Theoretical study of electro-thermo-acoustic instability in a magneto-plasma-dynamic thruster

The electro-thermo-acoustic instability has been hypothesized as a driver behind the near-anode plasma flow instability in the magneto-plasma-dynamic thrusters. In order to explain how this instability can be triggered, an extended Rayleigh's criterion emerging from the source term of a developed acoustic energy equation has been derived. This criterion states that the fluctuations of pressure (or velocity) and electric field in the sheath region must be in phase for the instability to be excited by the acoustics/plasma coupling. In addition, a characteristic equation deduced from a generalized wave equation has been solved to determine the growth rates and actual frequencies of unstable modes in terms of time lag between the plasma waves. By using this mathematical model, the plasma instability near the anode of Princeton benchmark thruster has been analyzed for the ratios of the squared discharge current to mass flow rate of 16, 64, and 144 (kA)2⋅s/g. As a significant result, it was shown that the calculated growth rates were positive, meaning that the electro-thermo-acoustic instabilities can arise at the all discharge current levels. This phenomenon has been justified by providing two mechanisms based on the Ohmic heating effect and anode starvation process, respectively.