Electron kappa distribution and steady-state Langmuir turbulence

Abstract

In a recent pair of papers, the present author discussed a self-consistent theory of asymptotically steady-state electron distribution function and Langmuir turbulence intensity in one [P. H. Yoon, Phys. Plasmas 18, 122303 (2011)] and three [P. H. Yoon, Phys. Plasmas 19, 012304 (2012)] dimensions. The resulting electron distribution function is a type of kappa distribution that features a non-Maxwellian energetic tail component. However, while the one-dimensional solution is rigorously correct, the three-dimensional solution, which was obtained using the cylindrical coordinate representation, contains two features that may be inconsistent for field-free plasmas. One is the assumption that the resonance condition can be approximated by ω-k·v≈ω-k∥v∥. Needless to say, this is not the most general condition. The second inconsistency is that while the electron distribution is isotropic in velocity, the Langmuir turbulence intensity depends on the wave propagation direction. While these features may not be too unrealistic in the presence of an implicit ambient magnetic field, they certainly cannot be correct if the plasma is genuinely unmagnetized. In the present paper, we rectify such shortcomings by properly reformulating the problem using a spherical coordinate system in a truly free-field plasma.