The coalescence of two Langmuir waves, L and L′, produces emission at twice the plasma frequency in type II and type III solar radio bursts. The analysis of the coalescence process is usually simplified by assuming the head-on approximation, where the wavevectors of the coalescing waves satisfy kL′ ≈ −kL, corresponding to the two Langmuir waves meeting head on. However, this is not always a valid approximation, particularly when the peak of the Langmuir spectrum lies at small wavenumbers, for narrow band spectra, and for spectra with broad angular ranges. Realistic Langmuir wave spectra are used to investigate the effects of relaxing the head-on approximation.
