Analysis and Modeling of the Charged Particle Beam Dynamics in the Charlton Trap

The dynamics of charged particles in the Penning–Malmberg–Surco trap with a rotating electric field [1–3] (the Charlton trap) is investigated. Two different algorithms for determining Lyapunov characteristic exponents for solutions of a nonstationary system describing the dynamics of particles in a trap are constructed and realized. This allows us to construct approximate analytical solutions and analyze the behavior of the envelope of the particle beam, and not only of individual trajectories. The asymptotic stability of motions of charged particles is checked for a different choice of the system parameters and their relations.     

Invariants and radiation of some nonstationary systems

In this paper formulas are obtained by means of the coherent-state method for calculating the radiation power of a nonstationary quantum system ofN charged particles whose Hamiltonian is a general quadratic form with respect to coordinates and momenta. The transitions between the coherent states and the Fock states of this system are discussed. The radiation is calculated both in the dipole approximation and strictly. As an example, the radiation of a charge in homogeneous varying electric and magnetic fields is found. The classical limit is considered.     

High-Speed Scattering of Charged and Uncharged Particles in General Relativity

After a brief consideration of the high-speed scattering of two point charges we thoroughly discuss high-speed scattering for a charged particle by a fixed mass and of two uncharged particles of comparable masses. We use perturbation technique over Minkowski spacetime in the de Donder gauge and solve the field equations and the resulting equations of motion (which take the reaction of the particles' quasistatic self-field into account) by iteration. The obtained energy-momentum conservation laws allow the computation of second-order corrections for the scattering angle and the cross section. The asymptotic structure of the far-field indicates synchrotron radiation (electromagnetic and gravitational, respectively) which causes an energy loss whose reaction on the motion is briefly considered in the low-velocity limit including bound motion. (For neutral particles this is a third-order effect).     

General form of the equation of motion of a charged particle

The most general form of the equation of motion of a charged particle is derived. The equation allows for an arbitrary self-field and is consistent with energy-momentum conservation, angular momentum conservation and the Dirac mass renormalization.     

Use of the quadratic Stark effect to determine the concentration of charged particles in a plasma from the broadening of lithium and sodium lines

The Stark constants for the quadratic Stark effect have been calculated for a number of spectral lines of sodium and lithium atoms. To evaluate the contours of the spectral lines, the nonstationary collision theory has been used for electron broadening, and Holtsmark's theory for ionic interactions. Satisfactory agreement with experimental data has been obtained. The concentration of the charged particles has been measured in a dc arc.     

Simulation of nonstationary electrohydrodynamic flows in a symmetric system of electrodes of the wire-wire type

Computer simulation is carried out for the process of formation of electrohydrodynamic flows emerging in a system of two parallel wires as a result of symmetric injection from each electrode (2D case). Simulation is performed using the ANSYS system. A simulation algorithm is developed for nonstationary electrohydrodynamic flows. The results of simulation are presented. Analysis of the results shows that the evolution of electrohydrodynamic flows is accompanied by the formation of thin oppositely charged liquid streams moving in opposite direction from near-electrode charged layers.     

Distribution function of an electron beam in a focusing magnetic field

The distribution function of electrons moving in an axially symmetric focusing magnetic field is constructed. The macromotion and self-field of the beam are taken into account. The nonrelativistic and relativistic limits are discussed. Upon switching off the magnetic field the distribution functions obtained change into the Maxwell-Boltzmann distribution. The motion of charged particles in a focusing magnetic field is the simplest model for investigation of a beam of particles, for example, electrons, in storage or accelerator rings. In accordance with the well-known theorem of N. Bohr, a magnetic field has no effect on the distribution function for a one-dimensional distribution of electrons with respect to the momenta. However, the situation is altered if macromotion occurs in a static system, for example, the revolution of electrons in storage or accelerator rings. Maintaining the focusing of the beam in an equilibrium orbit, the magnetic field thereby affects the electron distribution function. For an actual electron beam the distribution function is determined by the initial conditions of formation of the beam; however, as a result of scattering processes it will approach some steady-state equilibrium distribution function. We will discuss the problem of finding such a distribution function in the nonrelativistic and relativistic cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 35–40, July, 1978.The author thanks Professor I. M. Ternov of Moscow University for his constant interest in this research and Professor V. G. Bagrov of Tomsk University for help in the research.     

非线性共振及束晕-混沌的场强参数特性

通过计算和分析周期聚焦磁场强度和表征束自生场强度的束导流系数的变化对强流粒子束运动特征的影响,系统研究了强流粒子束的非线性共振和束晕现象。采用庞加莱截面技术对束核包络振荡及其单粒子运动轨迹进行了数值模拟,清楚地展示了不同情况下束核包络非线性振荡以及对应的试验粒子空间分布。结果表明:束核自生场使得束核包络发生非线性振荡,随着束核自生场和聚焦磁场的增加,伴随着束核共振岛的出现,单粒子空间分布出现越来越多的束晕粒子。     

Quantum-hydrodynamic approach to the problem of electron exchange between atomic particles and nanosystems

The application of quantum-hydrodynamic methods for solving the problem of electron exchange between atomic particles and solid surfaces, and nanosystems has been examined. The derivation of a system of equations that is alternative to the nonstationary Schrödinger equation is given to describe the dynamics of electronic processes with variable charge and current densities. A comparison of results of solving the nonstationary Schrödinger equation and the quantum-hydrodynamic system of equations shows that both approaches give a good coincidence. The numerical solution to the system of quantum-hydrodynamic equations has a number of advantages, because it does not lead to oscillations at the boundary of the computational mesh and nor to the problem of exponential growth in numerical complexity for many-electron systems.     

