磁边界效应对径向磁场中等离子体束流运动轨迹的影响

根据离子与径向磁场的约束关系，用面向对象的单元粒子法模拟了极向偏转器中等离子体束流在均匀和非均匀径向磁场中的运动情况，得到了在磁边界效应下极向偏转器内部畸变电场的分布，分析了对质量分离的影响。模拟成果对质量分离器、质谱分析仪及材料提纯等装置的研制、特殊位形电磁场控制多质量束流等相关领域的研究有参考价值。     

等单元长度多间隙加速结构的束流动力学特性

等单元长度多间隙加速结构是一种非同步加速结构,当粒子在加速结构中的速度变化很明显时,粒子在每个间隙的相位是不相同的,薄透镜近似下的束流纵向运动方程没有考虑粒子在加速结构中的速度变化,这在单腔的能量增益相对于粒子能量很小的情况下是合理的,但是当粒子在加速结构中的速度有明显变化时,这种处理方式是不够的。本文从带电粒子在电磁场中的运动方程出发,通过目前普遍采用的理论建立了束流在这种加速结构中的纵向运动方程,通过数值方法得到了粒子在这种结构的相运动,计算了不同初始能量的粒子在不同的电场梯度及单元数的加速腔中运动的能量变化情况。结果显示:粒子相运动与不考虑粒子速度变化的薄透镜近似下的相运动轨迹有明显差异,当粒子速度变化超过一定值后,薄透镜近似下束流纵向运动方程在计算束流能量增益时与同步相位之间满足的余弦关系不再成立,并给出了能量增益变化曲线相对余弦曲线的偏离情况与电场梯度、间隙数、初始能量等参数的关系。     

混合层中柱状粒子运动的研究

本文在直接数值模拟混合层流场的基础上,求解柱状粒子运动方程而得到粒子运动轨迹,说明粒子在混合层中的不同区域,其运动轨迹也不同,有的呈现波状轨迹,有的呈现环状轨迹,有的是混合轨迹。粒子的混合程度与St数有关。文中结论对工程应用有指导意义。     

霍尔推力器放电通道溅射腐蚀计算

 为了预示霍尔推力器的寿命,建立了推力器粒子束放电通道的2维电磁场模型,模拟的推进剂为氙。利用PIC方法跟踪粒子在电磁场中的运动。磁场的求解采用拉普拉斯方程,电场的求解采用泊松方程。电子由阴极喷入通道,并在电磁场中与原子发生电离碰撞生成离子。在跟踪离子的过程中记录下撞击到内外壁面的离子个数、角度和能量。利用记录下的参数进行腐蚀计算,得到当溅射阈值能量分别为10,20,30,40,50 eV时通道壁面的腐蚀速率。推力器放电通道出口附近的最大腐蚀速率约为1.7×10^-9 m/s。     

E2》H2的均匀正交电磁场中带电粒子的相对论运动

通过求解带电粒子在均匀电场中与坐标系选取无关的三维矢量相对论运动方程,进而利用洛伦兹变换方法,求得了带电粒子在E2>H2的均匀正交电磁场中相对论运动轨迹的一般三维矢量式.并使用Mathematica软件在直角坐标系中描绘了相应的粒子相对论运动轨迹图.     

带电粒子在正交恒定电磁场中运动状态的分析

由洛伦兹力公式出发,分析带电粒子在相互垂直的恒定电磁场中运动的方程,由此得到一些常见的运动轨迹,并给出带电粒子在电磁场中的一种新的轨迹——长辐旋轮线．     

带电粒子在正交电磁场中运动分析及运动轨迹的计算机描绘

本文运用力和运动的分离与合成方法,分析带电粒子在正交电磁场中运动的轨迹、速度和加速度,简化了解题方法,并采用CAI课件描绘其运动轨迹,使学生在强化物理概念的同时得到综合能力的培养。     

负径向电场对荷电粒子运动的影响及其数值模拟

从负径向电场产生的电漂移改变荷电粒子运动的极向运动速度着手,推导出在负径向电场存在时安全因子的表达式,分析了安全因子对荷电粒子漂移位移和运动轨迹的影响。建立了在负径向电场条件下,荷电粒子在梯度磁场和曲率磁场中运动数学模型。通过数值模拟,获得了通行粒子、香蕉粒子的漂移位移和运动轨迹所呈现出的新特点和规律:负径向电场改变了荷电粒子的最大漂移位移。当荷电粒子的极向运动速度增加时,最大漂移位移减小,反之增大;改变了荷电粒子的运动轨迹,通行粒子的轨亦可能变为香蕉粒子的轨迹,香蕉粒子的轨迹可能变为通行粒子的轨迹,当电场达到足够的强度时,均成为在极向上顺时针运动的通行粒子轨迹。     

