Abstract　 　　  

 I will report a new non-resonant instability of Alfvén waves (AWs) driven by compensated currents. Such currents set up in response to energetic ion beams occurring in many space and astrophysical plasmas, like foreshock regions in the solar wind and around supernova remnants. Depending on the beam/plasma temperature ratio, the instability proceeds in the magnetohydrodynamic regime (MHD AW instability) or in the kinetic regime (instability of kinetic Alfvén waves - KAWs). At relatively high plasma temperatures, kinetic effects of the background ion gyroradius are important making the KAW instability stronger than its MHD counterpart. The KAW growth time can be very short, approaching the proton gyroperiod in the terrestrial foreshock ahead of the quasi-perpendicular bow shock region. The oblique Alfvén instability driven by the cosmic rays in the interstellar and intergalactic plasmas develops mostly in the MHD regime and can hardly extend in the KAW regime. The cross-field wavelengths of generated Alfvén modes can be short enough to trigger stochastic acceleration of cosmic rays.