Chaos and bifurcations in periodic windows observed in plasmas

Tunable Optical Frequency Comb Generated Using Periodic Windows in a Laser and Its Application for Distance Measurement

A novel method for the generation of an optical frequency comb (OFC) is presented. The proposed approach uses a laser diode with optical feedback and operating at a specific nonlinear dynamic state named periodic window. In this case, the laser spectrum exhibits a feature with a series of discrete, equally spaced frequency components, and the repetition rate can be flexibly adjusted by varying the system parameters (e.g., external cavity length), which can provide many potential applications. As an application example, a dual-OFC system for distance measurement is presented. The results demonstrate the system's ability to achieve target distance detection, underscoring its potential for real-world applications in this field.

Numerical simulation of the bifurcation-remerging process and intermittency in an undriven direct current glow discharge

As a complex nonlinear medium, gas discharge plasma can exhibit various nonlinear discharge behaviors. In this study, in order to investigate the chaos phenomenon in the subnormal glow region of an undriven direct current glow discharge, a two-dimensional plasma fluid model is established coupled with a circuit model as a boundary condition. Using the applied voltage as control parameter in the simulation, the complete period-doubling bifurcation and inverse period-doubling bifurcation processes in the oscillation region are found, and the influence of the applied voltage on the spatiotemporal distribution of plasma parameters during the bifurcation-remerging process is examined. In addition, the spatial distribution of the plasma parameters of the bifurcation-remerging process is also examined. Also, a series of periodic windows are present in the chaotic region, where the positions and relative order are generally consistent with the universal sequence. Additionally, this study showed that the intermittent chaos appears near the period-3 window, and the bursts appearing in the approximate periodic motion becomes more and more frequent as the control parameters move away from the saddle-node bifurcation point, which shows the typical type-I intermittent chaos characteristics.

Striated microdischarges in an asymmetric barrier discharge in argon at atmospheric pressure

The investigation of striated microdischarges in barrier discharges in argon at atmospheric pressure is reported. Microdischarges were investigated by means of electrical measurements correlated with intensified CCD camera imaging. The scaling law theory known from low-pressure glow discharge diagnostics was applied in order to describe and explain this phenomenon. The investigated microdischarge is characterized as a transient atmospheric-pressure glow discharge with a stratified column. It can be described by similarity parameters i/r≈0.13 A/cm, pr≈5 Torr cm, and 3<λ/r<5 with the current i, pressure p, interval of subsequent striations λ, and radius of the plasma channel r. An attempt to describe the mechanism of creation of a striated structure is given, based on an established model of the spatial electron relaxation.

Parametric investigation of nonlinear fluctuations in a dc glow discharge plasma

Glow discharge plasmas exhibit various types of self-excited oscillations for different initial conditions like discharge voltages and filling pressures. The behavior of such oscillations associated with the anode glow has been investigated using nonlinear techniques like correlation dimension, largest Lyapunov exponent, etc. It is seen that these oscillations go to an ordered state from a chaotic state with an increase in input energy, i.e., with discharge voltages implying occurrence of inverse bifurcations. These results are different from the other observations wherein the fluctuations have been observed to go from ordered to chaotic state.

Observation of period multiplication and instability in a dc glow discharge

The temporal dynamics in the fluctuations of the plasma floating potentials from an undriven dc glow discharge argon plasma at an intermediate gas pressure of 250mTorr and at the range of discharge currents I=6-50mA are investigated. In this study, the discharge current I is used as the plasma system's bifurcation parameter in analogy with the parameter space of a numerical dynamical system. Over several regions of the discharge current, the floating potential fluctuation time series data has been indicative of random noise, periodic oscillations, and irregular fluctuations. As the bifurcation parameter (discharge current) is increased, the Fourier spectrum of the data shows increased signs of period multiplication, quasiperiodicity, and instabilities. In addition, the computations of the correlation dimension provide some insight into the complex nature of the instabilities in the glow discharge plasma.

Transitions to spatiotemporal chaos and turbulence of flute instabilities in a magnetized plasma

The spatiotemporal transition scenario of flute instabilities from a regular to a turbulent state is experimentally investigated in the plasma column of a thermionic discharge. The same transition scenario, i.e., the Ruelle-Takens route to turbulence, is found for both the Kelvin-Helmholtz and the Rayleigh-Taylor instabilities. It is demonstrated that the transition can be more or less smooth, according to the discharge mode. In both cases, a strong radial dependence is observed, which is linked to the velocity shear layer in the case of the Kelvin-Helmholtz instability.

