Spontaneous emission of radiation from localized Langmuir perturbation

The radiation at the first and second harmonics of the electron plasma frequency (ω_e) from localized Langmuir oscillations is computed for a field-free plasma. The localized perturbations are assumed to have cylindrical symmetry about the direction of propagation of the localized perturbation. It is shown that when the wavelengths of the excited modes are much greater than the scale lengths of the Langmuir perturbation, a quadrupole radiation pattern is recovered for emission at 2ω_e. An application to type III solar radio bursts is discussed briefly.