Phased Antenna Arrays Based on Vircators: Numerical Experiments

We present the results of numerical simulation of two different design schemes for phased antenna arrays (PAAs) based on vircators, i.e., microwave oscillators with virtual cathodes. The active and passive schemes of PAA design are analyzed separately. It is shown that in the case of an active PAA scheme, the degree of tuning the vircator to the master oscillator increases with increasing power of the latter, while in the case of a passive PAA scheme, the coherence degree of two vircators due to waveguide coupling increases with increase in the coupling coefficient.     

Coherent beam combining of hybrid phase control in master oscillator-power amplifier configuration

A novel scalable architecture for coherent beam combining with hybrid phase control involving passive phasing and active phasing in master oscillator-power amplifier configuration is presented. Wide-linewidth mutually injected passive phasing fibre laser arrays serve as master oscillators for the power amplifiers, and the active phasing using stochastic parallel gradient descent algorithm is induced. Wide-linewidth seed laser can suppress the stimulated Brillouin scattering effectively and improve the output power of the fibre laser amplifier, while hybrid phase control provides a robust way for in-phase mode coherent beam combining simultaneously. Experiment is performed by active phasing fibre laser amplifiers with passive phasing fibre ring laser array seed lasers. Power encircled in the main-lobe increases1.57 times and long-exposure fringe contrast is obtained to be 78% when the system evolves from passive phasing to hybrid phasing.     

Characteristics of generation in a chain of unidirectionally coupled low-voltage vircators

The output power of generation in a chain of unidirectionally coupled low-voltage vircators upon variation in controlling parameters of a system is studied. It is shown that at a certain set of controlling parameters, the output power of the generator chain grows sharply. Physical processes occurring in the system are analyzed by plotting space-time diagrams of the motion of charged particles of the electron flow with a virtual cathode. The obtained results are in good agreement with the data from a previous experimental study on signal amplification in a low-voltage vircator.     

Synchronization in arrays of coupled self-induced friction oscillators

We investigate synchronization phenomena in systems of self-induced dry friction oscillators with kinematic excitation coupled by linear springs. Friction force is modelled according to exponential model. Initially, a single degree of freedom mass-spring system on a moving belt is considered to check the type of motion of the system (periodic, non-periodic). Then the system is coupled in chain of identical oscillators starting from two, up to four oscillators. A reference probe of two coupled oscillators is applied in order to detect synchronization thresholds for both periodic and non-periodic motion of the system. The master stability function is applied to predict the synchronization thresholds for longer chains of oscillators basing on two oscillator probe. It is shown that synchronization is possible both for three and four coupled oscillators under certain circumstances. Our results confirmed that this technique can be also applied for the systems with discontinuities.     

Coherent beam combining of pulsed fiber lasers with hybrid phase control

We demonstrate a scalable architecture for coherent combining of all-fiber pulsed lasers with hybrid phase control involving passive phasing and active phasing for the first time. Synchronized and passive phased pulsed laser array is built by intra-activity phase modulation. Active phase control on the passive phased pulsed laser array using stochastic parallel gradient descent algorithm provides stable in-phase coherent beam combining pattern in a turbulent atmosphere. The fringe visibility is increased from 0 two 0.43 and the power encircled in the main-lobe is 1.616 times increased when the system evolves from passive phasing to hybrid phasing. The architecture can be easily scaled up to high power by increasing power of each individual laser, number of laser elements and introduction of power amplifiers, which will lead a promising way for scaleable high power coherent beam combining of pulsed lasers.     

BEPCⅡ直线加速器相控系统PAD的研制

相位和幅度测量是BEPCⅡ直线加速器相控系统中最重要的部分之一. 基于模拟和 数字I/Q解调器, 构建了两种PAD, 并分别在实验室和速调管长廊进行了测试. 基于LMS方法的校准算法用于补偿模拟I/Q解调器的各种不匹配误差. 实验 证明, 两种PAD都能正常稳定地运行, 可以满足相控系统对相位和幅度测量的要求.     

