Nonlinear dynamics of a driven mode near marginal stability

Technical Report · Fri Sep 01 00:00:00 EDT 1995

DOI:https://doi.org/10.2172/120914· OSTI ID:120914

Berk, H L; Breizman, B N; Pekker, M

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.

• Research Organization: Univ. of Texas, Austin, TX (United States). Institute for Fusion Studies
• Sponsoring Organization: USDOE, Washington, DC (United States)
• DOE Contract Number: FG05-80ET53088
• OSTI ID: 120914
• Report Number(s): DOE/ET/53088-719; ON: DE96001772; TRN: 95:024562
• Resource Relation: Other Information: PBD: Sep 1995
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION
PLASMA WAVES
NONLINEAR PROBLEMS
BUMP-IN-TAIL INSTABILITY
KINETIC EQUATIONS
DISTRIBUTION FUNCTIONS
FREE ENERGY
INTEGRAL EQUATIONS
ELECTRIC FIELDS