Angle-averaged efficiencies for linear mode conversion between Langmuir waves and radiation in an unmagnetized plasma

Abstract

Linear mode conversion of Langmuir waves propagating in density irregularities leads to radio waves near the electron plasma frequency. Most previous work on this mechanism is for a single Langmuir wave interacting with a single planar density structure. This paper presents analytic and numerical estimates of the average conversion efficiency resulting from averaging over the distributions of the incoming Langmuir wave vectors and the orientations and length scales of density irregularities in an unmagnetized plasma. Significant mode conversion requires Langmuir wave vectors very closely aligned with the density gradient, within an angular width of order Ve∕c radians (Ve is the electron thermal speed and c the speed of light), and this width plays a major role in determining the average conversion efficiencies. Specifically, the two-dimensional (2D) averaged efficiency for planar irregularities with a uniform distribution of orientations is a factor of order Ve∕(2πc) smaller than the peak values ∼50% in the mode conversion window. Moreover, the analogous 3D average efficiency is estimated to be a factor Ve2∕(2π2c2) smaller than the peak values. For coronal and interplanetary values of Ve, the 2D and 3D average efficiencies are then 10−2–10−3 and 10−5–10−6, respectively. Appropriate averaging is thus vital when predicting the efficiency of linear mode conversion and inferring what mechanisms produce radio phenomena in space and the laboratory.