Method Of Smooth Perturbations Research Articles

On amplitude-phase fluctuations of a phase light wave in a turbulent medium

It is shown that the results of theoretical calculations of amplitude-phase fluctuations of a light wave in randomly inhomogeneous media, which are based on the assumption of a normal distribution law of the field-amplitude level with a simultaneous description of the phase gradient in accordance with the method of smooth perturbations, contradict experiments in the region of strong fluctuations.

Velocity of the Solar Wind as Determined from Interplanetary Scintillations.

The method of smooth perturbations is used to derive the equations for interplanetary scintillation in a (statistically) spherically symmetric solar wind with constant wind velocity. The expressions, valid in the limit of small scintillation index, are used to discuss the relation between the radial wind velocity and the observed projected velocity of the scintillation pattern. It is found that the pattern velocity is systematically less than the wind velocity by a substantial fraction, depending on the radial variation of the density fluctuations. If the fluctuations fall off as 1/r-squared the correction is 18 percent, whereas if the fluctuations are proportional to 1/r the correction is 57 percent. The effects may be even more severe if the solar wind is not spherically symmetric.

Multiple Scattering and the Method of Rytov*

Rytov’s method (method of smooth perturbations) has been used extensively to solve problems involving wave propagation in weakly inhomogeneous media. Critics of the method have questioned the closure procedure employed in the Rytov theory and have expressed doubt as to the range of validity of the solution. Some of the criticisms have claimed the method fails because it does not treat multiple scattering and that it is limited in applicability to precisely the same region as the Born single-scattering approximation. These criticisms are shown herein to be at fault. A multiple-scattering interpretation of the Rytov solution is given, thus lending support to those proponents of Rytov who claimed an extended range of applicability relative to the Born approximation.

On Rytov's Method

Rytov's method (method of smooth perturbations) has been used extensively to solve problems involving wave propagation in turbulent media. The closure procedure employed in the Rytov theory is, however, questionable. In this paper the Rytov result is compared with the results of the perturbation theory of linear stochastic operators. It is shown that the Rytov method does not yield the field correct to first order in the pertur‐bation parameter, and it is concluded that the method is not generally valid beyond the limits of the Born (single‐scatter) approximation.

Wave scattering in the neighborhood of a turning point treated by the method of smooth perturbations

Wave scattering in the neighborhood of a turning point treated by the method of smooth perturbations