The Effect of Pressure on the Plume Divergence in the Hall Thruster

The plume divergence in the Hall thruster due to the plasma pressure is analyzed by deriving and solving envelope equations. The evolution of the electron temperature and the radial expansion of the plasma beam are calculated self-consistently. The rate of decrease of the electron temperature due to the plasma radial expansion is affected by heat conduction along the plasma propagation. For the annular plasma jet exiting the Hall thruster, approximated as a slab, it is found that if the coefficient of the heat conductivity is large, the cooling of the electrons of the expanding plasma beam is small, and consequently, the plume divergence is larger. For the plasma beam approximated as cylindrical beyond the point at which it crosses the thruster axis, we show that a large amount of heat conduction does not slow the electron cooling. The plume divergence due to the plasma pressure is therefore smaller. The electron temperature is also affected by the intensity of the magnetic field beyond the cathode. A radial magnetic field at the thruster exhaust inhibits a large cross-field heat flux. On one hand, the smaller heat conductivity of the magnetized plasma results in a cooling of the electrons as they cross the magnetic field. On the other hand, however, the reduced mobility of the magnetized electrons results in an ambipolar electric field that tends to heat the electrons. We show that there is an optimal intensity of the magnetic field, at which the temperature of the electrons that cross the magnetic field is minimal and at which, therefore, the plume divergence is minimal.