On the possibility of phasing subapertures with a Zernike cell and an optically addressed spatial light modulator

The possibility of phasing a large number of subapertures with a spatial light modulator optically addressed by the output beam of a Zernike interferometer is investigated theoretically. The optimum parameters of the system, the requirements for its elements, the range of compensated distortions upon phasing, and the phasing quality are determined. It is demonstrated that the proposed technique allows one to compensate effectively for the wavefront distortions of the piston difference, the tilt, and the curvature type with a total depth of the phase relief up to 8λ. In this case, it is possible to obtain a beam with a Strehl ratio larger than 0.8.     

PAD Design for the Phasing System of BEPCⅡ Linac

Phase and amplitude measurement is one of the most important issues for the phasing system of BEPCⅡ linac. Two kinds of PAD, based on analog and digital I/Q demodulator respectively, have been constructed and tested in both laboratory and the klystron gallery of BEPCⅡ linac. A calibration algorithm based on LMS method is used to compensate the mismatches of the analog I/Q demodulator. Experiments show that both kinds of PAD run stably and can meet the requirements of the phasing system.     

Generation of soft X rays in a vircator with exploding anode foil

A soft X-ray generator is designed on the basis of a vircator the plasma anode of which is formed by electrical explosion of anode foil. The intensity of soft X-ray radiation (E _γ > 20 eV) produced by vircators with a metal and plasma anode is measured. Microwave pulses indicating the presence of a virtual cathode in the plasma beam are detected.     

Consequential noise-induced synchronization of indirectly coupled self-sustained oscillators

We consider the dynamics of identical self-sustained oscillators coupled via a common linear system (beam), which is perturbed by noise. We demonstrate that increasing the noise intensity induces complete synchronization between the oscillators and, surprisingly, their in-phase synchronization with the beam. This new phenomenon of in-phase synchronization of both the oscillators and the oscillating beam arises when the noise intensity exceeds a threshold value, and can not appear in the deterministic case where the beam stably oscillates in anti-phase with the synchronized oscillators (as it is in the case of the Huygens clocks synchronization). Similar behavior persists for slightly non-identical oscillators.     

Self-synchronization of coupled oscillators with hysteretic responses

We analyze a large system of nonlinear phase oscillators with sinusoidal nonlinearity, uniformly distributed natural frequencies and global all-to-all coupling, which is an extension of Kuramoto's model to second-order systems. For small coupling, the system evolves to an incoherent state with the phases of all the oscillators distributed uniformly. As the coupling is increased, the system exhibits a discontinuous transition to the coherently synchronized state at a pinning threshold.of the coupling strength, or to a partially synchronized oscillation coherent state at a certain threshold below the pinning threshold. If the coupling is decreased from a strong coupling with all the oscillators synchronized coherently, this coherence can persist until the depinning threshold which is less than the pinning threshold, resulting in hysteretic synchrony depending on the initial configuration of the oscillators. We obtain analytically both the pinning and depinning threshold and also expalin the discontinuous transition at the thresholds for the underdamped case in the large system size limit. Numerical exploration shows the oscillatory partially coherent state bifurcates at the depinning threshold and also suggests that this state persists independent of the system size. The system studied here provides a simple model for collective behaviour in damped driven high-dimensional Hamiltonian systems which can explain the synchronous firing of certain fireflies or neural oscillators with frequency adaptation and may also be applicable to interconnected power systems.     

Smorodinsky-Winternitz potentials: Coherent state approach

In this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem and the Kepler-Coulomb problem. In the first case we find the nonspreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three nonisotropic harmonic oscillators. All of these states evolve in physical-time. In the third case, the system is transformed into four oscillators and the parametric-time coherent states are constructed in two coordinate frames. In the fourth case, the system is transformed into two oscillators with the reflection symmetry and the parametrictime coherent states are constructed in two coordinate frames.     

Studies of Coupled Anharmonic Oscillator Problem Using Coherent States and Path Integral Approaches

The present review is devoted to the study of the problem of coupled anharmonic oscillators. A perturbative solution is obtained for the system of an undamped and the damped coupled anharmonic oscillators in the coherent state representation. The solution does not contain the vicious secular terms and shows, explicitly, the anharmonic effects of a coupled system. In order to derive the perturbative solution of a damped coupled system a new frame of time, called quasi time τ, has been exploited. The large quantum number behaviour of coupled anharmonic oscillators has been derived using the path integral method.     

