Parametrically excited instabilities near the hybrid resonant frequencies

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Abstract
The parametric excitation of the ordinary mode and the extraordinary mode propagating perpendicular to the magnetostatic field is investigated for the case of a cold uniform plasma. The pump wave is assumed to be another ordinary mode having its electric field oriented parallel to the magnetostatic field and its frequency exceeding the plasma frequency of the electrons. The extraordinary mode has three branches, namely, a high‐frequency branch, an intermediate‐frequency branch having a resonance at the upper hybrid resonant frequency, and a low‐frequency branch which in the regime of hydromagnetic frequencies is the Alfvén wave and which also has a resonance at the lower hybrid resonant frequency. The ordinary mode does not parametrically couple with the high‐frequency branch of the extraordinary mode but such a coupling takes place with the other two branches. This parametric coupling leads to instabilities of the extraordinary mode. Illustrative numerical results are presented for the parametric instabilities of the extraordinary mode near the upper hybrid resonant frequency, the lower hybrid resonant frequency, and the Alfvén wave frequency. Compared to the intermediate‐frequency branch, the requirements for the parametric interaction are found to be met easily for the low‐frequency branch. The dependence of the maximum growth rates of the parametric instabilities on the strength of the magnetostatic field is also examined.