Analysis of the Breathing Mode dynamics in Hall thrusters using a hybrid simulation*

The Breathing Mode (BM) is a macroscopic oscillation of the plasma in Hall Thrusters (HTs). In recent years, several studies have tried to explain theoretically and numerically the origin and development of this instability. Yet, some efforts are still required to fully characterize it. In the current work, we use a hybrid code, in which the neutral dynamics is treated with 1D Euler equations, while the dynamics of the charged species (electrons and single-charged positive ions) is reproduced by a 2.5D Particle-in-Cell (PIC) module. The ionization is self-consistently calculated within the Monte-Carlo collision (MCC) module. Thus, the consequent coupling of the neutral species dynamics with the charged species allows for replicating the BM mechanism. The data provided by the hybrid simulation allows us to analyze the microscopic processes that originate the BM and the relation between the variation of the various parameters. In particular, we analyze which is the relationship of the ionization with the charge and neutral densities and electron temperature variation at different stages of the BM cycle. From our results, it emerges that the temperature increment alone is not capable of sustaining the ionization. The particle creation appears to be dependent on the variation of both the gas and the plasma densities, along with the ionization rate coefficient. The hybrid code results allow us also to study the evolution of some quantities at different times of the BM cycle. For example, by analyzing the parameters fluctuations during a BM, we show that the diamagnetic drift is always lower than the ExB one and that the isothermal approximation is not valid in HT conditions. Moreover, we show that the effect of the anomalous transport is particularly strong during the BM growing phase, while it is much less marked when the current is low.