The propagation of waves in an extended, irregular mediumis studied under the "quasi-optics" and the "Markov random process"approximations. Under these assumptions, a Fokker-Planck equationsatisfied by the characteristic functional of the random wave field isderived. A complete set of the moment equations with different transversecoordinates and different wavenumbers is then obtained from thecharacteristic functional. The derivation does not require Gaussianstatistics of the random medium and the result can be applied to thetime-dependent problem. We then solve the moment equations for thephase correlation function, angular broadening, temporal pulse smearing,intensity correlation function, and the probability distribution of therandom waves. The necessary and sufficient conditions for strongscintillation are also given.
We also consider the problem of diffraction of waves by arandom, phase-changing screen. The intensity correlation function issolved in the whole Fresnel diffraction region and the temporal pulsebroadening function is derived rigorously from the wave equation.
The method of smooth perturbations is applied to interplanetaryscintillations. We formulate and calculate the effects of the solar-windvelocity fluctuations on the observed intensity power spectrum andon the ratio of the observed "pattern" velocity and the true velocityof the solar wind in the three-dimensional spherical model. The r.m.s.solar-wind velocity fluctuations are found to be ~200 km/sec in theregion about 20 solar radii from the Sun.
We then interpret the observed interstellar scintillationdata using the theories derived under the Markov approximation, whichare also valid for the strong scintillation. We find that theKolmogorov power-law spectrum with an outer scale of 10 to 100 pcfits the scintillation data and that the ambient averaged electrondensity in the interstellar medium is about 0.025 cm-3. It is alsofound that there exists a region of strong electron density fluctuationwith thickness ~10 pc and mean electron density ~7 cm-3 between thePSR 0833-45 pulsar and the earth.
