The Hall thruster is a technology mainly used for correction of satellite orbits and propulsion for deep-space missions. It has been demonstrated that an instability known as \(\mathbf{E} \times \mathbf{B}\) electron drift instability (EDI) arises in Hall thrusters, characterized by a high frequency and a small wave number, and can be responsible for the enhanced mobility of electrons in the channel. In this work we analyze the microturbulence due to the \(\mathbf{E} \times \mathbf{B}\) EDI using the spectral entropy, which measures the degree of order/disorder of a system by applying the Shannon information entropy. We perform numerical simulations of an axial-azimuthal two-dimensional model of a Hall thruster using the particle-in-cell method. Simulations are performed using xenon and argon as the neutral gas, and the \(\mathbf{E} \times \mathbf{B}\) EDI is observed as a large-amplitude wave in the spatial patterns of the azimuthal component of the electric field \(\boldsymbol{E_\phi }\) . The spectral entropy of \(\boldsymbol{E_\phi }\) is higher for xenon than argon, which indicates a higher degree of disorder in the azimuthal electric field fluctuations. The implication of these results on the anomalous electron transport in Hall thrusters is discussed.