The thermodynamic limit for jellium

The thermodynamic limit of the free energy, energy, pressure, and entropy is established for a neutral system of charged particles interacting with a fixed, uniformly charged background (jellium).     

On changing the size of the atmosphere of a vortex pair embedded in a periodic external shear flow

The dynamics of fluid particles in the vicinity of a self-propagating vortex pair, embedded in a nonstationary shear flow, is studied. When the shear flow is steady, the vicinity of the pair, which is called as a vortex atmosphere, consists of closed stream-lines, which coincide with fluid particles? trajectories. When the shear flow is nonstationary, the trajectories? behaviour changes drastically, then chaotic advection occurs. It is shown in the Letter that the vortex pair propagation velocity varies with the parameters (amplitude, and frequency) of the nonstationary shear flow. It is demonstrated, that changing of the mean velocity leads to changing of the size of the atmosphere.     

Failure and success of hydrodynamic interaction models

In suspensions with charged particles, electrostatic forces and hydrodynamic interactions are both important to describe the system. We study different models of hydrodynamic interaction for monopolarly charged particles in a non-polar liquid. In this case, there is no screening of the Coulomb repulsion, so the repulsion between all pairs must be taken into account. The particles are expected to drift away from each other, however at a lower rate when hydrodynamic interaction between the particles is taken into account. Existing, frequently used models of hydrodynamic interactions tend to overestimate the slowing down of the charged particles, even to the extent that the particles effectively attract each other. This is demonstrated for some selected particle setups. We find that these anomalies even occur in dilute systems, if they contain sufficiently many particles. We explain why these anomalies can be avoided by an approach, in which the superposition of interactions is done in the friction tensor instead of the mobility tensor.     

From the Liouville Equation to the Generalized Boltzmann Equation for Magnetotransport in the 2D Lorentz Model

We consider a system of non-interacting charged particles moving in two dimensions among fixed hard scatterers, and acted upon by a perpendicular magnetic field. Recollisions between charged particles and scatterers are unavoidable in this case. We derive from the Liouville equation for this system a generalized Boltzmann equation with infinitely long memory, but which still is analytically solvable. This kinetic equation has been earlier written down from intuitive arguments.     

Self-sustained oscillations in a plasma-wall system with strongly inhomogeneous diffusion of charged particles

A simple system with a hydrogen plasma confined by a magnetic field parallel to the bounding material wall is considered. The charged particles diffuse out of the plasma, recombine on the wall and return into the plasma volume as neutrals, which are ionized by electrons. It is demonstrated that macroscopic self-sustained oscillations are an intrinsic feature of such a system if the diffusion coefficient of charged particles is strongly inhomogeneous in the plasma.     

轴对称荷电动态黑洞的量子热效应

讨论了轴对称荷电动态黑洞的Hawking辐射,得到了局部事件视界面方程和温度.结果显示黑洞的形状和温度不仅随时间变化而且随角度变化. 关键词：     

Charged particles on a two-dimensional lattice subject to anisotropic Jahn-Teller interactions

The properties of a system of charged particles on a 2D lattice, subject to an anisotropic Jahn-Teller-type interaction and 3D Coulomb repulsion, are investigated. In the mean-field approximation without Coulomb interaction, the system displays a phase transition of first order. When the long-range Coulomb interaction is included, Monte Carlo simulations show that the system displays very diverse mesoscopic textures, ranging from spatially disordered pairs to ordered arrays of stripes, or charged clusters, depending only on the ratio of the two interactions (and the particle density). Remarkably, charged objects with an even number of particles are more stable than with an odd number of particles. We suggest that the diverse functional behavior-including superconductivity-observed in oxides can be thought to arise from the self-organization of this type.     

Coagulation of charged microparticles in neutral gas and charge-induced gel transitions

Coagulation of charged particles was studied using the mean-field Smoluchowski equation. The coagulation equation was generalized for the case of a conserved system of charged particles. It was shown that runaway cluster growth (gelation) solutions exist if the charge-dipole (induced) interaction of clusters is included. When clusters are in thermal equilibrium with the ambient gas, the charge-dipole interaction dramatically enhances the aggregation process and considerably increases the likelihood of a gelation transition.     

Optimal Convergence Rates of Classical Solutions for Vlasov-Poisson-Boltzmann System

The dynamics of charged dilute particles can be modeled by the two species Vlasov-Poisson-Boltzmann system when the particles interact through collisions in the self-induced electric field. By constructing the compensating function for multi-species particle system, the optimal time decay of global classical solutions to this system near a global Maxwellian is obtained through a refined energy method.     

小尺寸约瑟夫逊结的自场效应

本文指出交叉膜型小尺寸的约瑟夫逊结在不对称地提供结电流时,存在明显的自场效应,不对称自场将改变直流超导隧道电流与磁场关系的对称性。 关键词：