Signature of chaos in nonlinear drift-wave-induced transport

Eickermann, Th.; Spatschek, K. H.

doi:10.1103/physreve.51.1605

Cited by 6 publications

(3 citation statements)

References 17 publications

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“…The evolution of the correlation dimensionality together with the Lyapunov spectra quantitatively confirm the Ruelle-Takens transition scenario. It is worth noting that evidence for a Ruelle-Takens transition has been reported in recent theoretical investigations of nonlinear drift waves in weakly ionized plasmas [32].…”

Section: Temporal Dynamicsmentioning

confidence: 78%

Chaos and turbulence studies in low- plasmas

Klinger

Latten

Piel

et al. 1997

Plasma Phys. Control. Fusion

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This paper describes recent experimental investigations of the nonlinear dynamics of collisional current-driven drift waves in a linear low-β 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 modelocked 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.

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Section: Temporal Dynamicsmentioning

confidence: 78%

Chaos and turbulence studies in low- plasmas

Klinger

Latten

Piel

et al. 1997

Plasma Phys. Control. Fusion

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“…Averaging over one oscillation period or the azimuthal coordinate, respectively, this term leads to a nonvanishing contribution to radial particle transport, if a phase shift between the fluctuations of n e and exists, see, for example, [5]. In the case of large scale fluctuations this anomalous contribution to radial transport has been designated as convective transport [56]. For numerical evaluation of this term we write…”

Section: Radial Particle Transportmentioning

confidence: 99%

“…In a formal way we introduce a diffusion coefficient for the convective transport by writing (see e.g. [56])…”

Section: Radial Particle Transportmentioning

confidence: 99%

Investigation of oscillations and anomalous transport in a hydrogen hollow cathode discharge by a spatially three-dimensional two-fluid model

Biel

Kempkens

Uhlenbusch

1998

Plasma Phys. Control. Fusion

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A spatially three-dimensional two-fluid model for electrons and ions has been developed in order to describe the plasma state of a magnetized hollow cathode arc burning in hydrogen at low pressure. In this direct current (DC) supplied discharge strong self-excited periodical oscillations have been observed previously, where a helically shaped plasma column rotates eccentrically around the magnetic field axis. The theoretical description of this plasma is based on the system of two-fluid equations formulated by Braginskii. After some estimations and approximations derived from the experimental results and by limiting the discussion to stationary and low-frequency phenomena, the system of equations can be reduced and a secondorder differential equation of elliptic type for the plasma potential is derived. Using the measured spatial distributions of time resolved electron density and temperature as input data, this differential equation is solved numerically and the spatial distributions of the electric field, drift velocities, current densities and other quantities can be calculated. The results of our calculations show that an eccentrically rotating minimum of the plasma potential exists, while the arc current is concentrated in an annular region of maximum electron temperature. The magnitude of the radial particle transport coefficient is found to be in the order of the Bohm diffusion coefficient, which is about one order of magnitude larger than the classical diffusion coefficient. The measured oscillation frequencies can be explained by the (E × B) drift frequency.

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Reduced Two‐Field Equations and Anomalous Transport Scaling in Low‐Temperature Plasmas

Spatschek

Eickermann

1996

Contrib. Plasma Phys.

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After a review of more or less systematic approaches for normal as well as anomalous particle transport phenomena across a magnetic field, simplified macroscopic models are discussed. A reduced two-field model for collision-dominated low-temperature plasmas is presented. Although it looks similar to its high-temperature analogue (known as the Hasegawa-Wakatani equations), it has significant peculiarities which are discussed in detail. Some basic results following from the reduced two-field model, e.g. anomalous transport scaling close to the onset of collisional driftwave instability, are discussed. General OutlineClassical radial particle transport (perpendicular to an external magnetic field) is a detailed theoretical prediction which is hardly found to be true in experimental situations. Despite the sometimes lengthy algebra used in classical collisional transport theory, the resulting scaling is easy to understand. When, e.g., applying random walk arguments, the classical (collisional) diffusion coefficient D can be estimated as [l] .where A z is the (onedimensional) distance between two successive collisions occuring at times t and t + A t . Here, for simplicity, we have used a one-dimensional formulation.Without an external magnetic field, or for displacements along (11) an external magnetic field, we can rewrite expression (1) as where wt is the thermal velocity, and v is the collision frequency. Thus, obviously, collisions hinder a sc-called parallel transport. The situation is opposite for the particle transport across (I) an external magnetic field, since then the step size A x is of the order of the (thermal) Larmor radius e of a particle gyrating around a field line. We find DI x 4 e 2 v ,') Present address:

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Signature of chaos in nonlinear drift-wave-induced transport

Cited by 6 publications

References 17 publications

Chaos and turbulence studies in low- plasmas

Chaos and turbulence studies in low- plasmas

Investigation of oscillations and anomalous transport in a hydrogen hollow cathode discharge by a spatially three-dimensional two-fluid model

Reduced Two‐Field Equations and Anomalous Transport Scaling in Low‐Temperature Plasmas

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