Phase Description of Stochastic Oscillations

Schwabedal, Justus T. C.; Pikovsky, Arkady

doi:10.1103/physrevlett.110.204102

Cited by 64 publications

(90 citation statements)

References 25 publications

(23 reference statements)

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“…We would thus expect under some plasma conditions a global dynamics in which all the ELMs are "prompt," with each ELM directly following the previous one. We have identified just such a dynamics here on ASDEX Upgrade in which the excursions of the control system and perturbations in the plasma are completely phase synchronized, [24][25][26] with their synchronous oscillations coinciding with the occurrence times of all the natural ELMs. In such a synchronous state, continual nonlinear feedback between global plasma dynamics and control system is intrinsic to natural ELMing.…”

Section: Discussionmentioning

confidence: 99%

“…A ubiquitous aspect of such strongly connected, many component physical systems is the potential for self-organisation to synchronous states where nonlinear active feedback between global and local scales leads to emergent global dynamics. [24][25][26] Active control of the plasma is required to automatically maintain a global steady state and this is achieved by the control system's real-time monitoring of the plasma (Ref. 27 and references therein).…”

Section: Introductionmentioning

confidence: 99%

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Control system-plasma synchronization and naturally occurring edge localized modes in a tokamak

et al. 2018

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Edge Localised Modes (ELMs) naturally occur in tokamak plasmas in high confinement mode. We find in ASDEX Upgrade that the plasma can transition into a state in which the control system field coil currents, required to continually stabilize the plasma, continually oscillate with the plasma edge position and total MHD energy. These synchronous oscillations are one-to-one correlated with the occurrence of natural ELMs; the ELMs all occur when the control system coil current is around a specific phase. This suggests a phase synchronous state in which nonlinear feedback between plasma and control system is intrinsic to natural ELMing, and in which the occurrence time of a natural ELM is conditional on the phase of the control system field coil current.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Control system-plasma synchronization and naturally occurring edge localized modes in a tokamak

et al. 2018

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“…These signals reflect the control system and plasma behaving as a single nonlinearly coupled system, rather than as driver and response. If there were coupling between the global plasma environment, including the control system, and each of several growing modes in the plasma, these modes could become synchronized, [20][21][22] through their individual interactions with the global plasma/control system environment, without the need of coupling between the modes themselves. Large scale plasma motion would then develop on timescales characteristic of the dynamics of the global plasma environment.…”

Section: Discussionmentioning

confidence: 99%

The global build-up to intrinsic edge localized mode bursts seen in divertor full flux loops in JET

et al. 2015

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A global signature of the build-up to an intrinsic edge localized mode (ELM) is found in the temporal analytic phase of signals measured in full flux azimuthal loops in the divertor region of JET. Toroidally integrating, full flux loop signals provide a global measurement proportional to the voltage induced by changes in poloidal magnetic flux; they are electromagnetically induced by the dynamics of spatially integrated current density. We perform direct time-domain analysis of the high time-resolution full flux loop signals VLD2 and VLD3. We analyze plasmas where a steady H-mode is sustained over several seconds during which all the observed ELMs are intrinsic; there is no deliberate intent to pace the ELMing process by external means. ELM occurrence times are determined from the Be II emission at the divertor. We previously [Chapman et al., Phys. Plasmas 21, 062302 (2014); Chapman et al., in 41st EPS Conference on Plasma Physics, Europhysics Conference Abstracts (European Physical Society, 2014), Vol. 38F, ISBN 2-914771-90-8] found that the occurrence times of intrinsic ELMs correlate with specific temporal analytic phases of the VLD2 and VLD3 signals. Here, we investigate how the VLD2 and VLD3 temporal analytic phases vary with time in advance of the ELM occurrence time. We identify a build-up to the ELM in which the VLD2 and VLD3 signals progressively align to the temporal analytic phase at which ELMs preferentially occur, on a ∼2−5ms timescale. At the same time, the VLD2 and VLD3 signals become temporally phase synchronized with each other, consistent with the emergence of coherent global dynamics in the integrated current density. In a plasma that remains close to a global magnetic equilibrium, this can reflect bulk displacement or motion of the plasma. This build-up signature to an intrinsic ELM can be extracted from a time interval of data that does not extend beyond the ELM occurrence time, so that these full flux loop signals could assist in ELM prediction or mitigation.

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“…We require that the phase variable advances with uniform speed along the limit cycle. Given an arbitrary parametrization of a limit cycle by a cyclic variable θ, this can always be achieved by an appropriate reparametrization ϕ = ϕ(θ) [55,56]. The phase parameterization is unique up to the choice of start point.…”

Section: Active Oscillatorsmentioning

confidence: 99%

Hydrodynamic synchronization of flagellar oscillators

Friedrich

2016

Eur. Phys. J. Spec. Top.

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Abstract. In this review, we highlight the physics of synchronization in collections of beating cilia and flagella. We survey the nonlinear dynamics of synchronization in collections of noisy oscillators. This framework is applied to flagellar synchronization by hydrodynamic interactions. The time-reversibility of hydrodynamics at low Reynolds numbers requires swimming strokes that break time-reversal symmetry to facilitate hydrodynamic synchronization. We discuss different physical mechanisms for flagellar synchronization, which break this symmetry in different ways.

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Phase Description of Stochastic Oscillations

Cited by 64 publications

References 25 publications

Control system-plasma synchronization and naturally occurring edge localized modes in a tokamak

Control system-plasma synchronization and naturally occurring edge localized modes in a tokamak

The global build-up to intrinsic edge localized mode bursts seen in divertor full flux loops in JET

Hydrodynamic synchronization of flagellar oscillators

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