Analytical treatment of the nonlinear electron cloud effect and the combined effects with beam-beam and space charge nonlinear forces in storage rings

In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC Ⅱ. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations.     

Multiple Spatial Coherence Resonances and Spatial Patterns in a Noise-Driven Heterogeneous Neuronal Network

Heterogeneity of the neurons and noise are inevitable in the real neuronal network. In this paper, Gaussian white noise induced spatial patterns including spiral waves and multiple spatial coherence resonances are studied in a network composed of Morris-Lecar neurons with heterogeneity characterized by parameter diversity. The relationship between the resonances and the transitions between ordered spiral waves and disordered spatial patterns are achieved. When parameter diversity is introduced, the maxima of multiple resonances increases first, and then decreases as diversity strength increases, which implies that the coherence degrees induced by noise are enhanced at an intermediate diversity strength. The synchronization degree of spatial patterns including ordered spiral waves and disordered patterns is identified to be a very low level. The results suggest that the nervous system can profit from both heterogeneity and noise, and the multiple spatial coherence resonances are achieved via the emergency of spiral waves instead of synchronization patterns.     

BEPC中束束效应的计算模拟

独立开发并行的正负电子储存环的束束效应模拟程序SBBE?.通过求解自由空间内的Poisson方程计算束束作用力;单圈的传输映射中引入了辐射阻尼效应和随机效应.使用它对BEPC中的束束效应进行了计算模拟,并与实测数据进行比较.结果表明,SBBE可以较好地再现BEPC中由束束效应所引发的现象,具备一定的预言能力.本工作为BEPCⅡ的束束效应模拟研究.     

相位噪声诱发神经放电的单次或两次相干共振

神经元电活动可以从静息通过Hopf分岔到放电,放电频率有固定周期;也可以从静息通过鞍-结分岔到放电,放电频率接近零.在具有周期性的相位噪声作用下的Hopf分岔和鞍-结分岔点附近,都会产生相干共振.噪声的周期小于Hopf分岔点附近的放电的周期时,相位噪声可以引起神经系统产生一次相干共振,位于系统内在的固有频率附近;噪声的周期大于系统的固有周期时,相位噪声可以引起双共振,对应低噪声强度的共振产生在噪声频率附近,对应高噪声强度的共振产生在系统的固有频率附近;并对双共振的产生原因进行了解释.在鞍-结分岔点附近,无论噪声的周期是大是小,都只会引起一次共振,研究结果不仅揭示了相位噪声作用下平衡点分岔点相干共振的动力学特性和对应于两类分岔的两类神经兴奋性的差别,还对近期的相位噪声诱发产生单或双共振的不同研究结果给出了解释.     

On stochastic complex beam-beam interaction models with Gaussian colored noise

This paper is to continue our study on complex beam-beam interaction models in particle accelerators with random excitations Y. Xu, W. Xu, G.M. Mahmoud, On a complex beam-beam interaction model with random forcing [Physica A 336 (2004) 347-360]. The random noise is taken as the form of exponentially correlated Gaussian colored noise, and the transition probability density function is obtained in terms of a perturbation expansion of the parameter. Then the method of stochastic averaging based on perturbation technique is used to derive a Fokker-Planck equation for the transition probability density function. The solvability condition and the general transforms using the method of characteristics are proposed to obtain the approximate expressions of probability density function to order ε.Also the exact stationary probability density and the first and second moments of the amplitude are obtained, and one can find when the correlation time equals to zero, the result is identical to that derived from the Stratonovich-Khasminskii theorem for the same model under a broad-band excitation in our previous work.     

Spiral Waves and Multiple Spatial Coherence Resonances Induced by Colored Noise in Neuronal Network

Gaussian colored noise induced spatial patterns and spatial coherence resonances in a square lattice neuronal network composed of Morris-Lecar neurons are studied.Each neuron is at resting state near a saddle-node bifurcation on invariant circle,coupled to its nearest neighbors by electronic coupling.Spiral waves with different structures and disordered spatial structures can be alternately induced within a large range of noise intensity.By calculating spatial structure function and signal-to-noise ratio(SNR),it is found that SNR values are higher when the spiral structures are simple and are lower when the spatial patterns are complex or disordered,respectively.SNR manifest multiple local maximal peaks,indicating that the colored noise can induce multiple spatial coherence resonances.The maximal SNR values decrease as the correlation time of the noise increases.These results not only provide an example of multiple resonances,but also show that Gaussian colored noise play constructive roles in neuronal network.     

