Nonlinear dynamics of a driven mode near marginal stability

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The nonlinear dynamics of a linearly unstable mode in a driven kinetic system is investigated to determine scaling of the saturated fields near the instability threshold. To leading order, this problem reduces to solving an integral equation with a temporally nonlocal cubic term. This equation can exhibit a self-similar solution that blows up in a finite time. When the blow-up occurs, higher nonlinearities become important and the mode saturates due to plateau formation arising from particle trapping in the wave. Otherwise, the simplified equation gives a regular solution that leads to a different saturation scaling reflecting the closeness to the ... continued below

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16 p.

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Berk, H.L.; Breizman, B.N. & Pekker, M. September 1, 1995.

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Description

The nonlinear dynamics of a linearly unstable mode in a driven kinetic system is investigated to determine scaling of the saturated fields near the instability threshold. To leading order, this problem reduces to solving an integral equation with a temporally nonlocal cubic term. This equation can exhibit a self-similar solution that blows up in a finite time. When the blow-up occurs, higher nonlinearities become important and the mode saturates due to plateau formation arising from particle trapping in the wave. Otherwise, the simplified equation gives a regular solution that leads to a different saturation scaling reflecting the closeness to the instability threshold.

Physical Description

16 p.

Notes

INIS; OSTI as DE96001772

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  • Other Information: PBD: Sep 1995

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  • Other: DE96001772
  • Report No.: DOE/ET/53088--719
  • Grant Number: FG05-80ET53088
  • DOI: 10.2172/120914 | External Link
  • Office of Scientific & Technical Information Report Number: 120914
  • Archival Resource Key: ark:/67531/metadc627649

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

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  • September 1, 1995

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  • June 16, 2015, 7:43 a.m.

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  • Aug. 10, 2016, 2:14 p.m.

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Berk, H.L.; Breizman, B.N. & Pekker, M. Nonlinear dynamics of a driven mode near marginal stability, report, September 1, 1995; Austin, Texas. (digital.library.unt.edu/ark:/67531/metadc627649/: accessed October 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.