On the theory of pulse propagation and two-frequency field statistics in irregular interstellar plasmas

We have computed two-frequency second moments and pulse profiles for plane and spherical waves both propagating in an extended plasma and incident on a thin plasma phase screen located between the source and the observer. The various models we consider for the power spectrum of the interstellar elec tron density fluctuations versus wavenumber are the simple power-law model, the power-law model with an inner scale, the "beta = 4" model, and the squ are-law structure function model. The power-law model with spectral exponen t beta = 11/3 corresponds to the Kolmogorov turbulence spectrum. The beta = 4 model describes the random distribution in location and orientation of d iscrete objects with relatively sharp boundaries, such as shocks, across th e line of sight. An outer scale is included in the beta = 4 model to accoun t for the average size of such objects. The results for the various spectra l models generally lie between the extremes represented by the simple Kolmo gorov and square-law structure function models. In the strong scattering li mit, the diffractive decorrelation bandwidth is related to the scattering b roadening time via a Fourier uncertainty relation. We have computed numeric al values for the uncertainty constant for the various geometries and spect ral models and find values ranging over a factor of 2. For the Kolmogorov s pectrum, the value is less than that in the widely-used Taylor, Manchester, & Lyne (1993) catalog by factors of 1.98 and 2.34 for a point source in an extended medium and in screen geometries, respectively. Thus observers mus t use the appropriate constant when comparing observations with a specific spectral and geometrical model. We also note that high signal-to-noise rati o observations of the scattering tails of pulsar pulses may be used to cons train the various spectral models of the Galactic electron density fluctuat ions, independent of the distribution of the scattering material along the line of sight.