Lindhard势与形变超晶格系统的共振现

假设超晶格“折沟道”对粒子的作用等效为形状相似的周期调制; 利用Lindhard 展开势, 并在小振幅近似下, 将面沟道粒子的运动行为化为了具有硬特性的弹簧振子。 利用多重尺度法分析了共振线附近的粒子运动行为, 讨论了系统的主共振、 子共振和超共振。 计算了超晶格“折沟道”临界斜率与系统参数之间的关系, 为研究超晶格光磁电效应提供了理论分析。It is assumed that a periodic modulation is equivalent to the deflected channel of the superlattice. In the small amplitude approximation the particle motion equation has been reduced to the Duffing equation with a hard-spring properties by using Lindhard expanded potential. The main resonance, the sub-harmonic resonance and the super-harmonic resonance have been analysed by the multi-scale technique. The critical parameter of the deflected channelling has been calculated, the results provided a theory analyse for the photo-magneto-electric effects of the superlattice.      

形(应)变超晶格的沟道效应与系统的相平面特征

利用正弦平方势,把粒子运动方程化为具有δ力矩的摆方程.分析了无扰动系统的相平面特征,计算了扰动系统的退道效应.讨论了退道系数与晶格形变之间的关系.The particle motion equation has been reduced to the pendulum equation with a δ moment by using sine squared potential. The phase planar characteristics have been analysed for a non perturbed systeam . The dechanneling effects have been calculated numerically for a perturbed system. The relationship between the dechanneling fraction and superlattice deformation in resonance has been discussed.     

Crystalline undulator radiation and sub-harmonic bifurcation of system

Looking for new light sources, especially short wavelength laser light sources has attracted widespread attention. This paper analytically describes the radiation of a crystalline undulator field by the sine-squared potential. In the classical mechanics and the dipole approximation, the motion equation of a particle is reduced to a generalized pendulum equation with a damping term and a forcing term. The bifurcation behavior of periodic orbits is analyzed by using the Melnikov method and the numerical method, and the stability of the system is discussed. The results show that, in principle, the stability of the system relates to its parameters, and only by adjusting these parameters appropriately can the occurrence of bifurcation be avoided or suppressed.     

Chaotic Behavior of a Brownian Particle in a Periodic Potential

The classical deterministic dynamics of a Brownian particle with a time-dependent periodic perturbation in a spatially periodic potential is investigated. We have constructed a perturbed chaotic solution near the heteroclinic orbit of the nonlinear dynamics system by using the Constant-Variation method. Theoretical analysis and numerical result show that the motion of the Brownian particle is a kind of chaotic motion. The corresponding chaotic region in parameter space is obtained analytically and numerically.     

Continuous feedback control of KdV Burgers system

The chaos in the KdV Burgers equation describing a ferroelectric system has been successfully controlled by using a continuous feedback control. This system has two stationary points. In order to know whether the chaos is controlled or not, the instability of control equation has been analysed numerically. The numerical analysis shows that the chaos can be converted to one point by using one control signal, however, it can converted to the other point by using three control signals. The chaotic motion is converted to two desired stationary points and periodic orbits in numerical experiment separately.     

等效磁场与弯晶沟道辐射

引入场指标和等效磁场概念,把粒子在弯晶沟道中的运动行为等效为回旋加速器中的粒子运动.结果表明,描写粒子的运动方程是一个非线性薛定谔方程.在小振幅近似下找到了系统的严格解和粒子振动周期,导出了瞬时辐射强度和最大辐射频率. The sine-squared potential and the equivalent magnetic field intensity have been introduced, the motion equation of the particle in bent crystal has been derived, the motion equation and the oscillation period of the particle have been solved exactly by Jacobian elliptic fuanction and the first kind of complet elliptic integrals, the intensity and the spectral properties of channelling radiation in bent crystal discussed.     

LARRAZA-PUTTERMAN EQUATION INCLUDING VISCOSITY AND EXTERNAL DRIVE

The weak nonlinear modulation of the surface wave of a three-dimensional imcompressible fluidwithout rotation,which is contained in a rectangular trough is studied by using the method of multi-ple scales perturbation theory.The effects of viscid and external drive on the motion,which modifiesthe Larraza-Putterman equation,are considered.The results are consistent with that of Miles.     

