A 1-D time-dependent model of a hall thruster with side walls

Previous one-dimensional Hall thruster models predict some observed features correctly, but do not adequately treat the losses of energy and ionization to the side walls of the channel. Because those losses have important effects on the discharge dynamics and the thruster's efficiency and lifetime, their omission severely limits the utility of a model. The model reported here is obtained from a two- dimensional description by solving analytically for the radial variations of densities and velocities and then averaging over the radial coordinate in a way that retains the effects of the side walls. Our model also includes ion pressure, second ionization, a varying electron temperature, a diverging channel and a non-radial B field. It calculates the ion flux into the walls as well as the incident ion angles and energies as functions of axial position to predict the profile of erosion of the walls by sputtering. The collision and ionization rates are all treated as functions of the electron temperature. The derivation of the equations is explained and typical results of numerical solutions are presented.