Given the condition that the flow generated by a self-induced magnetic field is two-dimensional and steady, a model for the arc region of the plasma thruster is formulated based on magnetohydrodynamic (MHD) descriptions. Use is made of a generalized Ohm's law that includes the Hall and ion slip terms. Characteristics of the arc region are investigated as functions of system parameters. The study shows that the Hall effect causes the current to concentrate severely at the trailing edge of the anode, and it is suggested that if the plasma thruster is a coaxial type, it is better to have the cathode inside.
NomenclatureB = z component of magnetic field B B 0 = initial value of B at the leading edge of the anode d = separation between electrodes E X9 E y -x 9 y component of electric field E I = discharge current per unit span J x , J y = x 9 y component of current density / / = length of electrodes m = mass flow rate per unit span p -pressure Rm = magnetic Reynolds number S = Poynting vector u 9 v = x, y component of velocity u Vm = voltage parameter x, y = coordinate Y = specific heat ratio 8= geometric parameter X = Hall parameter IL = permeability p = mass density a = electrical conductivity T ei = electron-ion colHsion time $ = potential of E #o = potential difference between electrodes <* e " §Y ro frequency of electron