Competing processes of whistler mode and electrostatic mode instabilities induced by an electron beam are studied by a linear growth rate analysis and by an electromagnetic particle simulation. In addition to a background cold plasma we assumed an electron beam drifting along a static magnetic field. We studied excitation of whistler and electrostatic mode waves in the direction of the static magnetic field. We first calculated linear growth rates for the whistler mode and electrostatic mode instabilities, assuming various possible parameters in the equatorial magnetosphere. We found that the growth rate for the electrostatic instability is always larger than that of the whistler mode instability. A short simulation run with a monoenergetic electron beam demonstrates that a monoenergetic beam can hardly give energy to whistler mode waves as a result of competition with faster growing electrostatic waves, because the beam electrons are trapped and diffused by the electrostatic waves, and hence the growth rates for whistler mode waves become very small. A long simulation run starting with a warm electron beam demonstrates that whistler mode waves are excited in spite of the small growth rates and the coexisting quasi-linear electrostatic diffusion process.

The diffusion of the warm electron beam is explained by three different processes with different time scales. An electromagnetic diffusion follows the electrostatic diffusion, causing pitch angle scattering of the beam electrons to lower pitch angles. At the third stage the diffused electrons at high parallel velocities are further diffused down to a lower parallel velocity range because of the enhanced electrostatic fluctuations. The present simulation demonstrates that many grid points as well as an enormous number of time steps are required to simulate two coexisting instabilities with different time scales. Fewer numbers and fewer time steps lead to misunderstanding of the physics involved. ¿ American Geophysical Union 1987