研究离子推力器工作参数对输出特性的影响,通过离子推力器工作性能参数的理论计算公式,建立起离子推力器输入参数与输出参数的Simulink控制模型,根据模型分别对我国研制的30 cm口径以及20 cm口径离子推力器的工作输出参数进行了理论计算,并通过推力测量试验对理论值进行了比对和分析。比对结果表明:在推力理论计算过程中引入二价Xe离子比率和束流密度分布推力修正,以及推力均方误差修正后,推力理论值与实测值符合性较好,计算误差小于1 mN,证明了推力修正方法的合理性。     

Domain growth and finite-size-scaling in the kinetic Ising model

This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size-scaling ansatz for the time-dependent order parameter distribution function is proposed, and tested with extensive Monte-Carlo simulations of domain growth in the 2-D spin-flip kinetic Ising model. The scaling properties of the distribution functions serve to elucidate the configurational self-similarity that underlies the dynamic scaling picture. Moreover, it is demonstrated that the application of finite-size-scaling techniques facilitates the accurate determination of the bulk growth exponent even in the presence of strong finite-size effects, the scale and character of which are graphically exposed by the order parameter distribution function. In addition it is found that one commonly used measure of domain size-the scaled second moment of the magnetisation distribution-belies the full extent of these finite-size effects.     

轴对称系统等离子体数值模拟电荷、电流分配CIC方法

采用体积加权CIC方法,对轴对称系统等离子体模拟PIC方法中的节点电荷和电流计算进行了详细讨论,推导出节点电荷和电流的计算公式,可用于轴对称系统21／2维等离子体静电PIC模拟和电磁PIC模拟。     

Support Vector Driven Genetic Algorithm for the Design of Circular Polarized Microstrip Antenna

In this paper, a hybrid soft computing method for designing specific microstrip antenna is presented. Evolutionary algorithm such as genetic algorithm (GA) is one of the promising ways of finding global optimum solution from a multivariate nonlinear feature space. Being a stochastic iterative algorithm, it requires much computation power when the function to be optimized is complex and time consuming. Various meta-modelling techniques such as neural network, response surface methods, kriging, etc. can be used to model the process under optimization in order to reduce the computational expenses. In this paper, we investigate one such technique – support vector regression (SVR) – to model the complex analytical process. The model, thus obtained, is used for optimization using genetic algorithms. This approach is demonstrated for the design of circular polarized microstrip antenna at 2.6 GHz band. The results of SVR model are compared with other meta-models generated with neural network and response surface methodology.     

Effect of the inertial term of the ion momentum equation on fluid transport simulation for capacitively coupled plasma sources

Fluid-based simulations are widely used to analyze or optimize capacitively coupled plasma sources. Although the inertial term of the ion momentum equation affects the accuracy of the solutions, the equation has not been considered in the drift-diffusion approximation model in the numerical solution. Therefore, we, herein, improved the accuracy of the model by applying an effective electric field, considering the inertial term. First, the effective electric field, including the ion inertial term of the ion momentum equation, was derived. Subsequently, one-dimensional fluid simulations were conducted. The numerical results were compared with those of one-dimensional particle-in-cell (PIC) simulations. The results of the developed model were similar to those obtained in the case of solving the full-ion momentum equation, as well as more similar to the PIC simulation results than those obtained in the case of the drift-diffusion approximation.     

Polynomially scaling spin dynamics simulation algorithm based on adaptive state-space restriction

We report progress with an old problem in magnetic resonance -- that of the exponential scaling of simulation complexity with the number of spins. It is demonstrated below that a polynomially scaling algorithm can be obtained (and accurate simulations performed for over 200 coupled spins) if the dimension of the Liouville state space is reduced by excluding unimportant and unpopulated spin states. We found the class of such states to be surprisingly wide. It actually appears that a majority of states in large spin systems are not essential in magnetic resonance simulations and can safely be dropped from the state space. In restricted state spaces the spin dynamics simulations scale polynomially. In cases of favourable interaction topologies (sparse graphs, e.g. in protein NMR) the asymptotic scaling is linear, opening the way to direct fitting of molecular structures to experimental spectra.     

Acoustic emission monitoring of the Syracuse Athena temple: scale invariance in the timing of ruptures

We perform a comparative statistical analysis between the acoustic-emission time series from the ancient Greek Athena temple in Syracuse and the sequence of nearby earthquakes. We find an apparent association between acoustic-emission bursts and the earthquake occurrence. The waiting-time distributions for acoustic-emission and earthquake time series are described by a unique scaling law indicating self-similarity over a wide range of magnitude scales. This evidence suggests a correlation between the aging process of the temple and the local seismic activity.