Nonlinear dynamics of a driven mode near marginal stability | Zendy

H. L. Berk | Zendy; B. N. Breǐzman | Zendy; M. Pekker | Zendy

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Nonlinear dynamics of a driven mode near marginal stability

Author(s) -

H. L. Berk,

B. N. Breǐzman,

M. Pekker

Publication year - 1995

Publication title -

osti oai (u.s. department of energy office of scientific and technical information)

Language(s) - English

Resource type - Reports

DOI - 10.2172/120914

Subject(s) - instability , scaling , nonlinear system , physics , saturation (graph theory) , marginal stability , mathematics , mode (computer interface) , dynamics (music) , statistical physics , mathematical analysis , classical mechanics , mechanics , quantum mechanics , geometry , computer science , combinatorics , acoustics , operating system

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

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