High energy particles from stochastic acceleration

Summary form only given, as follows. The ion-acoustic waves were observed by the OGO-5 satellite and Vela-3 satellite, etc. in the precursor region of Earth´s bow shock and magnetosphere. In space plasmas, the ion-acoustic waves turbulence can be excited by strong current, large magnetic field gradient or Langmuir wave turbulence. The stochastic acceleration is effective when charged particles are in a plasma turbulence region for a sufficiently long time. The turbulent stochastic acceleration may transform and distribute the energy from turbulent sources to a few fast particles. When the velocity of fast particles increase, they can absorb a larger number of plasmons and thus the particle energy will rapidly be increased and create high energy particles from keV to MeV.