光在两层平板介质中传输的时域P3方程

生物表面组织是多层介质,目前只有光在单层介质中传输的P3方程,本文给出了光在两层平板介质中传播的P3方程的时域解,编写蒙特卡罗模拟进行验证。结果表明P3时域方程与蒙特卡罗模拟符合很好,说明双层平板介质的P3方程正确地反映了光子在介质中的迁移。与扩散时域方程相比,在峰值位置附近,P3时域方程测量的反射率和透射率更加准确,在远离峰值时,P3方程与扩散方程结果一致。双层平板介质的P3时域方程扩展了P3方程的应用范围,可以替代扩散方程,也可以代替单层平板介质的P3方程,可以更好地研究光在生物组织中的传播过程。     

基于微可压液体的统一对流扩散型流体力学方程组

为了表达上的方便及求解格式的统一,通常采用统一的方程形式来表达连续方程,动量方程、能量方程、湍动能方程和耗散方程等.除了连续方程外,其他方程都可以写成对流扩散方程的形式,由于没有扩散项,连续方程比较特别,也相对不便处理.在微可压液体区,通过合理的数学推导,不作任何近似、假定与简化,本文得到一套全新的连续方程形式.该新方程以压力为未知变量,是对流扩散型的,使得所有的流体动力学方程组都具有完全统一的方程形式.     

Kaluza理论的运动定律

本文指出,如同在广义相对论中粒子运动方程是场方程的推论一样,在引力场与电磁场的Kaluza统一理论中,粒子的运动方程也是场方程的一个推论,即带电粒子在引力场和电磁场中的运动方程可以从Kaluza统一理论中的场方程推导出来。本文进而在Minkowski时空的条件下,借助Maxwell理论的Kaluza形式,得到Maxwell方程也包含了带电粒子运动方程的结论。 关键词：     

应用于碱卤化物固体的通用状态方程

提出一种能精确考虑固体结合能的通用状态方程,并且在高压和膨胀区域都具有正确的行为,不会出现物理上不正确的振荡现象.将新方程与文献中的典型方程应用于15种碱金属卤化物和一种碱土金属氧化物,结果表明新方程在给出正确结合能数据的同时,能够很好地拟合实验压缩数据.由Vinet方程和Morse方程定出的参数随数据范围变化很明显,新方程定出的参数随数据范围变化不明显.新方程的通用性优于Vinet方程和Morse方程. 关键词： 固体 通用状态方程 结合能 碱金属卤化物     

直线加速Kinnersley黑洞中Dirac粒子的热辐射

在直线加速Kinnersley时空中,将相互耦合的Dirac方程化为二阶方程,采用新的乌龟坐标变换,在视界面附近消除二阶方程中的耦合化成了标准波动方程,得到辐射温度函数和Hawking热辐射谱. 关键词： 黑洞 Dirac方程 乌龟坐标变换 Hawking辐射     

含有广义守恒律的生长方程标度奇异性的直接标度分析

利用直接标度分析方法研究一个含有广义守恒律生长方程的标度奇异性,得到强弱耦合区域的奇异标度指数.作为其特殊情况,这个方程包含Kardar-Parisi-Zhang（KPZ）方程、 Sun-Guo-Grant（SGG）方程以及分子束外延（MBE）生长方程,并能对其进行统一的研究.研究发现, KPZ方程和SGG方程,无论在弱耦合还是在强耦合区域内都遵从自仿射Family -Vicsek正常标度规律;而MBE 方程在弱耦合区域内服从正常标度,在强耦合区域内能呈现内禀奇异标度行为.这里所得到生长方程的奇异标度性质与利用重正化群理论、数值模拟以及实验相符很好. 关键词： 标度奇异性 强耦合 弱耦合     

非线性光纤光学中非线性薛定谔方程推导逻辑的探讨

非线性薛定谔方程是描述光脉冲在光纤中非线性传输的基本方程,广泛应用于光纤通信、光纤激光器等领域。在现有的非线性光纤光学的经典教材中对非线性薛定谔方程的推导,采用的是直接在非线性介电常数中引入非线性折射率效应。本文指出了该方法对于传输方程非线性项处理的局限甚至不妥之处,给出了一种非线性薛定谔方程较严格的推导方法,即从非线性的波动方程出发,讨论不同非线性效应的非线性极化强度驱动源的不同表现形式,并将方程作横向积分处理。本文详细阐述了从非线性源的角度出发推导非线性薛定谔方程的方法,并以四波混频等非线性效应为例,帮助读者理解非线性效应对于传输方程的影响;此外,还探讨了在推导非线性薛定谔方程中的正负频表示等问题。     

Lam函数和非线性演化方程的多级准确解的不变性

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程 .并在Lam 方程和Lam 函数的基础上 ,应用Jacobi椭圆函数展开法求出了非线性演化方程的多级准确解 ,从而得到了多级准确解中存在的守恒形式 .     

