The onset of Alfvénic turbulence

An investigation is conducted on how low-frequency, ω<Ωi, magnetohydrodynamic oscillations in a warm plasma may undergo a transition from a coherent state to one of turbulence. A driven/dissipative derivative nonlinear Schrödinger (DNLS) equation is derived from the fluid equations. The time evolution of an arbitrary spectrum of waves is analyzed in the case where one k-mode is unstable, with the rest damped. It is found that the transition from order to chaos in the driven/dissipative system is correlated with the existence or absence of ‘‘breathing’’ solitons in the associated conservative system.