Observational dispersion relations

Pulse propagation in plasmas has been widely studied in relation to instabilities and their classification as convective or absolute. Such analyses emphasize the importance of considering the summation of a spectrum of modes, rather than simply making deductions from Brillouin dispersion relations plotted either for real frequency and complex wavenumber, or for complex frequency and real wavenumber. In particular, erroneous conclusions may be drawn about the magnitude and direction of propagation of a transient pulse. In this paper, the point of view is taken that an observer remote from the source would measure an 'observational dispersion relation'. The nature of this dispersion relation is examined for absorbing or convectively unstable plasmas by asymptotic analysis, and for different source waveforms. Illustrative results are presented for propagation in cold plasmas and for beam-plasma interaction.