Abstract
We study the nonlinear interactions of an inhomogeneous cold beam of electrons of arbitrary density with an inhomogeneous cold plasma in the presence of an external static magnetic field. The formation of waves of double frequency at the inlet of the beam into the plasma is considered. Far enough from the plasma boundary inwards, the external static magnetic field may increase the amplitude of the fundamental waves, and the electric field component of waves with double frequency will remain stronger than that of the basic frequency. In addition, it is found that the inhomogeneity of electron beams has more effect on the generation of the second harmonic wave.
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