# A Fokker-Planck Framework for Studying the Diffusion of Radio Burst Waves in the Solar Corona

## TL;DR

This paper develops a Fokker-Planck model to analyze how radio burst waves diffuse and scatter in the solar corona, explaining observed source sizes and intensity profiles.

## Contribution

It introduces a comprehensive Fokker-Planck framework for different scattering regimes of radio waves in the solar corona, including static, isotropic, and time-dependent fluctuations.

## Key findings

- Radio waves are accelerated near the source and diffuse outward.
- Source sizes are larger than the intrinsic source due to angular diffusion.
- Observed intensity profiles show sharp rise and exponential decay, matching observations.

## Abstract

Electromagnetic wave scattering off density inhomogeneities in the solar corona is an important process which determines both the apparent source size and the time profile of radio bursts observed at 1 AU. Here we model the scattering process using a Fokker-Planck equation and apply this formalism to several regimes of interest. In the first regime the density fluctuations are considered quasi-static and diffusion in wavevector space is dominated by angular diffusion on the surface of a constant energy sphere. In the small-angle ("pencil beam") approximation, this diffusion further occurs over a small solid angle in wavevector space. The second regime corresponds to a much later time, by which scattering has rendered the photon distribution near-isotropic resulting in a spatial diffusion of the radiation. The third regime involves time-dependent fluctuations and, therefore, Fermi acceleration of photons. Combined, these results provide a comprehensive theoretical framework within which to understand several important features of propagation of radio burst waves in the solar corona: emitted photons are accelerated in a relatively small inner region and then diffuse outwards to larger distances. En route, angular diffusion results both in source sizes which are substantially larger than the intrinsic source, and in observed intensity-versus-time profiles that are asymmetric, with a sharp rise and an exponential decay. Both of these features are consistent with observations of solar radio bursts.