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Summary form only given, as follows: Linear instabilities of counterstreaming ion beams are well known. We have studied here the nonlinear evolution of such instabilities using a 2.5-D particle-in-cell code. The instabilities lead to the generation of non-resonant zero-frequency and a resonant ion cyclotron modes. For sufficiently large counterstreaming velocities, the non-resonant mode dominates. The anomalous cyclotron resonance of this mode with the beam ions causes a strong pitch angle scattering, generating hat-shaped velocity distribution functions in the phase space perpendicular to the ambient magnetic field. The scattering can be effective in trapping the ions in a magnetic mirror.