用二维含时Fokker-Planck方程分析Tokamak中α粒子的输运

按分布函数的定义不同,描述高能带电粒子在等离子体中输运的-Planck方程有不同的形式。从数值计算的观点出发对两种不同形式的Fokker-Planck方程作了比较和评价,并指出Fokker-Planck碰撞项可解释为速度空间的对流扩散项。在此基础上用有限差分方法求解二维(速度一维,几何一维)含时Fokker-Planck方程,编制了计算程序CAPT,并将其应用于α粒子的输运研究。最后计算了典型的Tokamak D-T聚变堆参数下α粒子的损失,并给出了堆内α粒子的分布及损失α粒子的速度分布。     

Third adiabatic invariant and the collisionless distribution function of particles in a tokamak

It has been shown that the distribution function of an ensemble of particles with a given energy in a collisionless regime in a tokamak is formed as a function primarily of the third adiabatic invariant, particularly in the near-axis region. In the periphery of the plasma column, the contribution of the toroidal component of the canonical momentum/longitudinal adiabatic invariant to the distribution function becomes noticeable. The coordinate dependence of the ensemble distribution function in the velocity space is determined predominantly by the trajectories of charged particles.     

Space distribution and energy straggling of charged particles via Fokker-Planck equation

Summary The Fokker-Planck equation describing a beam of charged particles entering a homogeneous medium is solved here for a stationary case. Interactions are taken into account through Coulomb cross-section. Starting from the charged-particle distribution as a function of velocity and penetration depth, some important kinetic quantities are calculated, like mean velocity, range and the loss of energy per unit space. In such quantities the energy straggling is taken into account. This phenomenon is not considered in the continuous slowing-down approximation that is commonly used to obtain the range and the stopping power. Finally the well-known Bohr or Bethe formula is found as a first-order approximation of the Fokker-Planck equation. The authors of this paper have agreed to not receive the proofs for correction.     

Cooling kinetics of a granular gas of viscoelastic particles

The evolution of a granular gas of viscoelastic particles in the homogeneous cooling state is studied. The velocity distribution function of granular particles and the time dependence of the mean kinetic energy of particles (granular temperature) are found. The noticeable deviation of the distribution function from the Maxwell distribution and its non-monotonous evolution are established. The perturbation theory with respect to the small dispersion parameter is elaborated and the analytical expressions for the asymptotic time dependence of the velocity distribution function and the granular gas temperature are derived.     

Electromagnetic radiation of a charged tachyon moving in a dispersive medium

At the present time a number of studies [1–6] have considered the possible properties of ultrarelativistic tachyon particles. In particular, [5, 6] were dedicated to analysis of the radiation of charged tachyons in a vacuum. The goal of the present study is to analyze the radiation emitted by charged tachyons in an immobile dispersive medium. We will consider the following problem: a charged particle moves with velocity v in an immobile dispersive medium and at time t=0 decays to neutral particles and a charged tachyon which moves at a velocity v₀. The tachyon in turn, because of collisions with neutral particles of the medium, at time t= forms a charged particle (electron) also moving with velocity v.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 130–134, June, 1978.In conclusion, the author expresses his sincere thanks to Professor Ya. P. Terletskii for his interest and aid in the study.     

Analytical solutions for the energy distribution of charged particles in a weak electric field

The paper deals with the stationary distribution of charged particles moving in a material medium, having scattering and absorption properties, in which a uniform electric field is present. The purpose of the work is finding analytical solutions in simplified but physically significant situations and comparing different approximations based on a spherical-harmonics expansion of the velocity distribution. Received: 28 July 1998     

热核反应中次级粒子的总产额和能谱

本文从核反应运动学的基本图象出发,推导了在等离子体中热核反应所产生的次级粒子的总产额和能谱的一般表达式,并对利用热核反应所产生的次级粒子作为诊断等离子体参数的工具作了简要讨论。 关键词：     

Angular Velocity Distribution of the Electric Microfield in Plasma

In theory of the spectral line shapes, the conventional scheme use two approximations for the local electric field (microfield) due to all charged particles of the plasma. The quasi‐static approximations for the ions and the impact approximation for the electrons. The first approximation consists to say that the electric field is constant during the characteristic time. In this work we shall transpose the idea of the first approximation, to the angular velocity of the microfield whereas its strength is kept constant and equal to its mean value. We shall use the Holtsmark approach and the independent particles model (due to Margeneau and Lewis) to compute the static distribution function of the angular velocity of the microfield. In the first approach (Holtsmark), the distribution shows a Lorentzian behavior, whereas the second approach (Margenau and Lewis) shows a gaussian behavior. Subsequently, we have applied the obtained static distribution to show the effect on the broadening of Lyman‐alpha line for a plasma composed of He⁺ ions. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A combined model for pseudorapidity distributions in p-p collisions at center-of-mass energies from 23.6 to 7000 GeV

