Type II radio bursts: 1. New entirely analytic formalism for the electron beams, Langmuir waves, and radio emission

Abstract

Type II radio bursts drift in frequency as shock waves and coronal mass ejections (CMEs) move through the Sun's corona and the solar wind. This paper extends the theoretical models for type II radio bursts of Knock et al. (2001, 2003), Knock and Cairns (2005), Cairns and Knock (2006) and Schmidt and Gopalswamy (2008). The theory treats the acceleration of electrons at the shock, formation of electron beams, growth of Langmuir waves, and conversion of Langmuir energy into radiation. An entirely analytical and more general formalism is developed, which includes kappa electron velocity distribution functions for the plasma electrons and the shock‐reflected electron beam. The radiation model also includes the plateauing of the electron beam, which releases energy for the Langmuir waves. This paper has two parts. First, the new entirely analytical formalism is presented. Second, first numerical results for synthetic radio images and synthetic dynamic spectra are discussed, gained by applying our radiation model to MHD simulations of a shock driven by a CME. The results are compared with earlier analytic approaches. This work is also applicable to other shock‐related emissions in space and astrophysical plasmas.