One- and two-dimensional simulations of electron beam instability: Generation of electrostatic and electromagnetic 2f(p) waves

We have performed computer simulations of the self-consistent nonlinear evo lution of electrostatic and electromagnetic 2f(p) waves excited by electron beams with electromagnetic particle code. In both one- and two-dimensional periodic systems an electrostatic 2f(p) wave is generated at twice the wav e number of forward propagating Langmuir waves by wave-wave coupling. This wave grows with the forward propagating Langmuir wave in the nonlinear stag e of the simulations. The electrostatic 2f(p) wave in the simulations is sa turated at about -20 similar to -30 dB of that of the Langmuir waves. It is larger than the value expected from observations in the terrestrial electr on foreshock. The electromagnetic 2f(p) wave is only excited in two-dimensi onal systems. The magnitude of the electromagnetic 2f(p) wave is correlated with the backward propagating Langmuir wave, not with the electrostatic 2f (p) wave. This result suggests that the electromagnetic 2f(p) wave is excit ed by the wave-wave coupling of forward and backward propagating Langmuir w aves. The typical power density estimated from a reasonable amplitude of La ngmuir wave is of the same order or much weaker than the value typically ob served around the electron foreshock.