Scintillations in astrophysics. II - an analytic solution of the fourth-order moment equation

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Astrophysics, Cosmic Plasma, Plasma Turbulence, Plasma-Electromagnetic Interaction, Scintillation, Wave Equations, Integral Equations, Plasma Density, Plasma Slabs, Screens, Series Expansion, Taylor Series, Turbulence Effects

Scientific paper

An analytic solution to the equation describing the correlated behavior of intensity at two different wavenumbers and two different spatial positions for electromagnetic waves originating from a common source is presented. The solution is for waves passing through a turbulent medium in which the plasma density has a Gaussian spectrum of irregularities. The analytic solution is valid for all spatial separations, all wavenumbers, and all positions in the medium. It satisfies the global energy conservation theorem and the pointwise boundary conditions, and reproduces the Taylor series expansion result in the limit of a 'thin' medium. A Taylor series expansion approximation is also presented, together with a 'thin screen' approximation, and their regimes of validity are outlined. Tatarskii's (1971) 'single-scattering approximation' is considered and commented on.

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