Oscillations in dc driven barrier discharges: numerical solutions, stability analysis, and phase diagram

A short gas-discharge layer sandwiched with a semiconductor layer between planar electrodes shows a variety of spatiotemporal patterns. We focus on the spontaneous temporal oscillations that occur while a dc voltage is applied and while the system stays spatially homogeneous; the results for these oscillations apply equally to a planar discharge in series with any resistor with capacitance. We define the minimal model, identify its independent dimensionless parameters, and then present the results of the full time-dependent numerical solutions of the model as well as of a linear stability analysis of the stationary state. Full numerical solutions and the results of the stability analysis agree very well. The stability analysis is then used for calculating bifurcation diagrams. We find semiquantitative agreement with experiment for the diagram of bifurcations from stationary to oscillating solutions as well as for amplitude and frequency of the developing limit cycle oscillations.

Period doubling cascade in glow discharges: local versus global differential conductivity

Short planar glow discharges coupled to a resistive layer exhibit a wealth of spontaneous spatiotemporal patterns. Due to similarities with other pattern forming systems that are described by reaction-diffusion models, several authors have tried to derive such models from discharge physics. We investigate the temporal oscillations of the discharge system and find a cascade of period doubling events. This shows that the inner structure of the discharge is more complex than can be described by a two-component reaction-diffusion-model with negative differential conductivity. We also derive an alternative reduced model.

Transitions of macroscopic structures and self-induced chaos observed in plasmas by a dc hollow cathode discharge having features of nonlinear open systems

A novel experimental investigation is presented on the connection between discontinuous transitions of macroscopic structures of plasma and self-induced chaotic oscillations characterized by the positive Lyapunov exponents lambda(L) through the period-doubling route in a dc hollow cathode discharge, which has features of nonlinear open systems. We have clarified experimentally that there appear different discharge modes accompanying the discontinuous transitions, and detailed qualitative explanations are presented about the mechanism of those transitions. It is shown that fundamental frequencies of the self-induced periodic oscillations with nonpositive lambda(L) change with the changes of discharge current, and the amplitude of chaotic oscillations with the positive lambda(L) jumps up almost one order higher than that of nonchaotic ones with the nonpositive lambda(L). The self-induced chaotic oscillations with the positive lambda(L) have been observed near two edges of discontinuous transitions of plasma structures, suggesting that the chaotic mode is associated with the discontinuous transition of macroscopic structures in some nonlinear open systems.

Experimental real-time phase synchronization of a paced chaotic plasma discharge

Experimental phase synchronization of chaos in a plasma discharge is studied using a phase variable lift technique (i.e., phase points separated by 2pi are not considered as the same). Real-time observation of synchronized and unsynchronized states is made possible through a real-time sampling procedure. Parameter space regions of synchronization and unsynchronization are identified, and a set of equations is suggested to model the real plasma circuit.

Spatiotemporal laser perturbation of competing ionization waves in a neon glow discharge

The experimental verification of spatiotemporal periodic pulling, a specific but universal phenomenon associated with driven, nonlinear, spatiotemporal systems, is reported as part of a study characterizing the ability of dc and chopped laser light to induce periodic pulling in ionization waves propagating in a neon glow-discharge plasma. The degree to which a single-mode laser beam at a metastable transition of 6401 A (1s(5)-2p(9)) influences the discharge is found to depend on the location and magnitude of the perturbation. Cases of ac (chopping the light) and dc perturbation are presented. In a range of chopping frequencies above and below the ionization wave's undriven frequency, the wave can become synchronized to the perturbation. This entrainment range is shown to depend on the frequency difference between the wave and the perturbation, as well as on the perturbation distance from the cathode. Hysteresis is found in the value of the perturbation frequency associated with transitions into and out of entrainment. Outside of entrainment, periodic pulling of a self-excited, propagating, ionization wave by the laser perturbation is observed. This is a case of frequency pulling, or temporal periodic pulling. Inside of entrainment, the chopped laser light controls the frequency and amplitude of the mode. By properly adjusting the frequency and amplitude of one mode with respect to a second mode, periodic pulling of one ionization wave by the mode-locked, propagating, original ionization wave is demonstrated. This is a case of spatiotemporal pulling, involving both wavelength pulling and frequency pulling. Under proper conditions, competition between temporal and spatiotemporal periodic pulling results in a modulation in the dynamics of the system, a process referred to as dynamics modulation.