Complex dynamics of a distributed parametric oscillator

The dynamics of a system with three parametrically coupled waves with delayed feedback is considered. Results of the detailed numerical simulation of the onset of self-modulation, as well as complex dynamic and chaotic regimes, are presented. The relation of self-modulation regimes with the formation and propagation of solitons is investigated. It is discovered that as the pump parameter increases, the synchronization of phases of the interacting waves, which is characteristic of stationary generation and periodic self-modulation regimes, is violated, and the system goes to a chaotic regime via intermittency.     

Self-Modulation and Chaotic Regimes of Generation in a Relativistic Backward-Wave Oscillator with End Reflections

We study self-modulation and chaotic regimes of generation in a relativistic backward-wave oscillator in the presence of reflections of radiation from the boundaries of a slow-wave structure. The onset of self-modulation is examined in detail in the cases of weak and strong reflections. A numerical simulation of transition-to-chaos scenarios is performed over a wide range of parameters. The relation of bifurcation transitions between different regimes to the formation of spatio-temporal structures in the electron beam is discussed.     

Complex dynamics of a double-cavity delayed feedback Klystron oscillator

The complex dynamics of a model double-cavity delayed feedback klystron oscillator is considered. The self-oscillation and stationary oscillation conditions are analyzed theoretically. The results of numerical simulation of the self-modulation and chaotic regimes are presented, and routes to chaos at the center and boundaries of the oscillation zone are studied in detail. The effect of space charge forces on the oscillator dynamics is discussed.     

Self-modulation lasing regimes in a fast-flow CO<Subscript>2</Subscript> laser

Numerical simulation of self-modulation lasing regimes has been carried out for a CO₂ laser with transverse flow of the active medium through an unstable resonator with inhomogeneous internal pumping. Two types of steady-state self-modulation oscillation differing in the feedback mechanism were observed. The type of lasing regime and the conditions of its realization depend both upon the pumping profile and upon the composition and pressure of the working mixture, which makes it generally possible to control temporal characteristics of lasing.     

On the theory of self-modulation instability in an FEL amplifier due to stimulated scattering of counterpropagating waves

We present the results of numerical simulation of the self-modulation processes in an amplifier based on the effect of stimulated scattering of two counterpropagating transverse electromagnetic waves by a relativistic electron beam (FEL amplifier). Two models of the studied system are considered. One model allows for the effects of overbunching of electrons and is based on the modified method of macroparticles. The other is a simplified wave model obtained in the approximation that the amplitude of a combination wave is small if the nonlinearity of the electron-beam processes is negligibly small. The mechanisms of self-modulation are studied. The scenarios of transition to chaos, observed with increase in the input-signal intensity and system length, are examined. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 6, pp. 471–484, June 2007.     

Complex dynamics of a simple distributed self-oscillatory model system with delay

A simple model for a distributed self-oscillatory system with cubic nonlinearity and delay is presented. Conditions for oscillation self-excitation and stationary oscillation conditions, as well as the stability of the oscillations, are analyzed. Nonstationary self-modulation regimes (including conditions of complex dynamics and chaos) are simulated numerically over a wide range of control parameters. As the factor of nonequilibrium grows, regular and chaotic regimes alternate in a complex manner. The transitions to chaos may follow all scenarios known for finite-dimensional systems. The model suggested is somewhat akin to a number of earlier finite-dimensional models aimed at studying mode competition in resonance electron masers.     

Nonstationary processes in a diffraction-output orotron

The nonlinear dynamics of an orotron with diffraction output is studied. The evolution of the longitudinal field distribution is described by means of a parabolic equation subject to the condition of zero reflection at the collector end of the interaction space. For stationary regimes, the regions of high efficiency are delineated on the parameter plane, with the parameters being the departure from the critical frequency and the reduced length of the interaction space. From numerical results, the parameter plane is divided into the regions of stationary operation, periodic self-modulation, and stochastic self-modulation. It is demonstrated that self-modulation oscillating modes can be obtained most easily if the effective bounce frequency slightly exceeds the cutoff frequency, with the former being the blinking frequency of the dipole comprising an electron and its reflection in the regularly corrugated slow-wave guide.     

