Periodic Pulling and Turbulence in a Bounded Plasma

Abrams, R.H.; Yadlowsky, E. J.; Lashinsky, H.

doi:10.1103/physrevlett.22.275

Cited by 55 publications

(18 citation statements)

References 5 publications

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“…A theoretical model based on the Van der Pol equation is well established for such plasma phenomena. 8,9 In particular, it is proposed by Hioki and Okuda 9 for conditions very similar to ours. The inherent fluctuation with an amplitude which is saturated before the cell injection in the weakly unstable plasma is nonlinearly coupled with a cell during its lifetime.…”

Section: Forced Organization Of Flute-type Turbulence By Convective Csupporting

confidence: 77%

Forced organization of flute-type turbulence by convective cell injection

Iizuka¹,

Huld²,

Pécseli³

et al. 1988

Phys. Rev. Lett.

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Nonlinear interactions between flute-type turbulence and an externally excited convective cell in a strongly magnetized plasma are investigated. During the interaction the azimuthal-mode-number spectrum of the turbulence is deformed and a broad spectrum evolves, indicating an inverse cascade. As a result of a modification in phase and amplitude of the fluctuations, an organized structure is created in the turbulence. The macroscopic behavior is well explained by a Van der Pol-type equation.PACS numbers: 52.35. Mw, 52.35.Fp, 52.35.Ra The self-organization process in turbulent and linearly unstable systems is one of the most interesting and important phenomena in nonlinear plasma dynamics as well as in fluid dynamics. 1 It has been demonstrated for two-dimensional flows, for instance, that the situation consisting of very many vortices is deformed through a coalescence of these vortices to create ultimately a large-scale structure, indicating an inverse cascade in the turbulence. 2 In distinction from these spontaneous organizations, we here report a forced organization of turbulence in a plasma, accompanied by an inverse cascade. This process is the result of a nonlinear interaction between spontaneously generated turbulence and an externally excited convective cell. 3,4 The experiment is carried out in a linear machine, 3,5 where a plasma is produced by surface ionization of cesium on a hot tantalum plate of 3 cm diam. The plasma column is confined by an axial magnetic field Bo («0.35 T). Typical parameters are as follows: central plasma density /in~ 10 9 cm ~3, and temperatures T e « T t -0.2 eV. Outside the central plasma column, a residual or scrapeoff plasma layer exists with the same temperature but a reduced plasma density. 5 A convective cell is excited by our applying a positive square-wave pulse of 20-jUS duration to an 8-mm-diam disk which is placed in the residual plasma outside the main plasma column. The repetition rate of the pulses is 50 Hz. Between the pulses the bias of the disk is equal to that of the cold end plate (-15 V).In the residual plasma, fluctuations always appear, which show many features of a flute-type instability. 6,7 The driving mechanism for the instability which gives rise to these oscillations was identified as the azimuthal Kelvin-Helmholtz, or velocity shear, instability; see Ref.6. Fluctuations in floating potential were measured by two probes with exposed spherical platinum tips of 1 mm diam. 3,4 High-input impedance amplifiers (100 Mft) with bandwidth 300 kHz were placed in the intermediate vicinity of the probes. Probes and detecting circuits were tested by measurements of grid-excited ion acoustic waves. 3 Figure 1(a) shows a typical frequency spectrum of the potential fluctuations. We find that the fluctua-tion around /o == 5.2 kHz is associated with an m=2 azimuthal mode number and propagates approximately with the local EoXBn velocity, where Eo is the radial electric field at the plasma edge. This result was explicitly confirmed by the measurement of Eo. By changin...

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Section: Forced Organization Of Flute-type Turbulence By Convective Csupporting

confidence: 77%

Forced organization of flute-type turbulence by convective cell injection

Iizuka¹,

Huld²,

Pécseli³

et al. 1988

Phys. Rev. Lett.

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“…In a similar manner to the experimental results, if the external frequency is then increased to approach the internal frequency, the two oscillations begin to interact, with the internal frequency shifting toward the externally applied frequency. This frequency pulling 15 is a result of the incomplete entrainment of an oscillatory nonlinear system by a periodically varying driving force, and is observed experimentally when the instability jumps between the driven and natural frequencies of the system. Increasing the external frequency further results in the internal frequency merging with the drive frequency, a phenomenon that has previously been referred to as mode locking, phase locking, synchronization, 13 or frequency entrainment.…”

Section: B Van Der Pol Plasma Dynamicsmentioning

confidence: 93%

“…Mechanisms for suppressing various kinds of internal instabilities in magnetized and unmagnetized plasma systems have been investigated. [11][12][13][14][15][16] Keen and Fletcher 12,13 investigated the suppression of an ion acoustic instability by inducing density perturbations at various frequencies close to and far away from the instability frequency. They termed it synchronous and asynchronous suppression, respectively.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear instability dynamics in a high-density, high-beta plasma

Corr

Boswell

2009

Physics of Plasmas

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“…Abrams, Yadlowsky, and Lashinsky [27] and Lashinsky, Rosenburg, and Detrick [28], however, recognized that not one, but two different classes of oscillations exist when the system is not entrained and obtained spectra from both classes in experiments involving plasma drift waves. One class, labeled "combination oscillations, " consists of components at frequencies that are combinations of fo, fD, and IfD fol The other class, labeled "almost-periodic oscillations, " occurs when the values of driving amplitude and frequency are close to the region of entrainment in parameter space.…”

Section: Introductionmentioning

confidence: 99%

Experimental verification of periodic pulling in a nonlinear electronic oscillator

Koepke

Hartley

1991

Phys. Rev. A

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An experimental investigation of entrainment and the phenomenon known as periodic pulling is described. Periodic pulling refers to the incomplete entrainment of an oscillatory nonlinear system by a periodically varying driving force. The process whereby the system s oscillation frequency is pulled toward the driving frequency stops short of complete synchronization and is interrupted at regular intervals. In this way, periodic pulling produces pulselike amplitude and frequency modulation in the system s oscillatory response. Associated with these combined, nonsinusoidal modulations is an asymmetric, or single-sided, spectral peak made up of spectral components at frequencies incommensurate with the undriven {spontaneous) and driving frequencies. The system being investigated uses a unijunction transistor as the nonlinear element in an electrical circuit. The behavior of the system is shown to resemble that predicted for a forced van der Pol oscillator with an adjustable nonlinear restoring force.For certain ranges of driving frequency and amplitude, when the system is not entrained to the driving force, periodic pulling is shown to alter the system's oscillatory response significantly from that expected for conventional amplitude modulation involving two sinusoids. The essential features of the periodic pulling phenomenon are observed and compared, with good agreement, to a model.

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Periodic Pulling and Turbulence in a Bounded Plasma

Cited by 55 publications

References 5 publications

Forced organization of flute-type turbulence by convective cell injection

Forced organization of flute-type turbulence by convective cell injection

Nonlinear instability dynamics in a high-density, high-beta plasma

Experimental verification of periodic pulling in a nonlinear electronic oscillator

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