In p-p collisions, the charged particles produced consist of two leading particles and those frozen out from the hot and dense matter created in the collisions. The two leading particles are in the projectile and target fragmentation regions, respectively, which, in this paper, are conventionally supposed to have Gaussian rapidity distributions. The hot and dense matter is assumed to expand according to unified hydrodynamics, a hydrodynamic model which unifies the features of the Landau and Hwa-Bjorken models, and freeze out into charged particles from a space-like hypersurface with a fixed proper time of τFO. The rapidity distribution of these charged particles can be derived analytically. The combined contribution from both leading particles and unified hydrodynamics is then compared against experimental data from a now available center-of-mass energy region from 23.6 to 7000 GeV. The model predictions are consistent with experimental measurements.     

Investigation of electrostatic charge distribution within the reactor wall fouling and bulk regions of a gas–solid fluidized bed

The distribution of charge within the wall fouling region and bulk of a fluidized bed reactor was investigated. Experiments were conducted in a 0.1 m in diameter carbon steel fluidization column under atmospheric conditions. Polyethylene particles were fluidized with extra dry air at 1.5 the minimum fluidization velocity (bubbling flow regime) for 1 h. Using an online Faraday cup measurement technique, the net charge-to-mass ratio (q/m), as well as the size distribution of all particles adhered to the column wall and those in the bulk of the bed was determined. The wall particles were found to be predominantly negatively charged while those which did not adhere to the wall were predominantly positively charged. The charge distribution within each region was then investigated by a custom made charged particle separator that separated the particles according to their charge magnitude and polarity. It was determined that although the net charge of the wall layer particles was negative, a significant amount of positively charged particles existed within each sample and therefore the entire wall particle layer. This suggests that the wall layer was formed through layering between positively and negatively charged particles. Particles in the bulk of the bed also consisted of bipolarly charged particles.     

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。     

Electron distribution function and recombination coefficient in ultracold plasma in a magnetic field

The electron distribution function and diffusion coefficient in energy space have been calculated for the first time for a weakly coupled ultracold plasma in a magnetic field in the range of magnetic fields B = 100?50000 G for various temperatures. The dependence of these characteristics on the magnetic field is analyzed and the distribution function is shown to depend on the electron energy shift in a magnetic field. The position of the “bottleneck” of the distribution function has been found to be shifted toward negative energies with increasing magnetic field. The electron velocity autocorrelators as a function of the magnetic field have been calculated; their behavior suggests that the frequency of collisions between charged particles decreases significantly with increasing magnetic field. The collisional recombination coefficient α _B has been calculated in the diffusion approximation for a weakly coupled ultracold plasma in a magnetic field. An increase in magnetic field is shown to lead to a decrease in α _B and this decrease can be several orders of magnitude.     

Kinetic description of the Coulomb explosion of a spherically symmetric cluster

The particle distribution function is calculated for the Coulomb explosion of a spherically symmetric charged cluster formed through the interaction of intense ultrashort laser pulses with a cluster gas. The particle density and mean velocity distributions as well as the energy spectra of the accelerated particles are obtained. These characteristics are analyzed in detail for a cold cluster plasma, where the kinetic effects determine the physics of multiple flows emerging after the turnover of the cluster particle velocity profile. We find the boundaries of the multiple-flow regions and study the characteristics of an exploding cluster as a function of its initial density profile. The energy spectra of the accelerated ions are obtained for a cluster plasma with a specified cluster size distribution.     

Analytical solutions of the Rayleigh flow problem for a rarefied gas of a nonhomogeneous system of charged particles

A two-stream Maxwellian distribution function with two unknown parameters corresponding to the mean velocity and the shear stress is used to obtained an approximate analytic solution of the Rayleigh flow problem for a rarefied gas of a nonhomogeneous system of charged particles. For small magnetic field, solutions are presented for the four moments equations and the Maxwell's equations. The dynamical behaviour of the electron and ion gas is examined.     

