纳秒脉冲下变压器油两相流注放电仿真研究

为揭示液体电介质击穿过程中形成的气体放电通道对液体电介质放电过程的影响,以针—板电极间隙变压器油为研究对象,基于等离子体流体力学模型,引入了液体电介质放电过程中气相放电通道对电离机制及自由电荷迁移率的影响,建立了用于模拟脉冲电压下液体电介质放电过程的两相流体模型,仿真研究了纳秒脉冲下针板电极流注放电的起始与发展过程。仿真结果表明：采用Heaviside方程可以在模型的不同区域同时实现气相物理过程和液相物理过程的模拟与计算。气相物理过程的引入导致流注尾部电场显著降低,流注头部电场进一步增强,使流注通道的发展速度要高于传统液相模型,有助于加深对纳秒脉冲下液体电介质中预击穿流注的起始、发展过程的认识和理解。     

Sixth order compact scheme combined with multigrid method and extrapolation technique for 2D poisson equation

We develop a sixth order finite difference discretization strategy to solve the two dimensional Poisson equation, which is based on the fourth order compact discretization, multigrid method, Richardson extrapolation technique, and an operator based interpolation scheme. We use multigrid V-Cycle procedure to build our multiscale multigrid algorithm, which is similar to the full multigrid method (FMG). The multigrid computation yields fourth order accurate solution on both the fine grid and the coarse grid. A sixth order accurate coarse grid solution is computed by using the Richardson extrapolation technique. Then we apply our operator based interpolation scheme to compute sixth order accurate solution on the fine grid. Numerical experiments are conducted to show the solution accuracy and the computational efficiency of our new method, compared to Sun–Zhang’s sixth order Richardson extrapolation compact (REC) discretization strategy using Alternating Direction Implicit (ADI) method and the standard fourth order compact difference (FOC) scheme using a multigrid method.     

The lifetime of positive streamers in a pulsed point-to-plane gap in atmospheric air

A determination has been made of the lifetime of positive streamers produced in atmospheric air in a positive point-to-plane gap to which was applied a 40 nsec, 40 kV voltage pulse. The streamer tips have been detected at a given plane in the gap by means of a photomultiplier and high speed oscilloscope. It was found that the streamer tips continued to propagate in the gap, long (up to 35 nsec) after the voltage pulse was removed, in accordance with the predictions of a recently presented model of streamer propagation. Association of this long lifetime with the properties of an isolated tip was made possible by the detection of a new phenomenon at the anode. At the end of the voltage pulse a second luminosity was observed to leave the anode and to extend along the paths of the primary streamers for about one third of their length. This is shown to be the maximum extent of a more highly conducting trunk, behind and separated from the streamer tip, affecting both the propagation of the tip and the eventual transition of a streamer to a breakdown spark.     

抛物方程的多重非均匀网格模型及其应用

提出了抛物方程的多重非均匀网格模型,以准确求解三维空间存在多辐射源的电波传播问题。通过对不同辐射源建立不同的坐标系,并对其仿真空间采用不同的非均匀网格划分,构建了抛物方程的多重非均匀网格模型。在此基础上,实现了三维多辐射源问题的并行计算。实例仿真了空间存在四个辐射源的电波传播特性。结果表明,抛物方程的多重非均匀网格模型能够准确求解多源的空间电磁场分布特性,且在该算例中,并行技术使得抛物方程的计算速度提升了2.41倍,极大地提高了抛物方程对三维多源问题的求解效率。     

抛物方程的多重非均匀网格模型及其应用

提出了抛物方程的多重非均匀网格模型,以准确求解三维空间存在多辐射源的电波传播问题。通过对不同辐射源建立不同的坐标系,并对其仿真空间采用不同的非均匀网格划分,构建了抛物方程的多重非均匀网格模型。在此基础上,实现了三维多辐射源问题的并行计算。实例仿真了空间存在四个辐射源的电波传播特性。结果表明,抛物方程的多重非均匀网格模型能够准确求解多源的空间电磁场分布特性,且在该算例中,并行技术使得抛物方程的计算速度提升了2.41倍,极大地提高了抛物方程对三维多源问题的求解效率。     

The velocity of streamer tips in impulse point-to-plane corona in air,using Lichtenberg figure techniques

Positive and negative streamer lengths were measured in point-to-plane impulse corona in air at atmospheric pressure using Lichtenberg figure technique. Applying short time pulses from 9 to 40 nsec duration time-distance plots were obtained, which allowed one to determine the streamer tip velocity. For a 4 cm gap, a 1 mm diameter point, and a 30 kV pulse an average tip velocity of 1.8×10⁸ cm/sec was found. Comparing these data withHudson's photomultiplier measurement, we may identify the Lichtenberg figure with the “primary” streamer ofHudson. The negative streamer tip velocity in the cathode part of the gap was approximately an order of magnitude smaller than the positive streamer velocity.     

