Theory of type II radio emission from the foreshock of an interplanetary shock

Abstract

We present an analytical model for type II solar radio bursts and then apply it to an observed type II event. Electron beams are produced in the foreshock of an interplanetary shock via shock drift acceleration. Reflection is treated in the de Hoffman‐Teller frame with efficiencies modeled by a losscone that incorporates the effects of the static cross‐shock potential ϕ. Stochastic growth theory is used to treat electron beam driven Langmuir wave growth in the type II foreshock. Nonlinear wave‐wave interactions are used as the mechanisms for converting Langmuir wave energy into freely propagating radio emission. The electron beams produced in the foreshock have a wide range of speeds and number densities. These electron beams are qualitatively consistent with observations in a type II foreshock as well as earlier theoretical predictions, and observations in Earth's foreshock. Significant levels of Langmuir waves and ƒ p and 2ƒ p emission are predicted. In particular, the predicted volume emissivities are similar to those predicted for type III bursts. The simple model developed for the source environment of the type II event on August 26, 1998, produces fluxes in reasonable agreement with observation.