Self-organization of temporal structures in a multiequilibrium self-excited oscillator system with frequency control

An analysis is made of the nonlinear dynamics of a model of a self-excited oscillator system with automatic fine tuning of the frequency and possessing more than one equilibrium state. It is shown that, depending on the delay parameters of the control loop and the initial frequency detuning, various periodic and stochastic temporal structures may be formed, accompanied by the generation of various limit cycles and chaotic attractors in phase space. Reasons for the onset of self-modulation are set forth, and the position of the different oscillation regions is established. The main bifurcations are studied together with scenarios for the transformation of the oscillator self-modulation modes as a function of the parameters. Zh. Tekh. Fiz. 67, 1–8 (March 1997)     

Nonlinear theory of nonparaxial laser pulse propagation in plasma channels

Nonparaxial propagation of ultrashort, high-power laser pulses in plasma channels is examined. In the adiabatic limit, pulse energy conservation, nonlinear group velocity, damped betatron oscillations, self-steepening, self-phase modulation, and shock formation are analyzed. In the nonadiabatic limit, the coupling of forward Raman scattering (FRS) and the self-modulation instability (SMI) is analyzed and growth rates are derived, including regimes of reduced growth. The SMI is found to dominate FRS in most regimes of interest.     

Some special features of the transition to chaos in the self-modulation of surface spin waves

The results of experimental investigations of the transition from regular to stochastic self-modulation of intense surface spin waves are presented. It is found that the transition to chaos follows the scenario of a sequence of period-doubling bifurcations. The fractal dimensions and the Kolmogorov entropy are determined for different regimes. The experiments are performed on an apparatus consisting of a microwave oscillator with a spin-wave delay line in the feedback circuit. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 243–246 (25 August 1997)     

Nonstationary generation in free electron lasers

Evolution of the alternating field structure in the high-Q multimode cavity excited by the beam of relativistic electron oscillators is described by a self-consistent set of equations. Stationary and pulse injection regimes are investigated. The injection current increasing over the threshold, three consecutive stages take place: a) stationary single-mode generation (or, correspondingly, generation of identical pulses), b) periodic and c) stochastic self-modulation.     

强流相对论环形电子束自调制振荡研究

 主要研究了强流相对论环形电子束在等位谐振腔内的非线性自调制振荡，用小信号理论分析了电子起振的条件，得出了电子起振的扰动频率。基于该理论分析，又提出了一种不外加磁场的新型高功率微波器件，该器件主要由一个圆柱谐振腔和一个同轴波导输出腔构成。用2.5维MAGIC粒子模拟软件对该非线性过程进行数值模拟，分析了输入电压、电流对输出微波功率的影响。模拟结果表明这种结构中确实存在非线性不稳定性，自调制的扰动频率则由电子束的初始能量、电荷密度和电子束的半径以及谐振腔的空间结构给定。利用谐振腔长为4.7 cm、二极管电压为2.8 MV、电流为20 kA的电子束，可以得到频率为4.29 GHz、功率为6 GW的微波输出，束-波转换效率约为11%。     

Experimental evidence of absolute and convective instabilities in optics

Experimental evidence of convective and absolute instabilities in a nonlinear optical system is given. In optics, the presence of spatial nonuniformities brings in additional complexity. Hence, signatures characterizing these two regimes are derived based on analytical and numerical investigations. The corresponding noise-sustained and dynamical patterns are observed experimentally in a liquid crystal layer subjected to a laser beam with tilted feedback.     

Self-modulation and nonlinear diffraction of strong light fields in dispersive media

The problem of space-time self-modulation of strong laser fields is solved by the method of successive approximations. The nonlinear diffractional and nonlinear dispersive transformations of beam width and pulse duration are studied with emphasis on the reciprocal effects of nonlinear diffraction and dispersion. The effect of incomplete initial time and space coherence on the space-time parameters of a laser field and the conversion of its coherent properties is examined.Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 6/7, pp. 525–532, June–July, 1992.     

