  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.
