正弦平方势与小振幅近似下的弯晶沟道辐射

在理想情况下和经典力学框架内,引入正弦平方势,把粒子在弯晶中的运动方程化为具有外力矩的摆方程。并对系统的相平面特征进行了数值分析。在小振幅近似下,把粒子运动方程化为具有硬特性的弹簧-振子系统,用Jacobian椭圆函数和椭圆积分解析地给出系统的解和粒子运动周期。讨论了弯晶沟道辐射频率、无量纲偏转角和辐射谱的一般特征。指出利用沟道辐射作为激光的可能性。以正电子在碳单晶中沟道辐射为例进行了具体计算,得到了与其他工作基本一致的结果。     

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.     

晶体摆动场辐射系统的全局分叉与混沌行为

引入正弦平方势,在经典力学框架内和偶极近似下,考虑到运动阻尼和非线性影响,把粒子在晶体摆动场中的运动方程化为具有阻尼项和受迫项的广义摆方程.利用Jacob椭圆函数和椭圆积分分析了无扰动系统的相平面特征,并解析地给出了系统的解和粒子振动周期; 进一步利用Melnikov方法分析相平面上三类轨道的分叉性质和进入Smale马蹄意义下的混沌行为,找到系统的全局分叉与系统进入混沌的临界条件.结果表明,系统的临界条件与它的物理参数有关,只需适当调节这些参数就可以原则上避免、抑制分叉或混沌的出现.     

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.     

晶体摆动场辐射系统的全局分叉与混沌行为

引入正弦平方势,在经典力学框架内和偶极近似下,考虑到运动阻尼和非线性影响,把粒子在晶体摆动场中的运动方程化为具有阻尼项和受迫项的广义摆方程.利用Jacob椭圆函数和椭圆积分分析了无扰动系统的相平面特征,并解析地给出了系统的解和粒子振动周期; 进一步利用Melnikov方法分析相平面上三类轨道的分叉性质和进入Smale马蹄意义下的混沌行为,找到系统的全局分叉与系统进入混沌的临界条件.结果表明,系统的临界条件与它的物理参数有关,只需适当调节这些参数就可以原则上避免、抑制分叉或混沌的出现. 关键词： 晶体摆动场辐射 Melnikov方法 分叉 混沌     

带电粒子的参数X射线辐射及弯晶系统的稳定性

寻找新光源, 特别是企图利用PXR作为激光光源引起了人们广泛关注。 要成功获得相干（衍射）的PXR光源, 粒子的运动必须是稳定的。 但是由于晶体弯曲,系统可能变得不稳定, 从而对PXR的反射、 衍射、 聚焦和谱分布均会产生直接影响。 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常数力矩的摆方程。 利用Jacobian椭圆函数和椭圆积分分析了系统的相平面特征。 结果表明, 系统的稳定性与弯晶“曲率”Q有关, 当条件0≤Q<1满足时, 系统是稳定的。 An exploration of a new light source by PXR as Laser gived rise to extensive attention. The particle motion must be stable in order to obtain coherent PXR source. But, an instability of system is possible due to the effect of bent crystal, thus the reflection, the diffraction, the focus and the spectral distribution of PXR will be effected.In the classical mechanics frame and dipole approximation the particle motion equation in bent crystal is reduced to the pendulum equation with a constant momentum by the sine squared potential.The phase planar properties are analysed by means of Jacobian elliptic function and the elliptic integral. It shows that the stability of the system is related to the curvature Q of the bent crystal. When the condition 0≤Q<1 is satisfied, the system is stable。     

变曲率弯晶的粒子退道行为

利用正弦平方势和变曲率的抛物线近似描写了弯曲硅单晶的粒子退道效应,进一步证实利用弯晶来偏转(或控制)带电粒子运动方向的可能性。导出弯晶的退道系数并讨论了它的可能应用。 关键词：     

二维晶化束的平均场概念和单粒子模型(Ⅰ)

引入平均场概念和单粒子模型讨论了储存环中二维晶化束的小尺度运动行为,并利用能量最小原理导出了粒子方位角分布的不连续性和晶化束的结构相变     

超晶格量子阱作为光学双稳态器件的相平面特征及其稳定性

辐射强度与量子阱沟道的接受度有关,而接受度的大小则直接取决于量子阱宽度、深度以及电子束流的品质等因素.电子束可以用离子注入机或加速器提供,也可以用电压偏置的方法来获得.利用加速器理论中的相平面分析方法,分析了这种双稳态系统的相平面特征及其稳定性.引入正弦平方势,在经典力学框架内和电压偏置情况下,把粒子运动方程化为具有固定力矩的摆方程,用Jacobian椭圆函数和第一类椭圆积分解析地给出了无扰动系统的解和振动周期,并用数值方法分析了扰动情况下的相平面特征和系统的稳定性.为超晶格量子阱光学双稳态器件的设计提供了基本的理论分析.     

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.     

Small amplitude approximation and stabilities for dislocation motion in a superlattice

Starting from the traveling wave solution, in small amplitude approximation, the Sine-Gordon equation can be re- duced to a generalized Duffing equation to describe the dislocation motion in a superlattice, and the phase plane properties of the system phase plane are described in the absence of an applied field. The stabilities are also discussed in the presence of an applied field. It is pointed out that the separatrix orbit describing the dislocation motion as the kink wave may transfer the energy along the dislocation line, keep its form unchanged, and reveal the soliton wave properties of the dislocation motion. It is stressed that the dislocation motion process is the energy transfer and release process, and the system is stable when its energy is minimum.     

