Full PIC simulations of beam-generated parametric instabilities and radio emissions in the solar wind

Solar radio emissions are electromagnetic waves emitted in the solar wind plasma, observed at the local plasma frequency and at twice the plasma frequency [1]. To describe their origin a multi-stage model has been proposed which considers a succession of non-linear three-wave interaction processes. Electron beams accelerated by solar flares or shocks travel in the solar wind plasma and provide the free energy for the development of plasma instabilities. The model describes how the electron beam propagation in the background plasma leads to the excitation of Langmuir waves, their decay into ion-acoustic, secondary Langmuir waves, and finally generating electromagnetic waves. A good understanding of the process would allow to infer the kinetic energy transformed from the beam to em waves, so that the radio waves recorded by spacecraft can be used as diagnostic for the electron beam propagating in the solar wind. Few issues related to the influence of density fluctuations on the generation of primary Langmuir waves are presented [2]. Even if the electrostatic problem has been extensively studied, only recently full electromagnetic simulations were attempted[3]. Here we present the detailed analysis of large scale 2D electromagnetic Particle In Cell simulations of the entire process, and we highlight the generation of various types of waves by the different parametric instabilities. We estimate the ratio of beam energy transformed into electromagnetic waves depending on the initial conditions and we also show that their emission is expected in the entire solid angle. The role of the size and the resolution of the simulation box is also investigated.