Lamé函数和非线性演化方程的多级准确解的不变性

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.并在Lamé方程和Lamé函数的基础上,应用 Jacobi椭圆函数展开法求出了非线性演化方程的多级准确解,从而得到了多级准确解中存在的守恒形式.     

正则形式的QED约束关联动力学(Ⅱ)等时关联格林函数的运动方程与二体关联近似

本文把多时关联格林函数的运动方程转变成等时关联格林函数的运动方程,包括电子和光子的密度矩阵的运动方程以及等时顶点的运动方程,在二体关联截断近似下,给出运动方程,高斯定律及Ward恒等式的明显表达式.     

带状电子束的空间电荷场

 利用理论分析和数值计算的方法研究了矩形波导内均匀电流密度的带状电子束模型的空间电荷场,给出了该带状电子束模型的空间电荷场的解析表达式,并研究了空间电荷场随带状电子束的几何参数和物理参数的变化规律。研究表明：在不改变电流密度的前提下,更宽的电子束可以传输更强的束流,而空间电荷场并不随束宽度的增大而增大,但是增加电子束厚度会使空间电荷场显著增强,从而不利于高流强电子束的传输;对于相同电流的带状电子束,保持电子束厚度不变,增大电子束宽度,相应地降低电流密度是降低空间电荷场的一个很好的途径,而保持电子束的宽度不变,增大束厚度,相应地降低电流密度只会使沿着电子束截面宽度方向的电场减小,而沿着电子束截面厚度方向的电场基本不变;对于相同电流和电流密度的带状电子束,更宽、更薄的电子束横截面尺寸能使沿着电子束截面宽度方向的电场降到更低,而沿着电子束截面厚度方向的电场只是略有减小。     

High current density ion-beam extraction

High current density (up to 700 mA/cm²) ion-beam extraction has been studied by 3D code KOBRA3-INP [INP, Junkerstr. 99, 65205 Wiesbaden, Germany]. Ion beams with such high current densities can be generated by ECR ion source driven by 37.5 GHz/100 kW gyrotron [Golubev S.V. et al. Trans. Furion Sci. Technol., 47, n. 1T, fuste 8, 345]. The influence of plasma parameters on extracted ion beam has been investigated. Different geometries of extraction system and applied potentials have been simulated to optimize extracted and transported ion beam current. KOBRA3-INP code has been applied to simulate ion-beam transport as well. The results of simulations have been compared with experimental results. Good agreement between measurements and simulations was always found by varying ion-beam space-charge compensation degree.     

2-D corona field computation in configurations with ionising and non-ionising electrodes

An efficient method is proposed for the computation of the electric field strength and of the space-charge density in configurations of at least three ionising and non-ionising electrodes. The physical model is derived under the assumptions commonly accepted for the study of corona fields. The mathematical model makes use of a conformal mapping that converts the actual boundary-free field zone into a rectangular domain with well-defined boundary conditions. The finite-difference method is then used for solving the differential equations that describe the ionic space-charge and electric field distribution. The computational procedure was employed for studying the simple case of the drift zone of the corona discharge generated between a so-called dual electrode and a grounded plate. The dual electrode consisted of an ionising wire (diameter 0.22 mm) located at 20 mm from a tubular metallic support (diameter 25 mm). The computed current–voltage characteristic and current density distribution at the surface of the collector plate were in good agreement with the experimental data obtained for this combined corona–electrostatics electrode arrangement.     

A new approach for evaluating the current and charge density distributions in electron guns and beams

Current and space-charge density distribution calculation is of great significance for numerical analysis and design of high-current electron guns and beams. When the electrons’ thermal initial velocities are taken into account, though there have been some numerical methods published, the calculation is very complicated. By introducing equivalent meridional potential and projection trajectory theory, the curvilinear axis trajectory equation for electrons neighboring to a central curved trajectory in rotationally symmetric electro-magnetic fields is derived in first- and second-order approximations. The evolution equation of the current density distribution of toroidal electron sub-beams is derived and it can be used to calculate the current and charge density distribution in electron beams and guns in iteration calculation. A compact numerical algorithm for calculating round high-current electron guns and beams was developed and related program was written as well. As examples, the evolution of the current density distribution of a Pierce gun and a periodic magnetic focusing high-current electron beam is simulated. This proves that this method is effective and practical.     

