Waves generated by reflected and accelerated electrons at a nearly perpendicular shock

Abstract

Aims. We study a generation of waves by reflected and accelerated electrons at a nearly perpendicular shock. Methods. A shifted loss-cone distribution of reflected and accelerated electrons at a nearly perpendicular shock is derived analytically. Then in a simplified form called here cone beam, this distribution is incorporated into a 2D relativistic electromagnetic particle-incell model and the wave generation is studied. Results. Numerical modelling shows not only a generation of Langmuir and high-frequency electromagnetic waves, as expected, but also an efficient generation of whistler waves by the normal Doppler resonance process. While the intensity of Langmuir waves increases with the increase in the cone beam energy in a parallel direction to the magnetic field, the whistlers are most effectively generated for high values of the perpendicular beam energy. There are indications that the whistlers participate in conversion processes generating the high-frequency electromagnetic waves. Conclusions. Using a numerical model we found an efficient generation of Langmuir, whistler, and electromagnetic waves by electrons reflected and accelerated at a nearly perpendicular shock. Results are discussed in connection with the herringbone structure of type II radio bursts. The possible role of transmitted electrons is mentioned.