The Debye sheath has a significant effect on the performance of Hall thrusters. The dynamic characteristics of the two-dimensional sheath is investigated using the 2D-3V particle-in-cell method in this paper. The numerical results show that while the sheath exhibits the one-dimensional stability when the electron temperature is relatively low, it behaves as a two-dimensional (both in time and space) oscillating characteristic when the electron temperature is high. Moreover, it is found that the oscillating frequency is the same order as the electron plasma frequency and the spatial wavelength is equal to the length of the electrostatic wave.

A two-dimensional particle in cell model is used to simulate the sheath oscillation in stationary plasma thrusters. The embedded secondary electron emission (SEE) submodel is based on that of Morozov but improved by considering the electron elastic reflection effect. The simulation results show that when the SEE coefficient is smaller than one due to the relative low electron temperature, one-dimensional static sheath can be found; as the electron temperature increase, the SEE coefficient approaches to one and temporal oscillation sheath appears; when the electron temperature increases so high that the SEE coefficient is beyond one, the sheath oscillates not only in time but also in space.

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