Hénon-Heiles Hamiltonian for coupled upper-hybrid and magnetoacoustic waves in magnetized plasmas

Abstract

We show that the coupled mode equations for the stationary propagation of upper-hybrid and magnetoacoustic waves in magnetized electron-ion plasmas with negative group dispersion can be exactly derived from the generalized Hénon-Heiles Hamiltonian. The parameter regimes for the integrable cases of the coupled mode equations have been explicitly obtained. For positive group dispersion of the upper-hybrid waves, the relevant governing equations lead to a novel Hamiltonian where the kinetic energy is not positive definite.