周期弯晶作为束流控制元件的动力学稳定性

在经典力学框架内和偶极近似下,引入正弦平方势,把粒子运动方程化为具有阻尼项和受迫项的广义摆方程。利用Melnikov方法讨论了沟道运动次谐分叉及其稳定性, 导出了周期弯晶的临界条件和退道长度。结果表明, 要试图获得高的引出效率, 除了要求弯晶长度必须小于退道长度外, 还必须保证沟道粒子的运动是稳定的。对临界条件的分析表明, 系统的稳定性与它的参数有关, 只须适当调节系统参数, 就可以保证周期弯晶作为引出元件的稳定性。In the classical mechanics frame and with a dipole approximation the particle motion equation in the periodic bent crystal is reduced to the general pendulum equation with a damping term and the forced term by using the sine squared potential． This paper discusses the problem of the sub harmonic bifurcation of the periodic orbit and the stabilities of the channeling motion by using Melnikov method, so as to derive the critical condition and the dechanneling length of the periodic bent crystal. The results show that channeling motion must be stable in addition that the crystal length is smaller than the dechanneling length in order to ensure higher extracted efficiency. The analysis of the critical condition shows that the system stabilities are related to its parameters. Just by properly regulating the parameters of the system, the dynamic stabilities by the use of periodic bent crystal as beam control cell can be ensured.     

正弦平方势与环形加速器的弯晶束流引出

在经典力学框架内和偶极近似下, 引入正弦平方势, 把粒子在弯晶中的运动方程化为具有固定力矩的摆方程。 利用Jacobian椭圆函数和椭圆积分分析了系统的相平面特征。 导出了弯晶的最大偏转能量、 退道系数和退道长度。 计算结果表明, 对于曲率半径为1 m, 能量为1.0 GeV的质子, Si(110)面沟道的引出效率为70%; 对于MeV范围的粒子, 退道长度大约是μm量级; 对于TeV范围的粒子, 退道长度可达1 m以上。 In the classical mechanics frame and the dipole approximation the particle motion equation in bent crystal is reduced to the pendulum equation with a constant momentum by using the sine squared potential.The phase planar properties are analysed by means of Jacobian elliptic function and the elliptic integral. The maximum deflected energy, the dechanneling factor and the dechanneled length are derived. The results show that the extrated efficiency is 70% for a proton beam with energy E=1.0 GeV moved in the channel on Si(110) if a radius of curvature R=1 m; and dechanneled length is of the order of μm for the particles with MeV energy; the dechanneled length is above 1 meter for the particle with TeV energy.     

Solution of the Dirac Equation for Ring-Shaped Modified Kratzer Potential

We propose a new exactly solvable potential which is formed by modified Kratzer potential plus a new ring-shaped potential η cot2θ/r2. The solutions of the Dirac equation with equal scalar and vector ring-shaped modified Kratzer potential are found by using the Nikiforov-Uvarov method. The nonrelativistic limit of the energy spectrum has been discussed.     

双频激励下超晶格系统的混沌行为

假设超晶格“折沟道”对粒子的作用等效为形状相似的周期调制; 引入正弦平方势, 在小振幅近似下, 把粒子运动方程化为具有双频激励的Duffing方程。 用Melnikov方法分析了系统的混沌行为。 结果表明, 当外场为双频激励时, 系统将存在不同的次谐和超次谐分叉序列。 由于系统的混沌行为与系统参数有关, 于是, 只需控制材料组分、 或掺杂浓度, 就可望达到避免或控制混沌的目的, 为半导体超晶格的制备及其光磁电效应提供了理论分析。     

