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For compressible MHD more types of waves appear, the fast and slow magnetoacoustic waves, including velocity fluctuations parallel to wave vectors, i.e., vk k0.
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The condition for interaction of two Alfv́nic wave packets, corresponding to "opposite sense of correlation" of v and b, is sometimes described as "opposite directions of propagation." This is actually misleading and not fully correct For example, the same condition applies in a two dimensional geometry perpendicular to a uniform mean magnetic field, even though there is, for this case, no propagation along the mean field. Furthermore, the condition for interaction of the packets also applies when there is no mean magnetic field and, therefore, no propagation.
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The condition for interaction of two Alfv́nic wave packets, corresponding to "opposite sense of correlation" of v and b, is sometimes described as "opposite directions of propagation." This is actually misleading and not fully correct. For example, the same condition applies in a two dimensional geometry perpendicular to a uniform mean magnetic field, even though there is, for this case, no propagation along the mean field. Furthermore, the condition for interaction of the packets also applies when there is no mean magnetic field and, therefore, no propagation.
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