An ion beam resonates with R-mode waves at two frequency bands. These are a high frequency RH mode (&ohgr;≫&OHgr;2) and a low frequency RL mode (&ohgr;~&OHgr;H2O+), where &OHgr;2 and &OHgr;H2O+ are cyclotron frequencies of protons and water ions, respectively. We study the nonlinear evolution of beam-generated RH waves by one-dimensional hybrid computer experiments. Both wave-particle and subsequent wave-wave interactions are examined. We find that the RH waves through the interaction with an ion beam formed by pick-up heavy ions near comets, grow to a level of Bw/Boh 0.23. The waves saturate by wave-wave interactions (via the decay instability) supplying energy to backward travelling daughter R-mode waves with slightly lower k (and hence low &ohgr;) as well as forward travelling longitudinal waves. The backward travelling daughter R-mode waves decay further to granddaughter waves with still lower k. We show that this inverse cascading process occurs faster than the growth of the RL mode instability and produces a wide band wave spectrum which extends from the wavenumber of beam-excited RH mode to much lower k. The nonlinearly excited longitudinal sound waves play a role in heating solar wind protons. ¿ American Geophysical Union 1989