Asymptotic equilibrium between Langmuir turbulence and suprathermal electrons

Abstract

In both laboratory and natural environment such as the solar wind, suprathermal, or non-Maxwellian electron distributions are frequently observed. Electron velocity distribution functions containing non-Maxwellian, power-law energetic tail component are often modeled by the so-called kappa distribution, but their physical origin is not clearly understood. In a series of publications, the present author and his colleagues discussed the self-consistent formation of kappa-like distributions as a result of electron-Langmuir turbulence interaction process. However, these discussions were either based upon numerical initial value solution of the weak turbulence equation or by direct particle-in-cell simulation method. It was not evident that the formation of kappa-like state, which was demonstrated during the long-time evolution of the system, did indeed correspond to the genuine asymptotically steady-state solution or not in a mathematical sense. The present paper presents the self-consistent asymptotic solution of the electrons-Langmuir turbulence system and shows that the non-Maxwellian kappa-like state does indeed correspond to a rigorous solution.