正极性纳秒脉冲电压下变压器油中流注放电仿真研究

建立了二维轴对称流体模型, 仿真研究了正极性纳秒脉冲电压下变压器油中针-板电极流注放电的起始与发展过程, 得到了不同的外施电压幅值、脉冲上升沿时间与电极间隙距离下油中流注放电的形貌、 电场强度与空间电荷密度分布等. 仿真结果表明: 空间电荷加强了流注头部前方电场, 使流注通道更易于向前推进, 形成"电离波"; 随着外施电压幅值升高, 流注发展的平均速度显著变大; 较陡的脉冲上升沿形成的放电半径较大, 对应的最大电场强度值变小; 随着电极间隙距离的增加, 流注发展平均速度变快. 仿真显示纳秒脉冲下放电中油温无明显升高, 表明此类放电过程没有明显的油气化现象. 我们认为, 场致电离是油中带电粒子产生的主导机制; 空间电荷效应增强流注前方电场使得电离进一步发展, 最终导致击穿. 本研究有助于加深对变压器油中放电起始、发展直至击穿过程的认识以及对液体电介质中电离机制的理解. 关键词： 变压器油 流体模型 流注放电 空间电荷效应     

Calculation of the electroelastic Green’s function of the hexagonal infinite medium

The electroelastic 4 × 4 Green’s function of a piezoelectric hexagonal (transversely isotropic) infinitely extended medium is calculated explicitly in closed compact form ((73) ff. and (88) ff., respectively) by using residue calculation. The results can also be derived from Fredholm’s method [2]. In the case of vanishing piezoelectric coupling the derived Green’s function coincides with two well known results: Kröner’s expressions for the elastic Green’s function tensor [4] is reproduced and the electric part then coincides with the electric potential (solution of Poisson equation) which is caused by a unit point charge. The obtained electroelastic Green’s function is useful for the calculation of the electroelastic Eshelby tensor [16].     

复代数方程组几种迭代法的比较

本文从二维非线性Schrödinger方程出发,推导出五对角的复代数方程组,并应用高斯-赛德尔迭代法、SOR迭代法、复双共轭梯度法以及预处理复双共轭梯度法等对求解的计算量进行了比较。同时,又将复代数方程组化成七对角的实代数方程组,用高斯-赛德尔迭代法、SOR迭代法以及PCG法(预处理共轭梯度法)等进行了比较。结果表明,PCG法在上述几种方法中是最有效的。本文还对SOR松弛因子的选择进行了讨论。     

A high‐accuracy complex‐phase method of simulating X‐ray propagation through a multi‐lens system

The propagation of X‐ray waves through an optical system consisting of many X‐ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite‐difference method is applied. The error of simulation is analytically estimated and investigated. It was found that a very detailed difference grid is required for reliable and accurate calculations of the propagation of X‐ray waves through a multi‐lens system. The reasons for using a very detailed difference grid are investigated. It was shown that the wave phase becomes a function, very quickly increasing with increasing distance from the optical axis, after the wave has passed through the multi‐lens system. If the phase is a quickly increasing function of the coordinates perpendicular to the optical axis, then the electric field of the wave is a quickly oscillating function of these coordinates, and thus a very detailed difference grid becomes necessary to describe such a wavefield. To avoid this difficulty, an equation for the phase function is proposed as an alternative to the equation of the electric field. This allows reliable and accurate simulations to be carried out when using the multi‐lens system. An equation for the phase function is derived and used for accurate simulations. The numerical error of the suggested method is estimated. It is shown that the equation for the phase function allows efficient simulations to be fulfilled for the multi‐lens system.     

Physical and mathematical modeling of the electron-beam-induced charging of ferroelectrics during the process of domain-structure switching

The results of modeling the dynamic charging processes that arise when ferroelectrics are under the action of an electron beam in a scanning electron microscope are presented. Implementation of the model is based on simultaneous solution of the continuity equation and Poisson equation with allowance for the radiation-stimulated intrinsic conductivity of the irradiated sample and with an initial charge distribution determined using the Monte Carlo method. The multidimensional boundary evolutionary problem is solved using grid methods. The model permits one to study the dynamics of the process of the electron-beam-induced charging of ferroelectrics. Estimates for the values of fields generated by charges accumulated during the irradiation process are presented for a set of modeling parameters corresponding to physical data obtained in experimental observations of the polarization switch for a ferroelectric lithium niobate crystal.     

Improved fictitious charge method for calculations of electric potential and field generated by point-to-plane electrodes

In the framework of standard tip-to-plane electrode geometry favorable to corona streamer discharge development at atmospheric pressure, this work is devoted to the improvement of fictitious charge method for calculations of electric potential and field repartition when the tip is powered by a DC voltage. It is in fact dedicated to implement the image charge method (generally used in plane-to-plane electrodes) in the case of a point-to-plane geometry. The numerical method is based on the solution an open system of n equations with m unknowns (n >> m) where m is the number of fictitious charges and n the number of contours at the surface of the tip electrode defining the boundary conditions. This numerical technique can accurately interpolate the shape of the electrode tip whatever its geometry and hence allows us to accurately calculate the electric potential and field even at a position very close to the electrode. It is noteworthy that the solution of such open system of equations cannot be obtained from conventional techniques (Cramer, Gauss, matrix inversion, etc.). We used the method of least squares which enables us to close the equation systems and to find the optimal solution fulfilling all the required boundary conditions. The present method is therefore based on the coupling between the conventional method of fictitious charges using image charge method and the optimization by the Least Squares Method. The results of simulation show that the punctual fictitious charges have given the most accurate results when the electrode has symmetry of revolution like the present geometry of a pen shape anode cylinder ended by a sharp tip set in front of cathode plane.     