Spatiotemporal multiple coherence resonances and calcium waves in a coupled hepatocyte system

Spatiotemporal multiple coherence resonances for calcium activities induced by weak Gaussian white noise in coupled hepatocytes are studied. It is shown that bi-resonances in hepatocytes are induced by the interplay and competition between noise and coupling of cells, in other words, the cell in network can be excited either by noise or by its neighbour via gap junction which can transfer calcium ions between cells. Furthermore, the intercellular annular calcium waves induced by noise are observed, in which the wave length decreases with noise intensity augmenting but increases monotonically with coupling strength increasing. And for a fixed noise level, there is an optimal coupling strength that makes the coherence resonance reach maximum.     

Parameter Diversity Induced Multiple Spatial Coherence Resonances and Spiral Waves in Neuronal Network with and Without Noise

Diversity in the neurons and noise are inevitable in the real neuronal network. In this paper, parameter diversity induced spiral waves and multiple spatial coherence resonances in a two-dimensional neuronal network without or with noise are simulated. The relationship between the multiple resonances and the multiple transitions between patterns of spiral waves are identified. The coherence degrees induced by the diversity are suppressed when noise is introduced and noise density is increased. The results suggest that natural nervous system might profit from both parameter diversity and noise, provided a possible approach to control formation and transition of spiral wave by the cooperation between the diversity and noise.     

Bunch beam cooling

Electron cooling is used for damping both transverse and longitudinal oscillations of heavy particle. The cooling of bunch ion beam (with RF voltage on) is important part of experiments with inner target, ion collision system, stacking and RF manipulation. The short length of an ion bunch increases the peak luminosity, gives a start-time point for using of the time-of-flight methods and obtains a short extraction beam pulse. This article describes the review of last experiments with electron cooling carried out on the CSRm, CSRe (China) and COSY (Germany) storage rings. The accumulated experience may be used for the project of electron cooler on 2.5 MeV (NICA) and 0.5 MeV HIAF for obtaining high luminosity, depressing beam-beam effects and RF manipulation.     

Inducement and enhancement of multiple coherence resonances in unidirectionally coupled neural systems: Random and time-periodic coupling strength

The effect of cooperative coupling strength (CCS), i.e., random coupling strength and time-periodic coupling strength, on multiple coherence resonances in unidirectionally coupled neural system has been investigated. Results show that noise, frequency and amplitude play efficient roles for the enhancement of various coherent behaviours. There exist an optimal frequency and an optimal amplitude which make the system to display the best coherent behaviours. Furthermore, the novel coherence biresonance (CBR) induced by frequency of CCS and coherence multiresonances (CMR) induced by amplitude of CCS, are found.     

正对撞束束补偿的理论和模拟研究

束束效应是限制对撞机性能提高的重要因素,其限制作用可以通过补偿机制来改善。针对正对撞束束效应,提出两种实现束束补偿的对撞机结构,并对实现束束补偿的原理和需要满足的条件进行分析。提出利用能量回收型直线加速器产生的电子束流进行正对撞束束补偿的方案,并且基于超级质子质子对撞机进行模拟研究,研究了补偿前后束流粒子分布、频移和粒子损失等变化情况。束束补偿可以减小束团内部粒子的频散,减小束流损失,提高束流寿命,可以大幅提高单束团流强,从而提高对撞机亮度。     

Nearly linear mappings and their applications

A simple 2-dimensional mapping is considered, both analytically and numerically, for which all nonlinear effects are of the same order as the perturbations and of the same origin. Properties of the stochastic instability are investigated, taking the beam-beam interaction in a storage ring as an important particular example of a dynamic system that can be modelled with such a mapping. The special case of time-dependent mappings is discussed. It is shown that low-frequency time dependence sharply decreases the critical perturbation strength for the stochastic transition.     

Effects of cavity resonances on sound transmission into a thin cylindrical shell

In the context of the transmission of airborne noise into an aircraft fuselage, a mathematical model is presented for the effects of internal cavity resonances on sound transmission into a thin cylindrical shell. The “noise reduction” of the cylinder is defined and computed, with and without including the effects of internal cavity resonances. As would be expected, the noise reduction in the absence of cavity resonances follows the same qualitative pattern as does transmission loss. Numerical results show that cavity resonances lead to wide fluctuations and a general decrease of noise reduction, especially at cavity resonances. Modest internal absorption is shown to greatly reduce the effect of cavity resonances. The effects of external airflow, internal cabin pressurization, and different acoustical properties inside and outside the cylinder are also included and briefly examined.     

