Proton phase space vortices generated by powerful beam driven electrostatic waves

We examine the saturation of electrostatic waves driven by proton beams moving at relativistic speeds through a plasma. We visualize the plasma phase space distribution after the saturation of the wave that has developed between the background electrons and the proton beams. A secondary instability grows between the background protons and a proton beam due to relativistic effects. We show how the saturated wave forms a proton phase space vortex that may generate cosmic ray electrons by its collapse.