Sébastien Neukirch
Institut Jean le Rond d'Alembert
Centre National de la Recherche Scientifique
Université Pierre et Marie Curie
Paris, France

tel: +33 1 44 27 72 61
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e-mail: sebastien.neukirch (-atat-) upmc.fr

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Integrals of motion and semi-permeable surfaces to bound the amplitude of a plasma instability

Sébastien Neukirch

Physical Review E 63 #3(2001) 036202

Abstract : We study a dissipative dynamical system that models a parametric instability in a plasma. This instability is due to the interaction of a whistler with the ion acoustic wave and a plasma oscillation near the lower hybrid resonance. The amplitude of these three oscillations obey a 3D system of ordinary differential equations which exhibits chaos for certain parameter values. By using certain 'integrability informations' we have on the system, we get geometrical bounds for its chaotic attractor, leading to an upper bound for its Lyapunov dimension. On the other hand we also obtain ranges of values of the system's parameters for which there is no chaotic motion.

PACS numbers : 05.45.ac / 02.30.Hq / 52.35.P

Key words : plasma instability, integral of motion, transversal surface, homoclinic bifurcation, Lyapunov exponent, ion acoustic wave, whistler.

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