The evolution of uniform, parallel propagating, low-frequency (≲ion cyclotron) wave trains is followed with a one-dimensional hybrid numerical code with fluid electrons and particle ions. We show that moderate amplitude (ΔB/B1 and instability exists for wavenumbers both below and above the wavenumber of an initial, left-handed wave train or pump wave. For corresponding parameters a fluid theory gives only a narrow range of instability above the pump wavenumber where decay and beat instabilities can occur.

In simulations wave energy inverse cascades to smaller wavenumbers and into a greater number of forward than backward going waves. In fluids energy by decay goes mostly to backward ones of smaller wavenumber, and energy by beat goes mostly to forward ones of larger wavenumber. Neither fluid instability explains simulation results. The instability is saturated by thermalizing ions and sometimes exciting small wavenumber electrostatic or acoustic modes. In constrast, saturation in fluids first occurs by generating the harmonics of the growing linear modes. Harmonic generation is mostly absent in simulations. Simulations are carried out to long times and mostly reach a limit beyond which no further significant evolution can occur. Application to Alfv¿nic fluctuations in the solar wind is discussed. ¿American Geophysical Union 1995