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.     

Observation of chaotic dynamics in a powerful backward-wave oscillator

Self-modulation regimes of generation in a powerful 10-micros X-band backward-wave oscillator were studied theoretically and experimentally. The sequence of the self-modulation patterns and corresponding bifurcation values observed as the current was increased were in good agreement with the results of simulations. It was found that at a current of 120 A chaotic self-modulation set in at a power of 2 MW and a relative spectral width of 4%.     

Study of the Nonlinear Dynamics of a Traveling-Wave-Tube Oscillator with Delayed Feedback

We present the results of numerical simulations of the nonlinear dynamics of a traveling-wave-tube (TWT) oscillator with delayed feedback. Basic properties of stationary single-frequency oscillation regimes are considered, and the onset of self-modulation is studied in detail. Various route-to-chaos scenarios corresponding to successively increasing values of the beam current are simulated numerically. It is shown that the basic scenario is a quasi-periodic route to chaos, while the beam deceleration in strongly nonlinear regimes causes transitions via intermittency to regimes based on modes with higher frequencies. Competition between these two scenarios leads to a complex picture of regular and chaotic self-modulation regimes in the parameter space. Such a behavior is typical of distributed electron–wave self-excited oscillators with delayed feedback.     

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.     

Dynamics of helical-wave emission in a fiber-coupled diode end-pumped solid-state laser

We have generated TEM_0,l ^* modes in an end-pumped microchip laser using a standard fiber-coupled diode. A rich set of dynamic behaviors, such as periodic and quasi-periodic self-modulation, chaotic pulsing and frequency locking was observed in the generated TEM_0,l ^* modes. Experimental results confirm the theoretical predictions that the locking occurs as a subcritical bifurcation and that a region of coexisting locked and unlocked states exists. Received: 14 November 2000 / Revised version: 22 January 2001 / Published online: 23 May 2001     

Observation of the chaotic spin-wave soliton trains in magnetic films

The transition from stationary to chaotic spin-wave soliton trains has been observed. The experiment utilized cw excitation of envelope solitons through self-modulation instability of spin waves. By increasing the spin-wave power, the secondary self-modulation instability succeeded the primary modulation instability, resulting in after-modulation of the soliton train amplitude. Further increase of the spin-wave power led to development of the higher-order instabilities, resulting in formation of the chaotic soliton train.     

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)     

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.     

Transition to fully developed chaos in a system of two unidirectionally coupled backward-wave oscillators

The chaotic dynamics of a system of two unidirectionally coupled backward-wave oscillators (BWOs) is studied in the case when a signal from the driving BWO in (periodic or chaotic) self-modulation mode is applied to the driven oscillator, which exhibits strong periodic self-modulation in the autonomous case. The oscillation evolution with the amount of coupling is traced. The use of a chain of coupled BWOs is shown to significantly reduce the threshold of transition to the regime of wide-band chaotic oscillations with a uniform continuous spectrum (so-called fully developed chaos), which is of interest for applications.     

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.     

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.     

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.     

Self-modulation oscillatory modes in a relativistic backward-wave oscillator

We present the results of numerical simulation of nonlinear dynamics in a relativistic backward-wave oscillator (BWO) over a broad range of parameters. A comprehensive study of the onset of self-modulation is carried out. It is found that the self-modulation boundary in the parameter plane has a complex shape. This is due to the competition between two different dynamical modes leading to the instability of single-frequency stationary oscillations. It is shown that the transition to chaos through period doubling bifurcations characteristic of a nonrelativistic BWO exists only for small values of the relativistic factor γ₀, while the transition through intermittency dominates for large γ₀. Higher College for Applied Sciences, State University of Saratov, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 6, pp.566–572, June 1999.     

Oscillation modes,transient chaos and its control in a modulation-doped semiconductor double-heterostructure

The nonlinear dynamics of real space transfer for a 2D electron gas in a system of two adjacent Al _x Ga_1–x As/GaAs-heterolayers under parallel current conduction has been investigated numerically. The mechanisms which have been taken into account are transfer of electrons by thermionic emission and nonresonant tunneling and the delayed dielectric relaxation of the interface potential barrier. We predict bistability of an asymmetric and a symmetric self-generated oscillation mode, a quasiperiodic route to chaos and transient chaos with mean transient times obeying a universal critical scaling law. Unstable periodic orbits of the chaotic repeller can be stabilized by a simple delayed feedback control, thus providing a widely tunable semiconductor oscillator.     

Low-frequency current oscillations in a linear hot-cathode discharge

Low-frequency (ω ⪡ ω_pi) plasma oscillations in the transition regime between the high and the low current mode of a thermionic hot-cathode discharge are investigated experimentally. This type of current oscillation often shows chaotic dynamics. The current oscillations are related to nonlinear short wavelength potential structures which are identified as ion bunches formed by a fluctuating ionization front. These ion bunches are separated by ion holes and move at ion thermal speed rather than ion acoustic speed. By entering the negative space charge region of the cathode sheath, the ion bunches trigger electron current fluctuations that provide the required feedback mechanism for the observed wave train formation.     

Self-modulation processes in a low-current rare-gas discharge at low pressures

Experimental investigations were made of self-modulation processes in a striated rare-gas discharge at low pressures and currents. It was found that interrelated self-modulation oscillations of the discharge current and of the voltage across the tube can develop in the discharge circuit. Depending on the resistance in the external circuit, either current or voltage self-modulation occurred. An important factor is that the transition from one form of self-modulation to the other does not produce quantitative changes in the spatial modulation of the time-averaged plasma luminescence on the discharge axis. It is shown that a qualitative interpretation of the observed phenomena can be given in terms of an equivalent striation voltage source in the anode region which exists because of interaction between traveling kinetic ionization waves and the discharge region near the anode, and also in terms of processes of a capacitative nature near the electrodes. State University, St. Petersburg. Ukhtinskii Industrial Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 103–108, January, 1997.     

Feasibility of creating a specialized reactimeter based on the inverse solution to kinetics equation with a current-mode neutron detector

The file-evaluation results of a reactimeter based on the inverse solution to the kinetics equation (ISKE) are presented, which were obtained using an operating hardware-measuring complex with a KNK-4 neutron detector working in the current mode. The processing of power-recording files of the BR-1M, BR-K1, and VIR-2M reactors of the Russian Federal Nuclear Center—All-Russian Research Institute of Experimental Physics, which was performed with the use of Excel simulation of the ISKE formalism, demonstrated the feasibility of implementation of the reactivity monitoring (during the operation of these reactors at stationary power) beginning from the level of ~5 × 10^–4β_eff.     

Yellow light generation by frequency doubling of a diode-pumped Nd:YAG laser

We demonstrate the generation of TEM₀₀ mode yellow light in critically type II phase-matched KTiOPO₄ (KTP) with intracavity frequency doubling of a diode-pumped Nd:YAG laser at room temperature. After a 150 μm thick etalon have been inserted into the cavity, the stability and beam quality of the second harmonic generation (SHG) is enhanced. A continuous wave (CW) TEM₀₀ mode output power of 1.67 W at 556 nm is obtained at a pump level of 16 W. The total optical to optical conversion efficiency is about 10.44%. To the best of our knowledge, this is the first Watt-level yellow light generation by frequency doubling of Nd:YAG laser.     

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.