Relaxation of relativistic plasmas under the effect of wave-particle interactions

We simulate the acceleration of electrons to relativistic energies due to the interaction of electrons with waves generated by longitudinal (i. e., electrostatic) streaming instabilities in plasmas. Two equal systems undergoing a streaming instability evolve, one according to the classical Newton's law and one according to the special relativity dynamics equation. The system that obeys Newton's law relaxes to a Maxwellian equilibrium distribution. In the case of the relativistic dynamics, the equilibrium distribution exhibits peaks in the phase space at high momenta and a larger number of particles at high energies. This steady electron population at higher energies could explain power-law energy distribution in many plasma physics and astrophysical systems.