三级近似束流光学计算程序

为了精确计算束流在离子光学系统中的传输,用Visual FORTRAN 6.5语言编写了一个计算程序,长约13000行. 此程序可以计算由三圆筒单透镜、三膜片单透镜、双元筒透镜、均匀场静电加速管、磁四极透镜、六极磁铁、静电四极透镜、偏转磁铁、螺线管透镜、ExB~正交电磁场分析器、静电偏转器、漂浮管、QWR(Quarter Wave Resonators)和SLR(Split Loop Resonators)射频加速元件等元件任意组成的离子光学系统. 粒子轨迹的计算可精确到三级近似. 粒子的分布类型也可以有多种选择. 程序具有最优化计算功能,即可以自动调整元件的参数,以实现所需要的光学条件. 各元件之后的横向和纵向相图以及系统的束流包络线以图形方式显示在屏幕上.     

非相对论下均匀斜交电磁场中正电荷的运动状况分析

文章对非相对论下均匀斜交电磁场中的正电荷+q进行了动力学矢量分析,将其运动分解为沿磁场方向的匀加速直线运动、垂直于电、磁场方向的匀速直线运动和垂直于磁场方向的匀速率圆周运动,进而推理出电荷完整的运动学方程;然后将运动学方程进行“约化”和简化,作出不同初速度下电荷在xy平面内的投影运动轨迹并加以分析,指出轨迹的若干特点及其内在的原因;举例作出电荷的空间轨迹图并指出其中蕴含的共性;对均匀正交电磁场情形下的3种特殊情况进行了讨论.此外,文末还指出本文解法的核心思想是参考系的切换.     

非均匀磁场中等离子体射流质量色散强度

研究了非均匀磁场中多质量射流的运动轨迹,推导出质量色散强度表达式。考虑到不同入射方式及羽流角度的情况下,应用MATLAB模拟射流的运动轨迹,计算出质量色散强度,并同均匀磁场中的质量色散强度大小相比较,以确定该种磁场中射流质量分离的效果。模拟结果表明:非均匀磁场中多质量射流的质量色散强度大于均匀磁场的情况,可实现等离子体射流的高效质量分离。     

Basic features of a charged particle dynamics in a laser beam with static axial magnetic field

In this paper, the trajectory and kinetic energy of a charged particle, subjected to interaction from a laser beam containing an additionally applied external static axial magnetic field, have been analyzed. We give the rigorous analytical solutions of the dynamic equations. The obtained analytical solutions have been verified by performing calculations using the derived solutions and the well known Runge-Kutta procedure for solving original dynamic equations. Both methods gave the same results. The simulation results have been obtained and presented in graphical form using the derived solutions. Apart from the laser beam, we show the results for a maser beam. The obtained analytical solutions enabled us to perform a quantitative illustration, in a graphical form of the impact of many parameters on the shape, dimensions and the motion direction along a trajectory. The kinetic energy of electrons has also been studied and the energy oscillations in time with a period equal to the one of a particle rotation have been found. We show the appearance of, so-called, stationary trajectories (hypocycloid or epicycloid) which are the projections of the real trajectory onto the (x, y) plane. Increase in laser or maser beam intensity results in the increase in particle’s trajectory dimension which was found to be proportional to the amplitude of the electric field of the electromagnetic wave. However, external magnetic field increases the results in shrinking of the trajectories. Performed studies show that not only amplitude of the electric field but also the static axial magnetic field plays a crucial role in the acceleration process of a charged particle. At the authors of this paper best knowledge, the precise analytical solutions and theoretical analysis of the trajectories and energy gains by the charged particles accelerated in the laser beam and magnetic field are lacking in up to date publications. The authors have an intention to clarify partly some important aspects connected with this process. The presented theoretical studies apply for arbitrary charged particle and the attached figures-for electrons only.     

