A theory of strong and weak scintillations with applications to astrophysics
<p>The propagation of waves in an extended, irregular medium is studied under the "quasi-optics" and the "Markov random process" approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is deri...
| Summary: | <p>The propagation of waves in an extended, irregular medium
is studied under the "quasi-optics" and the "Markov random process"
approximations. Under these assumptions, a Fokker-Planck equation
satisfied by the characteristic functional of the random wave field is
derived. A complete set of the moment equations with different transverse
coordinates and different wavenumbers is then obtained from the
characteristic functional. The derivation does not require Gaussian
statistics of the random medium and the result can be applied to the
time-dependent problem. We then solve the moment equations for the
phase correlation function, angular broadening, temporal pulse smearing,
intensity correlation function, and the probability distribution of the
random waves. The necessary and sufficient conditions for strong
scintillation are also given.</p>
<p>We also consider the problem of diffraction of waves by a
random, phase-changing screen. The intensity correlation function is
solved in the whole Fresnel diffraction region and the temporal pulse
broadening function is derived rigorously from the wave equation.</p>
<p>The method of smooth perturbations is applied to interplanetary
scintillations. We formulate and calculate the effects of the solar-wind
velocity fluctuations on the observed intensity power spectrum and
on the ratio of the observed "pattern" velocity and the true velocity
of 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 the
region about 20 solar radii from the Sun.</p>
<p>We then interpret the observed interstellar scintillation
data using the theories derived under the Markov approximation, which
are also valid for the strong scintillation. We find that the
Kolmogorov power-law spectrum with an outer scale of 10 to 100 pc
fits the scintillation data and that the ambient averaged electron
density in the interstellar medium is about 0.025 cm<sup>-3</sup>. It is also
found that there exists a region of strong electron density fluctuation
with thickness ~10 pc and mean electron density ~7 cm<sup>-3</sup> between the
PSR 0833-45 pulsar and the earth.</p> |
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