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A steady-state theory of a low-pressure discharge column in a magnetic field is derived in terms of the moments of the Boltzmann equation. For the electrons, the first-two moment equations are used with a scalar pressure. For the ions the first-three moment equations are used with an adiabatic assumption. Numerical solutions are given for the profiles of velocity, potential, density and ion stress tensor for both planar and cylindrical geometry for ranges of the parameters of practical interest. A discussion is given of the application of the theory to experimental situations.
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S. A. Self (1967) studied this question.
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