Interpretation of an empirical systematics of coherence widths

On the basis of the continuity equation, the concept of a complex potential, and the exciton model of nuclear reactions, an expression was derived that establishes the relation between three time characteristics associated with different reaction stages. It is shown that an empirical systematics relating the coherence widths to the temperature of compound nuclei is a high-temperature limit of this expression, which determines empirical coefficients in terms of quantities similar to volume absorption integrals per nucleon that appear in optical-model calculations. The possibility of estimating the energy dependence of these quantities on the basis of experimental data on the total widths of neutron resonances, measured mean lifetimes of compound nuclei, and data on coherence widths is discussed.     

Full counting statistics as a probe of quantum coherence in a side-coupled double quantum dot system

We study theoretically the full counting statistics of electron transport through side-coupled double quantum dot (QD) based on an efficient particle-number-resolved master equation. It is demonstrated that the high-order cumulants of transport current are more sensitive to the quantum coherence than the average current, which can be used to probe the quantum coherence of the considered double QD system. Especially, quantum coherence plays a crucial role in determining whether the super-Poissonian noise occurs in the weak inter-dot hopping coupling regime depending on the corresponding QD-lead coupling, and the corresponding values of super-Poissonian noise can be relatively enhanced when considering the spins of conduction electrons. Moreover, this super-Poissonian noise bias range depends on the singly-occupied eigenstates of the system, which thus suggests a tunable super-Poissonian noise device. The occurrence-mechanism of super-Poissonian noise can be understood in terms of the interplay of quantum coherence and effective competition between fast-and-slow transport channels.     

Applicability of the probability model to absorption of monochromatic radiation

A kinetic equation is derived for the forced population relaxation in a gas in the limiting case of sharp collisions (with complete loss of phase coherence). The solution is examined for the conditions under which it satisfies the basic kinetic equation of the transition model.     

Beam-beam limit in e+e- circular colliders

Beam-beam effects limit the luminosity of circular colliders. Once the bunch population exceeds a threshold, the luminosity increases at a slower rate. This phenomenon is called the beam-beam limit. Onset of the beam-beam limit has been analyzed with various simulation methods based on the weak-strong and strong-strong models. We have observed that an incoherent phenomenon is mainly concerned in the beam-beam limit. The simulation have shown that equilibrium distributions of the two colliding beams are distorted from Gaussians when the luminosity is limited. The beam-beam limit is estimated to be xi approximately 0.1 for a B factory with damping time of several thousand turns.     

Wavelet analysis of fine-scale structures in the Saturnian B and C rings using data from the Cassini spacecraft

A continuous wavelet transform with a complex Morlet basis offers an effective method for the analysis of an instant variable periodicity in the spatially inhomogeneous matter density in the radial structure of Saturn’s rings. An original algorithm that reduces the integral transform to solving a Cauchy problem for a partial differential equation is used for an analysis of the images of Saturn’s B and C rings, which were obtained in the second half of 2004 from the Cassini spacecraft. This paper is a continuation of our preceding study of the fine-scale structure of Saturn’s rings reported in Zh. Éksp. Teor. Fiz. 128, 752 (2005) [JETP 101, 646 (2005)].     

Two-frequency mutual coherence function for electromagnetic pulse propagation over rough surfaces

The propagation of a transient electromagnetic pulse over irregular terrain is considered. We model the wave propagation using the parabolic wave equation, which is valid for near-horizontal propagation. We model the effect of scattering from the rough terrain by introducing a surface-flattening coordinate transform. This coordinate transform simplifies the boundary condition of our problem, and introduces an effective refractive index into our wave equation. As a result, the problem of propagation over an irregular surface becomes equivalent to the problem of propagation through random media. The parabolic equation is solved analytically using the path integral method. Both vertically polarized and horizontally polarized signals are treated. Cumulant expansion is introduced to obtain an approximate expression for the two-frequency mutual coherence function. From the mutual coherence function, spatial and temporal dependence of the propagating signal can be determined. It can be shown that scattering from the irregular surface can cause broadening of the transient signal. This can have a significant impact on the performance of radio communication systems.