Transition from statistical Coulomb interactions to averaged space-charge effect

The statistical Coulomb interaction effect and the averaged space-charge effect, which broaden electron-beam size, have been studied to clarify their applicable regions and their transition region as a function of beam current. The beam size of a single beam segment can be analytically estimated by two theories based on different approaches: the expression of the trajectory displacement effect based on stochastic electron-electron interactions, and the beam radius equation based on the Coulomb repulsion force by averaged space charge. Both theories were compared with Monte Carlo simulation results for a beam-current ranging from 0.1 nA to 10 mA. It was confirmed that the beam size at the end of the focusing segment could be predicted by the expression of the trajectory displacement effect in a low beam current and by the beam radius equation in a high beam current. In addition, the beam sizes predicted by these theories were found to result in almost the same for a medium beam current. The theories transited as the beam-current increased.     

准矩形截面强流相对论带状电子束的传输

提出利用准矩形截面带状电子束传输强电流.相对于目前广泛采用的椭圆形截面带状电子束,在大横纵比,即电子束的宽度(横向)远大于厚度(纵向)的情况下,其厚度沿横向更加均匀,利用冷阴极爆炸发射容易产生.该电子束利于高功率微波发生器中腔体模式的控制和束波作用效率的提高,如果利用模块化的结构还可使阴极及聚焦磁铁在宽度上的扩展更加容易.首先给出了准矩形截面带状电子束空间电荷场的典型分布,然后根据该分布和束匹配的方法对相互独立的周期会切磁铁和边聚焦磁铁分别进行了设计.其中边聚焦磁铁的磁化方向与以往的纵向不同,为横向磁化,其激励的边聚焦磁场在电子束宽边的边缘附近的梯度更大,有利于横向的束匹配.最后根据理论分析的结果进行了粒子模拟.结果表明,300keV,3kA的准矩形截面强流相对论带状电子束可以在0.163T的周期会切磁场和0.064T的横向磁化边聚焦磁场中稳定传输,电流传输效率大于98%.     

Dependence of the transverse dynamics of the plasma electrons in the ion focus regime on the ratio of the radius of a relativistic electron beam to the radius of the ion channel

A study is made of the effect of the magnetic self-field of a relativistic electron beam propagating in the ion focus regime on the transverse dynamics of plasma electrons. For Gaussian radial profiles of the beam and the ion density in the channel, the maximum deviation of the plasma electrons from the axis of the beam-plasma system is determined as a function of the space-charge neutralization fraction, the ratio of the characteristic beam radius to the channel radius, and the net beam current.     

Drift compression of an intense neutralized ion beam

Longitudinal compression of a velocity-tailored, intense neutralized beam at 300 keV, 25 mA has been demonstrated. The compression takes place in a 1-2 m drift section filled with plasma to provide space-charge neutralization. An induction cell produces a head-to-tail velocity ramp that longitudinally compresses the neutralized beam, enhancing the beam peak current by a factor of 50 and producing a pulse duration of about 3 ns. This measurement has been confirmed independently with two different diagnostic systems.     

Analytical and simulation studies for diode and triode ion beam extraction systems

This work is concerned with ion beam dynamics and compares the emittance to aberration ratios of two-and three-electrode extraction systems. The study is conducted with the aid of Version 7 of SIMION 3D ray-tracing software. The beam dependence on various parameters of the extraction systems is studied and the numerical results lead to qualitative conclusions.     

Feasibility study on high current ion beam extraction from anode spot plasma for large area ion implantation

In this paper, we have investigated the feasibility of the high current beam extraction from anode spot plasma as an ion source for large area ion implantation. Experiments have been carried out with the ambient plasma produced by inductive coupling with radio-frequency (RF) power of 200 W at the frequency of 13.56 MHz. Anode spot plasmas are generated near the extraction hole of 2 mm in diameter at the center of a bias electrode whose area exposed to the ambient plasma can be changed. It is found that the maximum ion beam current is extracted at the optimum operating pressure at which the area of bias electrode exposed to ambient plasma is fully covered with the anode spot plasma whose size is dominantly determined by the operating pressure for given gas species. It is also observed that the extracted ion beam current increases nonlinearly with the bias power due to the changes in size and shape of the anode spot plasma. With the well-established anode spot plasma operating at the optimum gas pressure, we have successfully extracted high current ion beam of 6.4 mA (204 mA/cm²) at the bias power of 22 W (∼10% of RF power), which is 43 times larger than that extracted from the plasma without anode spot. Based on the experimental results, criteria for electrode design and operating pressure for ion beam extraction from larger extraction aperture are suggested. In addition, the stability of anode spot plasma in the presence of ion beam extraction through an extraction hole is discussed in terms of the particle balance model.