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We show, using a two-fluid approximation, that sound waves in a gas containing cosmic rays can be amplified if the scale height of the cosmic rays is less than a critical scale of order ϰ / a. ϰ and a are the cosmic-ray diffusion coefficient and gas sound speed, respectively. The non-linear development has been calculated numerically and we find that sound waves can grow into strong gas shocks. The instability is likely to have important effects on cosmic-ray modified shocks.
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Drury et al. (1986) studied this question.
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