Abstract
In experiments with a homopolar device Fahleson has observed that for low values of the discharge current the voltage drop across the plasma is proportional to the magnetic field and independent of the current and pressure. The rotational velocity corresponds to a kinetic energy for the ions equal to the ionization potential of the gas. These experiments have been analyzed using a steady-state continuum model of the flow in which the bulk of the gas rotates at a uniform velocity and the current is confined to thin Hartmann boundary layers on the end-walls. The voltage drop has been calculated as a function of current, pressure, magnetic field, and atomic species. The dependence on these parameters is in good agreement with the measurements under all conditions, while the magnitude of the voltage is generally smaller than the observed value by a factor of 2.
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