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The purpose of this note is to point out that the presence of more than one ion in a plasma opens up several possibilities for wave-wave coupling that are not available in a single-ion plasma. This can be demonstrated by using the ‘parallelogram construction’ on an ω-k diagram as discussed for whistler waves by Harker and Crawford [1969]. The basic requirement to satisfy energy and momentum conservation in wave-wave coupling is that the frequencies ω and wave vectors k of three waves satisfy ((1))
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Neil Brice (1974) studied this question.
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