Fokker-Planck modelling of coronal scattering of radiation from solar radio sources
Abstract
It has long been known that owing to turbulent scattering by density irregularities a radio point source in the solar corona is observed to have a finite angular extent. Recent high-time-resolution imaging spectroscopy of type III bursts with LOFAR show that the role wave transport effects in determining the observed spatiotemporal characteristics of solar radio bursts is as important as, or even more important than, the properties of the intrinsic source. In this work, we model turbulent scattering of a radio wave. Quasilinear theory is applied to obtain the diffusion tensor in wavevector space in the presence of a Kolmogorov spectrum of density fluctuations. The diffusion tensor is shown to take a Lorentz form familiar from plasma kinetic theory. Accordingly, the photon distribution function, in both space and momentum space, evolves in time according to a Fokker-Planck equation. This Fokker-Planck equation is solved analytically in the forward scattering regime from the source to the observer, assuming negligible back-scattering of rays along their paths, and the results used to determine forms for the angular broadening and arrival time profiles of the scattered radiation. The arrival time profile form, which has in the past been computed via pure probabilistic arguments, is instead derived in an analytic form amenable to universal scaling. The method is finally compared with the standard Gaussian or "two-moments" closure of the Fokker-Planck equation and to numerical Monte-Carlo simulations of this equation in the forward scattering regime.
- Publication:
-
2018 Triennial Earth-Sun Summit (TESS)
- Pub Date:
- May 2018
- Bibcode:
- 2018tess.conf11406B