Homoclinic chaos in a forced hydromagnetic cavity

We study the propagation of nonlinear MHD waves in a highly magnetized dissipative plasma cavity forced at its boundaries. This interacting wave system is analyzed by Galerkin and multiple-scale analyses leading to a simple dynamical system which shares the properties of both the van der Pol and the Duffing oscillator. The system is separated into a Hamiltonian part - possessing a double homoclinic loop to a saddle - and a perturbation. By means of the Melnikov function technique, we show that the saddle's stable and unstable manifolds intersect for suitable values of the forcing amplitude, provided the forcing frequency exceeds a critical value. Saddle-node and period-doubling sequences of bifurcations of periodic orbits (notably a period-three orbit) set in near the homoclinic intersection; these accumulate from below to the same critical value of the control parameter, at which a chaotic limit set appears with fractal dimension ≃ 2.25. Beyond this critical value chaos unfolds into periodic orbits, via saddlenode-bifurcations. Near one of these, the Alfvén wave's amplitude has an intermittent behaviour over long time-scales with a power chute of about 90% at the intermissions.