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Evolution of electron cross-field transport induced by an equilibrium azimuthal electric field in an $\mathrm{E}\times\mathrm{B}$ Hall thruster discharge under an azimuthally inhomogeneous neutral supply

The electron cross-field transport by the induced azimuthal electric field in a Hall thruster exhibits the mobility scaled by $1/B$. This study investigates parameters affecting this transport over a Hall thruster's distinct regions, such as the ionization, acceleration, and plume region. The main focus is on the nonzero equilibrium azimuthal electric field induced by an azimuthally inhomogeneous neutral supply. A fast Fourier transform analysis of the plasma structure reveals that the wavenumber $k$ of the azimuthal plasma structure increases from $k=2$, which is the input condition, to $k=4$ in the plume region, and that the total axial flux caused by the azimuthal electric field is mainly induced from the structures of the dominant Fourier components. The azimuthal phase relation between plasma potential and density is formed to maximize the axial electron flux at the plume region and starts varying along with other plasma properties as electrons flow toward the acceleration region. The spatial evolution of the effective axial mobility coefficient is extracted, and its regional characteristics are discussed.