From electrostatics to optics: The study on the soliton propagation in lead glass using the image beams method

We investigate the soliton propagation in lead glass with rectangle boundary by the method of image beams. This method is the analogue of the electric image method which is used to solve the Poisson type equation. In the general case that the beam width is much smaller than the boundary size, the soliton formation and the soliton steering are analytically studied independently. The critical power of the soliton formation is boundary independent. The boundary effect only provides, for the soliton steering, the dynamic force which is equivalent to the force between the soliton beam and the infinite number of image beams. The closed-form steering trajectories of the solitons are in good agreement with the experimental results.     

Mechanism for propagation of a positive leader

A model of leader breakdown in air is considered. The channel is formed due to heating of the streamer trace in the field of the streamer zone. A previous model of a streamer is generalized with allowance for recombination of charged particles. A mathematical model of heating of the streamer trace is developed. It is demonstrated that, at a given potential, the ignition of the channel is provided by streamers that possess a certain charge and the corresponding propagation velocity. This velocity determines the propagation velocity of a steady leader. The dependence of the leader velocity on the cloud potential is found. The results obtained are compared with the data from in-situ observations and laboratory studies.     

The space charge layer of the electrical probe taking into account the collisions

Technical Physics - The space charge layer of a cylindrical probe has been considered under moderate pressures. A precise solution of Poisson’s equation has been obtained in the approximation...     

等离子体粒子模拟的静电波谱响应特性

本文系统地分析了等离子体粒子模拟的静电波谱响应特性。我们引入了波谱响应函数的概念,并对有限大小粒子的高斯型、三角型和方块型分布及其在网格点附近的偶极展开,对Poisson方程的有限差分和FFT解法分别导出了响应函数表达式。分析讨论了有限大小粒子形状、宽度和处理方式,空间离散化和Poisson方程求解方法对粒子模拟波谱响应特性的影响及对短波噪声的抑制特性。     

Double charge layer in high-current electron avalanche

New experimental data reported in [6] allow completed electron avalanche to be represented as a double charge layer. Based on this model, qualitative explanation is given to the issues related to formation and growth of the streamer, and the structure of the ionized channel and its stability mechanism are considered. The model defines the conditions for the growth of the channel in weak fields and explains the increase in the velocity of the streamer’s motion towards the cathode.     

Measurement of the Dynamic Displacement Current as a New Method of Study of the Dynamics of Formation of a Streamer at a Breakdown of Gases at a High Pressure

The dynamics of formation of streamers in a “needle–plane” gap filled with air at atmospheric pressure has been studied. It has been shown that the time dependence of the dynamic displacement current measured by either a current shunt or a collector placed behind a grid electrode is determined by the rate of variation of the shape and dimensions of a streamer. The presence of a single peak on oscillograms of the dynamic displacement current means that a ball streamer is formed in the gap and does not cross the gap during the time of voltage application. The presence of two peaks on oscillograms of the dynamic displacement current means that the ball streamer crosses the gap and reaches the opposite electrode. In this case, the ball streamer is usually transformed to a cylindrical one. It has been shown that the measurement of the dynamic displacement current makes it possible to determine the time dependence of the electric field strength near the planar electrode.     

The Numerical Algorithm of Secondary Emission Microwave Electron Gun

a tracking algorithm using grid–based space charge fields is studied for the analysis of secondary emission microwave electron gun(semeg). the poisson equations of the space charge forces are determined in the bunchs rest frame with a multi–grid method. the particles equations of motion are solved with a fifth–order embedded runge–Kutta method. the results of the semeg by this algorithm are presented and compared with these by mafia algorithm.     

变像管相机中空间电荷效应的统计动力学分析

 从Boltzmann积分微分方程出发推出了保守势场中电子数密度按势能的分布规律,即Boltzmann统计分布。以此为基础,从统计动力学的角度详细分析了变像管相机中超短电子脉冲内部的空间电荷效应,通过求解Poisson方程得出了表征空间电荷效应的两个特征参量：空间电荷密度分布函数和速度分布函数,并对其按电位的动态变化规律进行了定性讨论。结果表明,限制变像管中的低电位区域和其中光电子脉冲从高电位向低电位传输的区域都将有助于优化整个变像管的性能。同时也重新讨论了光电阴极附近强加速场对光电子脉冲时间弥散的抑制作用,最终确定了其物理机制为不等位区间中电子脉冲空间分布的高度集中性。