带电粒子同超晶格的相互作用与系统的混沌行为

把超晶格“折沟道”对粒子的作用等效为形状相似的弱周期调制. 利用正弦平方势把粒子运动方程化为具有外周期弱调制的非线性微分方程，并利用Melnikov 方法分析了系统出现Smale 马蹄的临界条件. 预言了带电粒子同超晶格相互作用过程中, 系统可能出现的混沌行为, 为半导体超晶格材料的制备和半导体超晶格光磁电效应的研究提供了基本的理论分析. 关键词： 超晶格 非线性 微分方程 混沌     

Subbarrier interaction of channeling particles under the self-similar excitation of correlated states in a periodically deformed crystal

It has been shown that application of the periodic modulation of parabolic potential well parameters (in the case of charged particle channeling in crystals, i.e., periodic spatial modulation of the wall height of a potential well in the crystal channel) leads to the formation of the coherent channeling state in particles in this well. The formation of this state changes the interaction process between these particles and nuclei, and increases the barrier transparency by many times. For channeling this mode can be formed using, e.g., the longitudinal acoustic wave running along the channel axis. This wave changes the distance between nuclei and, accordingly, modulates the height of channel walls.     

准周期激励与应变超晶格的动力学稳定性

假设超晶格锯齿形沟道对粒子的作用等效为形状相似的周期场作用. 在经典力学框架内,引入正弦平方势,把粒子运动方程化为具有阻尼项和双频激励项的摆方程. 用Melnikov方法对单频激励系统的分叉与混沌进行分析;用Lyapunov方法对双频激励系统的稳定性进行讨论. 结果表明：在弱非线性情况下,双频激励系统存在局域不稳定,且这种不稳定将向全局扩展,直至混沌的出现;导致混沌的双频激励强度远小于单频激励强度;外加一个适当的超声场可望将这种敏感钝化,使系统的稳定性得到改善. 关键词： 超晶格 准周期激励 混沌 稳定性     

From collective periodic running states to completely chaotic synchronised states in coupled particle dynamics

We consider the damped and driven dynamics of two interacting particles evolving in a symmetric and spatially periodic potential. The latter is exerted to a time-periodic modulation of its inclination. Our interest is twofold: First, we deal with the issue of chaotic motion in the higher-dimensional phase space. To this end, a homoclinic Melnikov analysis is utilised assuring the presence of transverse homoclinic orbits and homoclinic bifurcations for weak coupling allowing also for the emergence of hyperchaos. In contrast, we also prove that the time evolution of the two coupled particles attains a completely synchronised (chaotic) state for strong enough coupling between them. The resulting "freezing of dimensionality" rules out the occurrence of hyperchaos. Second, we address coherent collective particle transport provided by regular periodic motion. A subharmonic Melnikov analysis is utilised to investigate persistence of periodic orbits. For directed particle transport mediated by rotating periodic motion, we present exact results regarding the collective character of the running solutions entailing the emergence of a current. We show that coordinated energy exchange between the particles takes place in such a manner that they are enabled to overcome--one particle followed by the other--consecutive barriers of the periodic potential resulting in collective directed motion.     

Memory function approach to the dynamics of interacting Brownian particles

We investigate some of the dynamic properties of diffusing particles described by a many-body Smoluchowski equation. The dynamic structure factor is expressed in terms of a memory function which is evaluated in the cases of i) weak interaction and ii) low particle density, but arbitrary interaction. A one-dimensional system with a hard-core pair potential is treated explicitly. Furthermore, by including a periodic single-particle potential, a model is obtained which has relevance to superionic conductors. For this case we discuss how the frequency-dependent conductivity is affected by the correlated motion of particles.     

晶体摆动场辐射及其共振线附近的粒子运动行为

寻找新光源,特别是短波长相干光源引起了人们的广泛注意,利用晶体摆动场辐射作为短波长相干光源是最有可能的方案之一,本文从势和场的观点出发,把周期弯晶产生的离心力视为离心势,将粒子运动方程化为Duffing型Mathieu方程,从能量观点出发讨论了系统的稳定性,用摄动法对共振线附近粒子的运动行为进行了分析;揭示了系统的跳跃现象和不稳定行为,结果表明,系统的稳定性与其参数有关,适当调节这些参数,系统的分叉和不稳定性原则上可以避免。