Nonlinear instability and chaos in plasma wave-wave interactions. II. Numerical methods and results

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In Part I of this work and Physics of Plasmas, June 1995, the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. It was shown that explosive instability arises from nonlinear coupling between modes of positive and negative energy, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. Several sets of waves are considered, comprising systems of two and three degrees of freedom. The time evolution is modelled with an explicit symplectic integration algorithm derived using Lie algebraic methods. When ... continued below

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48 p.

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Kueny, C.S. & Morrison, P.J. May 1, 1995.

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Description

In Part I of this work and Physics of Plasmas, June 1995, the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. It was shown that explosive instability arises from nonlinear coupling between modes of positive and negative energy, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. Several sets of waves are considered, comprising systems of two and three degrees of freedom. The time evolution is modelled with an explicit symplectic integration algorithm derived using Lie algebraic methods. When initial wave amplitudes are large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region for explosive triplets. Phase space orbits then experience diffusive growth to amplitudes that are sufficient for explosive instability, thus effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, small perturbations might still grow to arbitrary size via Arnold diffusion. Numerical experiments do not show diffusion in this case, although the actual diffusion rate is probably underestimated due to the simplicity of the model.

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48 p.

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OSTI as DE95013474

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  • Other Information: PBD: May 1995

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  • Other: DE95013474
  • Report No.: DOE/ET/53088--707
  • Report No.: IFSR--707
  • Grant Number: FG05-80ET53088
  • DOI: 10.2172/73039 | External Link
  • Office of Scientific & Technical Information Report Number: 73039
  • Archival Resource Key: ark:/67531/metadc708908

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  • May 1, 1995

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  • Sept. 12, 2015, 6:31 a.m.

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  • Dec. 18, 2015, 4:04 p.m.

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Kueny, C.S. & Morrison, P.J. Nonlinear instability and chaos in plasma wave-wave interactions. II. Numerical methods and results, report, May 1, 1995; United States. (digital.library.unt.edu/ark:/67531/metadc708908/: accessed August 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.