Analysis of the steady-state axial flow in the Hall thruster

Momentum and energy balance considerations are used to analyze the plasma flow in a Hall thruster at the limit of intense full ionization with no losses. Two cases are examined; one in which the ion velocity at the anode is zero, and the second in which an ion backflow exists near the anode. Analytical expressions are found for the current utilization and for the thruster efficiency in each case. In the first case an expression is also found for the electron temperature at the anode, while in the second case expressions are derived for the magnitude of the ion backflow into the anode and for the location of the ionization region along the channel. These dependencies are expressed in terms of the applied magnetic field and voltage, the mass flow rate, the thruster geometry and the ionization energy.