Finite amplitude Alfvén-cyclotron waves are believed to play an important role in coronal heating and nonthermal properties of velocity distribution functions. These effects are thought to be due to parametrically unstable Alfvén-cyclotron waves and electrostatic bursts of ion-acoustic like waves. It is shown here that large amplitude Alfvéncyclotron waves propagating in multi-ion plasmas with ...

The amplitude equation for an unstable electrostatic wave is analyzed using an expansion in the mode amplitude A(t). In the limit of weak instability, i.e. γ → 0+ where γ is the linear growth rate, the nonlinear coefficients are singular and their singularities predict the dependence of A(t) on γ. Generically the scaling |A(t)| = γ5/2r(γt) as γ → 0+ is required to cancel the coefficient singula...