Small-angle approximation for an ion beam in an external electromagnetic field

A small-angle approximation method is formulated for a curvilinear ion beam propagating in an electromagnetic field. The effects of particle velocity scatter and multiple elastic scattering on the beam path in a magnetic field, the electric field of a cylindrical capacitor, and mutually orthogonal electric and magnetic fields are considered. An analytical model for beam power compression is developed.     

Effect of polarization on a spin particle trajectory

It is demonstrated that the problem of determining the parameters of trajectories of spin particles and beam of rays in the case of radiation with allowance for polarization is reduced to a variational problem with higher derivatives. It is demonstrated that in the limit of small values of the curvature and torsion, the higher derivatives can be expressed through the parameters of the medium. In this case, the curvature and torsion together with the polarization projection onto the trajectory determine an analog of the 4-potential which in its turn specifies an analog of the electromagnetic field tensor where the projection of polarization onto the trajectory plays the role of charge for a charged particle. It is demonstrated that the Magnus optical effect for dissipative solitons is determined not only by helicity σ, but also by topological index m (by the projection of the orbital soliton momentum onto the soliton trajectory). In an inhomogeneous medium, a relationship between the Magnus optical effect and nonholonomicity of the field of unit vectors tangent to the trajectory is established.     

Space-time trajectories of quantum particles

The concept of trajectory is extended theoretically from classical mechanics through nonrelativistic and relativistic quantum mechanics. Forced motion of the particle as might be caused by an electromagnetic field is included in the equations. A new interpretation of the electromagnetic potential and the gauge transformation is presented. Using this formal structure, the problem of collecting particles into packets using trajectories is studied for both quantum mechanics and classical mechanics. Quantum mechanical trajectories are found to be significantly more restricted than those allowed by classical physics. The uncertainty principle comes from the second-order nature of the field equation without recourse to statistical arguments. The trajectories of particles in a quantum state can be calculated explicitly from the wave function (also see article in Volume 20, Number 6).     

基于焦散线方法的自加速光束设计

以艾里光束为代表的自加速光束是一类在自由空间中具有弯曲传播特性的新型特殊光束.这类光束因其具有无衍射、自加速和自修复等奇异特性引起了人们的广泛关注,有望应用于光学微粒操控、激光微加工、全光路由和超分辨成像等诸多领域.由于艾里光束只能沿着抛物线的轨迹传播,限制了其在实际应用中的灵活性,因而设计出能够沿着不同轨迹传播的自加速光束是这一研究领域的关键问题,而基于焦散线方法的自加速光束设计是解决该问题的有效途径之一.这一方法是将设计的传播轨迹与光学焦散线联系起来,通过分析形成该焦散线所需的光线簇构造出对应的初始场分布.基于该原理并经过不断发展,不同类型的自加速光束相继得以实现,并且借助维格纳函数还可以同时实现实空间和傅里叶空间的自加速光束设计,为自加速光束的应用提供了更多的可能性.本文对基于焦散线方法的自加速光束设计原理和进展进行全面介绍.     

基于Geant4的回旋加速器束流动力学计算

针对回旋加速器的束流动力学设计,基于Geant4模拟研究,提供一种可行的数值模拟方法。通过电磁场仿真软件Opera建立相应的电磁场数据导入到Geant4中进行插值计算,利用Geant4自带的电磁场微分方程与微分方程求解器计算粒子的平衡轨道,振荡频率以及加速轨道。其结果表明:对于横向运动而言,Geant4的计算结果与传统数值方法计算结果趋于一致;对于轴向运动而言,由于磁场插值方法的差异性,二者有一定的区别,对于在加速过程中的非平衡粒子,其能量变化围绕平衡粒子振荡。对于束损,通过限制粒子的运动时间,轴向位移加快计算效率,加入电极碰撞的判定使模拟更趋近实际情况。     

Homotopy analysis method to study a quadrupole mass filter

The homotopy analysis method (HAM) is applied to study the behavior of a hyperbolic rods of quadrupole mass filter and a sinusoidal potential form V(ac) cos(Ωt). Numerical computation method of a 20th-order HAM is employed to compare the physical properties of the confined ions with fifth-order Runge-Kutta method. Also, comparison is made for the first stability region, the ion trajectories in real time, the polar plots, and the ion trajectory in x?-?y plan. The results show that the two methods are fairly similar; therefore, the HAM method has potential application to solve linear and nonlinear equations of the charge particle confinement in quadrupole field.