Collective behavior of electronic fireflies

A simple system composed of electronic oscillators capable of emitting and detecting light-pulses is studied. The oscillators are biologically inspired, there are designed for keeping a desired light intensity, W, in the system. From another perspective, the system behaves like modified integrate and fire type neurons that are pulse-coupled with inhibitory type interactions: the firing of one oscillator delays the firing of all the others. Experimental and computational studies reveal that although no direct driving force favoring synchronization is considered, for a given interval of W phase-locking appears. This weak synchronization is sometimes accompanied by complex dynamical patterns in the flashing sequence of the oscillators.     

Engineering synchronization of chaotic oscillators using controller based coupling design

We propose a general formulation of coupling for engineering synchronization in chaotic oscillators for unidirectional as well as bidirectional mode. In the synchronization regimes, it is possible to amplify or to attenuate a chaotic attractor with respect to other chaotic attractors. Numerical examples are presented for a Lorenz system, Ro?ssler oscillator, and a Sprott system. We physically realized the controller based coupling design in electronic circuits to verify the theory. We extended the theory to a network of coupled oscillators and provided a numerical example with four Sprott oscillators.     

Frequency analysis with coupled nonlinear oscillators

We present a method to obtain the frequency spectrum of a signal with a nonlinear dynamical system. The dynamical system is composed of a pool of adaptive frequency oscillators with negative mean-field coupling. For the frequency analysis, the synchronization and adaptation properties of the component oscillators are exploited. The frequency spectrum of the signal is reflected in the statistics of the intrinsic frequencies of the oscillators. The frequency analysis is completely embedded in the dynamics of the system. Thus, no pre-processing or additional parameters, such as time windows, are needed. Representative results of the numerical integration of the system are presented. It is shown, that the oscillators tune to the correct frequencies for both discrete and continuous spectra. Due to its dynamic nature the system is also capable to track non-stationary spectra. Further, we show that the system can be modeled in a probabilistic manner by means of a nonlinear Fokker-Planck equation. The probabilistic treatment is in good agreement with the numerical results, and provides a useful tool to understand the underlying mechanisms leading to convergence.     

Construction of the Phasing System for BEPCⅡ Linac

In order to get high beam quality, a RF distribution system is required, with minimal phase drifts and errors in the BEPCⅡ linac. The additional installation of phase reference cables and monitoring equipments and stable RF distribution for BEPC linac are finished. The master oscillator is chosen to offer RF signal with low phase noise and a stable phase distribution system is built to deliver RF signal to each klystron. A phase and amplitude detector is constructed to measure the phase precisely and an IΦA unit is used for a phase shifter. Control software based on EPICS is used to connect all the units of the system, and a phasing method based on BPM is adopted to optimize the phase of each klystron. Now the phasing system is installed and tested in the klystron gallery of the BEPCⅡ linac.     

耦合分数阶混沌振荡器的主-从同步

近年来对分数阶系统的动力学研究得到了较为广泛的关注。本文研究了基于主-从耦合同步法的同步技术并实现了两个耦合的分数阶振荡器的混沌同步。仿真结果表明：在适当的耦合强度的调节下，该方法可实现两个耦合分数阶混沌振荡器的准确同步，且分数阶混沌振荡器的同步率明显慢于整数阶混沌振荡器的同步率；而耦合分数阶混沌振荡器在实现同步的过程中，随着阶数的提高，同步误差曲线变得平滑，这表明，系统阶数的提高改善了耦合混沌振荡器实现同步的平稳性。     

Dynamics of a magnetic domain system upon parametric excitation

The occurrence of translational motion in the domain system in a ferrite plate under harmonic parametric action is investigated. The domain dynamics is described on the basis of the numerical solution of differential equations for a system of connected oscillators. Transition scenarios from oscillatory to translational motion are described, depending on the changes in the nonlinearity constant and damping parameter for various numbers of oscillators.