统一流体力学模型与BNL-RHIC低能量区重离子碰撞中的赝快度分布

重离子碰撞产生的高温高密度物质假设按照统一流体力学模型的规律做时空演化,并最终经由一固有时为Tau_FO的类时超曲面冻析为带电粒子。统一流体力学模型是一种将Landau与Hwa-Bjorken两著名流体力学模型结合在一起的模型,是一种少有的可精确求解的理论之一。本文的研究表明:BNL-RHIC低能量区重离子碰撞中带电粒子的赝快度分布可由统一流体力学模型很好地描述。 这与高能区的情况不同,在那里,除了流体外,还需考虑带头粒子的贡献。The hot and dense matter created in heavy ion collisions is supposed to have spatiotemporal evolution according to unified hydro model, and finally freeze out into the charged particles via a space-like hypersurface with a proper time Tau_FO . The unified hydro model is a model which integrates Landau and Hwa-Bjorken two famous hydro models together. It is one of few hydro models which can solved exactly. Shown from the investigations in this paper, the pseudorapidity distribution of charged particles in heavy ion collisions at low BNL-RHIC energy region can be well described by unified hydro model. This is different from that at high nergy region, where, apart from fluid, the contribution from leading particles should be taken into account.     

Grand Canonical Ensemble Interpretation for Charged Particle Quantum Tunneling Radiation

In this paper, we present a grand canonical ensemble interpretation for the massive charged particles tunneling from a charged black hole. The probability distribution function corresponding the emission shell system is derived in details, and the expression is same as the tunneling rate in Parikh-Wilzeck framework. With this result, the statistical significance of the quantum tunneling radiation is discussed.     

离子推力器推力密度特性

离子推力器推力密度分布对航天器轨道维持和修正具有重要影响.采用粒子模拟-蒙特卡罗碰撞方法模拟束流等离子体输运过程,分析束流多组分粒子喷出数量和速度等微观参数,并计算得到单孔束流推力,结合放电室出口等离子体密度分布,进一步对推力密度分布特性分析,最后开展实验验证.研究结果显示:束流中单价离子、双荷离子以及交换电荷离子的推力贡献比分别为84.63%,15.35%和1.82%,可见推力主要来源于束流中的单价离子和双荷离子,交换电荷离子对推力贡献很小;推力密度分布具有较好的中心轴对称性,从推力器中心沿着径向先快速下降后趋于缓慢;与实验结果对比,经验模型相对误差约为4.1%,数值模型相对误差约为2.8%,相比经验模型,数值模型具有更好的准确性.研究结果可为离子推力器推力密度分布均匀性等优化提供参考.     

Potential Formation in Front of an Electrode Close to the Plasma Potential Studied by PIC Simulation

Potential formation in front of an electrode that has the potential which is close to the plasma potential is studied by particle‐in‐cell (PIC) simulations. The code BIT1 [D. Tskhakaya, R. Schneider, J. Comp. Phys., 225 , 829 (2007)] is used for this purpose. It is shown that this code is very appropriate for our analysis because of its ability to create charged particles by uniform volume production in the entire system and to maintain in the same time the Maxwellian electron velocity distribution function prescribed in the input file. It turns out that some modifications of the code are necessary in order to achieve small sheath potential drops and to detect the cutoff in the electron velocity distribution function. The modifications of the code are described. The small sheath potential drop is achieved by introducing a finite reflectivity of the electrons at the left electrode, while the expected cutoffs of the electron velocity distribution function are found by tracking the reflected electrons as separate particle species. The simulation results are compared to the theoretical model of Jeli? [N. Jeli?, Phys. Plasmas, 18 , 113504 (2011)]. The matching is very good and this is a sign that the PIC simulations are very appropriate tool for the analysis of this type of problems. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of the electrostatic powder coating process with a corona spray gun

In this paper results of investigations are described aiming to numerically simulate the electrostatic powder coating process using an extended commercial computational fluid dynamics (CFD) code. The fully three-dimensional turbulent flow was calculated. Based on the Lagrangian approach the trajectories of the powder particles were modelled considering electric and aerodynamic forces. In the calculations of the particle propagation both the particle size distribution and the particle charge distribution obtained through experiments have been applied. The model accounts for the space charge effect of the charged particles and the turbulence dispersion on the particle trajectories. It was found that the space charge plays an important role for the final spray pattern shape, also increasing the transfer efficiency. The numerical results, such as velocity profiles, static and dynamic film thickness on the target were in good agreement with experiment.     

Suspension and fall of heavy particles in random two-dimensional flow

We investigate the settling of heavy particles in a steady, two-dimensional random velocity field, and find instances in which particle suspension occurs. This leads to a bimodal velocity distribution that may explain some apparently conflicting results reported in the literature. The bimodal distribution is typically smeared out by a time dependence of the ambient flow but, if the time variation is slow, the settling rates of some particles will be as well. The resulting broadbanded velocity distribution of the settling particles will have significance for processes such as rain drop formation, in which the spread of particle velocities affects the statistics of particle collisions.