Non-equilibrium statistical mechanics of synchrotron-Cerenkov radiation

The synergic synchrotron-Cerenkov (SC) radiation emitted by a relativistic charged particle under the combined effect of the constant external magnetic field and the collective interactions in the ambient plasma (medium) is given in the framework of the non-equilibrium statistical mechanics developed by Prigogine and his co-workers. Starting from the formal solution of the Liouville equation, the one-particle distribution function is calculated. Restricting the motion of the test particle to a circular orbit in the plane normal to the magnetic field, we use the above distribution function to calculate the power emitted per unit solid angle by the test particle as a function of time. We have thus obtained the time evolution of the synergic SC radiation which in the asymptotic limit reproduces the results of Schwinger and his co-workers. It is also shown that the collective interactions within the system produces a shift in the frequency of the outcoming radiation.     

MRI edge enhancement as a diffusive discord of spin phase structure

The enhancement of magnetic resonance image intensity near impermeable boundaries can be nicely described by a new approach where the diffusional spin echo attenuation is linked to the correlation function of molecular motion. In this method the spin phase structure created by the applied gradient is considered to be a composition of plane waves with the wave vectors representing feasible momentum states of a particle in confinement. The enhancement of edges on the magnetic resonance images (MRI) comes out as a discord of plane waves due to particle motion. It results from the average of the wave phase by using the cumulant expansion in the Gaussian approximation. The acquired analytical expression describes the MRI signal space distribution where the enhancement of edges depends on the intensity and the duration of gradient sequence as well as on the length of the mean squared particle displacement in restricted geometry. This new method works well with gradients of general waveform and is, therefore, suitable for imaging sequences where finite or even modulated gradients are usually used.     

Statistical properties of two-dimensional periodic Lorentz gas with infinite horizon

We study the asymptotic statistical behavior of the 2-dimensional periodic Lorentz gas with an infinite horizon. We consider a particle moving freely in the plane with elastic reflections from a periodic set of fixed convex scatterers. We assume that the initial position of the particle in the phase space is random with uniform distribution with respect to the Liouville measure of the periodic problem. We are interested in the asymptotic statistical behavior of the particle displacement in the plane as the timet goes to infinity. We assume that the particle horizon is infinite, which means that the length of free motion of the particle is unbounded. Then we show that under some natural assumptions on the free motion vector autocorrelation function, the limit distribution of the particle displacement in the plane is Gaussian, but the normalization factor is (t logt)^1/2 and nott ^1/2 as in the classical case. We find the covariance matrix of the limit distribution.     

Phase velocities of plane waves in a pipe with a flow whose velocity varies along the radius

The phase velocities of plane waves in a pipe filled with a moving acoustic medium are studied for different laws of flow velocity variation along the pipe radius. The wave equation is solved by the discretization method, which breaks the entire pipe volume into individual cylinders under the assumption that, within each of the cylinders, the flow velocity of the medium is constant. This approach makes it possible to reduce the solution to the wave problem to solving Helmholtz equations for individual cylinders. Based on boundary conditions satisfied at the boundaries between neighboring cylinders, a homogeneous system of linear algebraic equations is obtained. From this system, with the use of the scattering matrices, a simple dispersion equation is derived for determining the phase velocities of plane waves. The stability of the numerical solution to the dispersion equation with respect to the number of cylinders is investigated. The phase velocities of quasi-homogeneous and inhomogeneous waves in a pipe are numerically calculated and analyzed for different velocities of a moving medium and different laws of flow velocity variation along the radius. It is shown that the variation that occurs in the phase velocity of a homogeneous plane wave in a pipe due to the motion of the medium is identical to the mean flow velocity for different laws of flow velocity variation along the radius. For inhomogeneous plane waves, the phase velocity increment exceeds the mean flow velocity several times and depends on both the law of wave amplitude distribution along the radius and the law of the flow velocity variation along the radius.     

Canonical Quantization of Systems with Time-Dependent Constraints

The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion for a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for the relativistic particle in a plane wave lead us to obtain the canonical phase space coordinates without using any gauge fixing condition. As a result of the quantization, we get the Klein-Gordon theory for a particle in a plane wave. The path integral quantization for this system is obtained using the canonical path integral formulation method.     

非相对论粒子高次谐波辐射作为短波长激光的可能性

在经典力学框架内,把粒子在周期外场中的运动方程化为摆方程,利用广义三角函数的Bessel展开讨论了系统存在高次谐波辐射的可能性,并在固定力矩情况下讨论了系统的基本特征。用Jacob ian椭圆函数和第一类椭圆积分解析地给出了无扰动系统的解和振动周期,并用数值方法分析了系统的相平面特征和它的稳定性。结果表明:当外力矩为零时,系统的接受度最大,俘获的电子数最多,辐射强度最强;随着外力矩增加,接受度降低;当无量纲的外力矩为1时,接受度为零,系统处于临界状态。临界状态与系统参数有关,只需适当调节参数,可望输出强度比较大的高次谐波辐射。