Two‐dimensional saturation of broadband electron acoustic waves in the foreshock region

Abstract

To analyze the saturation of beam‐driven electron acoustic waves that can occur in the electron foreshock region, fully self‐consistent two‐dimensional electrostatic simulations have been carried out. This has been done for the case of a negative energy beam mode that is excited when the beam velocity is lower than the thermal velocity of the background plasma. This mode can be excited well away from the electron foreshock boundary upstream from the Earth. The nonlinear saturation of the instability in the two‐dimensional case is due to spreading of the beam velocity and damping of the initially negative energy mode by the beam particles. Although the saturated wave energy contained in the waves propagating along the beam direction is dominant, a significant amount of wave energy appears in the direction propagating oblique to the beam causing perpendicular heating of beam particles. The electron acoustic wave growth in the simulations is in agreement with linear theory and previous theoretical predictions. An interesting unexpected result was the additional generation of low‐frequency part of the electron acoustic wave spectrum propagating in the direction opposite to that of the main spectrum of the electron acoustic waves. These backward propagating waves were found only in the wave spectrum transverse (oblique) to the beam direction.