T. Klinger

A probe array for the investigation of spatio-temporal structures in drift wave, turbulence

A probe array with 64 azimuthally arranged Langmuir probes is presented as a new diagnostic tool for the investigation of drift waves. A parallel data acquisition system provides full spatio‐temporal data of azimuthally propagating waves. For both regular and turbulent states of current‐driven drift waves, the information provided by such space‐time patterns is compared with results obtained from conventional two‐point correlation methods. The probe array allows one to directly estimate the time‐averaged wave number spectrum. In a turbulent state, the spectrum yields to a power law of S(k)∝k−3.6±0.1.

Chaos and turbulence studies in low- plasmas

This paper describes recent experimental investigations of the nonlinear dynamics of collisional current-driven drift waves in a linear low- discharge. It is shown that the bias of an injection grid leads to rigid-body rotation of the cylindrical plasma column that strongly destabilizes the drift waves, thus providing a control parameter for the drift-wave dynamics. In the nonlinear regime, when the control parameter is increased, the transition scenario from stability to weakly developed turbulence is studied. Two successive Hopf bifurcations, a mode-locked state and its gradual destabilization to chaos and finally turbulence follow the classical Ruelle - Takens transition scenario known from neutral fluids. In addition to the temporal dynamics, the spatiotemporal evolution of drift waves is studied by means of circular Langmuir probe arrays with high spatial and temporal resolution. With each Hopf bifurcation, a drift-mode onset is associated and the bifurcation from quasi-periodicity to mode locking corresponds to the transition from non-resonant to resonant mode interaction. The mode-locked state forms a persistent spatiotemporal pattern that is destabilized by the occurrence of defects. In contrast, the turbulent state is a fully disordered, intermittent state.

CONTINUOUS CONTROL OF IONIZATION WAVE CHAOS BY SPATIALLY DERIVED FEEDBACK SIGNALS

Abstract In the positive column of a neon glow discharge, two different types of ionization waves occur simultaneously. The low-dimensional chaos arising from the nonlinear interaction between the two waves is controlled by a continuous feedback technique. The control strategy is derived from the time-delayed autosynchronization method. Two spatially displaced points of observation are used to obtain the control information, using the propagation characteristics of the chaotic wave.

Van der Pol dynamics of ionization waves

Abstract The dynamics of interacting self-excited and driven ionization waves is studied experimentally. The transition from quasiperiodicity to mode-locking shows a phenomenon known as periodic pulling. As dynamical model, the forced van der Pol system is established. Its theoretical predictions are fully confirmed by experiment.

Controlling chaos in the Pierce diode

Abstract The chaotic state of the classical Pierce diode is studied using a particle-in-cell computer simulation. The dynamics of the chaotic state is analyzed by estimating ergodic measures of the reconstructed attractor that refine and extend previously reported results [Matsumoto et al., Phys. Plasmas 3 (1996) 177]. The chaos control algorithm suggested by Ott, Grebogi, and Yorke is systematically applied to stabilize periodic orbits up to periodicity four. This demonstrates successful chaos control in a plasma, i.e., a many particle system with long range collective Coulomb interaction.

Stable and unstable discharge modes of a multipole confined thermionic gas discharge at low pressure

The discharge modes and the nonlinear potential relaxation instability of a thermionic argon discharge operated at pressures of 0.02-0.2 Pa are studied experimentally and compared to particle-in-cell (pic) simulations. The plasma produced in a steel vessel with a filamentary cathode is confined by a magnetic box arrangement of permanent magnets. Depending on the discharge voltage, the neutral gas pressure, and the filament heating current, the discharge shows two stationary states with a pronounced hysteresis in the current-voltage characteristic. For a certain range of discharge parameters, sawtooth oscillations can be observed in the discharge current. One-dimensional (1D) particle-in-cell simulations reveal details about the mechanism of the oscillations which are confirmed by experiment. The plasma potential which reflects the microscopic mechanisms is measured by means of emissive probes with high spatial and temporal resolution. The coherence of the self-oscillating system is improved by mode locking it with an external driver. The results of the simulation-specifically formation of an electron hole and its transformation into a double layer-are confirmed experimentally.

LOW-FREQUENCY CURRENT OSCILLATIONS IN A LINEAR HOT-CATHODE DISCHARGE

Abstract 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.

Intermittency or noise – an experimental study on the ion-beam driven ion-acoustic instability

Abstract Ion-acoustic waves are destabilised in a double-plasma device by ion-beam-plasma interaction. The plasma system destabilises via a supercritical Hopf-bifurcation with the control parameter being subject to noise. This leads to erratic fluctuations between stable and oscillatory states. The experimental results, in particular the statistical properties, show that this has to be distinguished from type-I intermittency transition to chaos as reported previously for similar experimental setups.

Chaos in Plasmas: A Case Study in Thermionic Discharges

During the last six years a growing interest arose in the study of low frequency oscillations in plasma discharges and their transition to chaos. The first observation of a period-doubling route to chaos was reported nearly simultaneously from a helium glow discharge1 and from a filament cathode discharge at low pressure.2 In the helium glow experiment, moving striations were observed in a Plucker tube that cause periodic modulations of the discharge current. With increasing current the characteristic sequence of subharmonics at 1/2, 1/4, 1/8, and 1/16 of the natural frequency was observed, which ends up in an irregular, apparently chaotic state. More complex routes with mixtures of period doublings and quintuplings were also reported.1 The conditions in the filament cathode discharge are fundamentally different, because of its low pressure (p = 0.1 Pa), large dimension (d = 1.8 m), and mode of operation. In this experiment, the plasma is not self-oscillating but periodically pulsed, and period doubling and quadrupling is found when the pulse amplitude is increased. The obvious similarity of the dynamical behavior in so different discharge situations stimulated a number of more detailed investigations in this field. An intermittency route to chaos in a filament cathode discharge was reported for a periodically driven system.3 Self-oscillations in such discharges show period-doubling and intermittency4 as well as a quasiperiodic5 route to chaos. A low correlation dimension was found for this kind of undriven chaos.6