The parametric effect of an applied uniform oscillating electric field on both unmagnetized and magnetized plasmas is investigated. By using a perturbation method of multitime scales, we have shown that parametric excitation of transverse waves propagating obliquely to the applied field in an unmagnetized plasma is possible. The growth rate of the excited waves reaches a maximum for transverse propagation. Ion motion does not change the character of the parametric excitation except by reducing the growth rate. In a magnetized plasma it is shown that excitation of a pair of waves is possible where one is a Langmuir wave, propagating along the magnetic field and the other is a circularly polarized transverse wave propagating in the opposite direction.
An infinite, inhomogeneous electron plasma driven by a spatially uniform oscillating electric field is investigated. The multi-time perturbation method is used to analyze possible parametric excitations of transverse waves and to evaluate their growth rates. It is shown that there exist subharmonic excitations of: (1) a pair of transverse waves in an unmagnetized plasma and (2) a pair of one right and one left circularly polarized wave in a magnetoplasma. Additionally, parametric excitation of two right or two left circularly polarized waves with different frequencies can exist in a magnetoplasma. The subharmonic excitations are impossible whenever the density gradient and the applied electric field are perpendicular. However, parametric excitation is possible with all configurations.
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