One‐ and two‐dimensional simulations of electron beam instability: Generation of electrostatic and electromagnetic 2fp waves

Abstract

We have performed computer simulations of the self‐consistent nonlinear evolution of electrostatic and electromagnetic 2fp waves excited by electron beams with electromagnetic particle code. In both one‐ and two‐dimensional periodic systems an electrostatic 2fp wave is generated at twice the wave number of forward propagating Langmuir waves by wave‐wave coupling. This wave grows with the forward propagating Langmuir wave in the nonlinear stage of the simulations. The electrostatic 2fp wave in the simulations is saturated at about −20 ∼ −30 dB of that of the Langmuir waves. It is larger than the value expected from observations in the terrestrial electron foreshock. The electromagnetic 2fp wave is only excited in two‐dimensional systems. The magnitude of the electromagnetic 2fp wave is correlated with the backward propagating Langmuir wave, not with the electrostatic 2fp wave. This result suggests that the electromagnetic 2fp wave is excited by the wave‐wave coupling of forward and backward propagating Langmuir waves. The typical power density estimated from a reasonable amplitude of Langmuir wave is of the same order or much weaker than the value typically observed around the electron foreshock.