A treatment of the positive column with negative ions as the third species of charge carrier, in addition to electrons and positive ions, is given in the three-fluid approximation in the low-pressure limit. The relation to other work is demonstrated in various limiting cases, particularly treatments of the plasma sheath in the fluid and free-fall approximations. Confinement of the negative ions to the centre of the discharge is found for large values of the ratio of electron temperature to negative ion temperature.
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Franklin et al. (1992) studied this question.
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