Chaos-controlling technique for suppressing self-modulation in backward-wave tubes

A method for suppressing self-modulation in backward-wave tubes is proposed. Additional delay is introduced into the feedback circuit, owing to which the output signal amplitude affects the electron beam current that enters into the interaction space. Numerical simulations demonstrate that the operating current in the single-frequency oscillation mode may be increased roughly twofold.     

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采用洛伦兹变换推导出左旋椭圆偏振强激光在磁化等离子体中的非线性色散关系,根据Karpman方法推导出激光场包络的非线性控制方程,分析了在磁化等离子体中左旋椭圆偏振激光的调制不稳定性,得到了调制不稳定的时间增长率。分析结果表明,磁化等离子体中自调制不稳定的极大增长率较非磁化情况明显减小,且在激光等离子体临界面附近处调制不稳定性的时间增长率显著增大。     

强激光在磁化等离子体中的调制不稳定性

采用洛伦兹变换推导出左旋椭圆偏振强激光在磁化等离子体中的非线性色散关系,根据Karpman方法推导出激光场包络的非线性控制方程,分析了在磁化等离子体中左旋椭圆偏振激光的调制不稳定性,得到了调制不稳定的时间增长率。分析结果表明,磁化等离子体中自调制不稳定的极大增长率较非磁化情况明显减小,且在激光等离子体临界面附近处调制不稳定性的时间增长率显著增大。     

Steady state self-focusing, self-modulation of laser beam in an inhomogeneous plasma

Laboratory as well as PIC simulation experiments reveal strong flow of energetic electrons co-moving with laser beam in laser plasma interaction. Equation governing the evolution of complex envelope in slowly varying envelope approximation is nonlinear parabolic equation. Variational approach is used to solve this problem and a Lagrangian for the problem is set up. Assuming a trial Gaussian profile, authors solve the reduced Lagrangian problem for beam width and curvature. Two scale lengths for inhomogenity along the direction of propagation, one for nonlinearity and other for diffraction management are introduced. Self-focusing, self-modulation as well as self-trapping of the laser-electron-beam plasma system is studied under variety of parameters.     

Chaos and hyperchaos in a gyrotron

We study oscillation in a gyrotron with allowance for reflections from an output horn. Regions with different system behaviors, such as stationary oscillation, self-modulation, and complex-dynamics regimes are found in the parameter plane. The scenarios of appearance of chaotic oscillations are considered. It is shown that they can emerge via either a sequence of period-doubling bifurcations or destruction of quasiperiodic motion. For chaotic attractors, Lyapunov exponents are calculated and their dimensions are estimated on the basis of the Kaplan-Yorke formula. The dimension values turn out to be anomalously large, which is stipulated by the presence of a large number of high-Q eigenmodes in the gyrotron cavity due to operation near the cutoff frequency of an electrodynamic system. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 10, pp. 887–899, October 2006.     

Single-mode giga-hertz optical pulses generated by a self-modulation of the relaxation oscillation frequency in a semiconductor laser with subharmonic polarization-rotated optical feedback

In this research, single-mode 3.76 GHz optical pulses were generated in a Fabry-Perot type single-mode semiconductor laser with polarization-rotated optical feedback (PROF) at a round-trip feedback distance of 50.8 cm, corresponding to a feedback frequency of 0.59 GHz. Experimental results and numerical simulations revealed that the pulse generation mechanism involved a self-modulation of the laser’s relaxation oscillation frequency so that the oscillation frequency approximated to an integer multiple of the PROF round-trip feedback frequency. This effect is very different from similar experiments reported by many researchers before, in which the laser’s output was amplitude modulated by the feedback frequency and an ultra-short feedback distance was required to generate giga-hertz optical pulses. Investigations about some characteristics of the self-modulation mechanism will be reported in the paper.