Modulational instability of a Langmuir wave in plasmas with energetic   tails of superthermal electrons
  The impact of superthermal electrons on dispersion properties of isotropic plasmas and on the modulational instability of a monochromatic Langmuir wave is studied for the case when the power-law tail of the electron distribution function extends to relativistic velocities and contains most of the plasma kinetic energy. Such an energetic tail of electrons is shown to increase the thermal correction to the Langmuir wave frequency, which is equivalent to the increase of the effective electron temperature in the fluid approach, and has almost no impact on the dispersion of ion-acoustic waves, in which the role of temperature is played by the thermal spread of low-energy core electrons. It is also found that the spectrum of modulational instability in the non-maxwellian plasma narrows significantly, as compared to the equilibrium case, without change of the maximum growth rate and the corresponding wavenumber. 
I. V. Timofeev
physics.plasm-ph physics.geo-ph