Two-band whistler-mode waves excited by an electron bi-Maxwellian distribution plus parallel beams

The characteristics of whistler-mode waves excited by temperature anisotropic electrons, whose velocity distribution is a combination of bi-Maxwellian distribution and beam-like shapes, are investigated by both linear theory analysis and particle-in-cell simulation. A frequency gap is formed between two peaks, which is caused by the mode splitting of beam-like electrons. We have further investigated the influences of different parameters and found that the position of beam-like shape is the key parameter in determining the frequency of power gap. Moreover, the beam-like component on one direction will lead to the gap in the spectra of waves propagating in the opposite direction. Our study can shed light on the effects of beam-like electrons on the spectra of whistler-mode waves.