Advection-nonlinear-diffusion model of flare accelerated electron transport in Type III solar radio bursts

Electrons accelerated by solar flares and observed as type III solar radio bursts are not only a crucial diagnostic tool for understanding electron transport in the inner heliosphere but also a possible early indication of potentially hazardous space weather events. The electron beams travelling in the solar corona and heliosphere along magnetic field lines generate Langmuir waves and quasilinearly relax towards a plateau in velocity space. The relaxation of the electron beam over the short distance in contrast to large beam-travel distances observed is often referred to as Sturrok's dilemma. Here, we develop a new electron transport model with quasilinear distance/time self-consistently changing in space and time. The model results in a nonlinear advection-diffusion equation for the electron beam density with nonlinear diffusion term that inversely proportional to the beam density. The solution predicts slow super-diffusive (ballistic) spatial expansion of a fast propagating electron beam. The model also provides the evolution of the spectral energy density of Langmuir waves, which determines brightness temperature of plasma radiation in solar bursts. The model solution is consistent with the results of numerical simulation using kinetic equations and can explain some characteristics of type III solar radio bursts.