Nonlinear saturation of the parametric instability for three coupled oscillators

Technical Report · Sun Jan 01 04:00:00 EST 1984

OSTI ID:5250773

Simon, A; McKinstrie, C J; Williams, E A

The case of three parametrically coupled and damped oscillators is considered. One (with natural frequency ..omega../sub 0/) is externally driven at a frequency ..cap omega.. close to the sum (..omega../sub 1/ + ..omega../sub 2/) of the other two. In the vicinity of the parametric instability threshold, we determine the time-asymptotic oscillator amplitudes and nonlinear frequency shifts by using secular-free perturbation analysis. The resulting amplitudes are sensitive to the mismatch delta (= ..cap omega.. - ..omega../sub 1/ - ..omega../sub 2/), if ..cap omega.. and ..omega../sub 0/ are dissimilar, and rise sharply as delta ..-->.. 0. If ..cap omega.. is close to ..omega../sub 0/, the behavior is quite insensitive to delta, and models results obtained for parametric instabilities in plasma. The single parametrically-driven oscillator threshold result is also obtained and compared to a general small amplitude result of Landau. This Landau result is then generalized to two coupled oscillators and compared to a result obtained by perturbation analysis. These two cases all behave as the three-oscillator does when ..omega../sub 0/ and ..cap omega.. are dissimilar. All solutions are shown to be stable.

• Research Organization: Rochester Univ., NY (USA). Lab. for Laser Energetics
• DOE Contract Number: AC08-80DP40124
• OSTI ID: 5250773
• Report Number(s): DOE/DP/40124-T2; ON: DE85017582
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700107* -- Fusion Energy-- Plasma Research-- Instabilities
DAMPING
ELECTRONIC EQUIPMENT
EQUIPMENT
INSTABILITY
LANDAU DAMPING
NONLINEAR PROBLEMS
OSCILLATORS
PARAMETRIC INSTABILITIES
PLASMA
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
RAMAN EFFECT