Plasma structure and electron cross field in the z- θ plane of a Hall thruster E × B plasma under an azimuthally inhomogeneous magnetic field are studied by both experimental and numerical approaches. The work is intended to identify a primary role of electron dynamics on the structure formation by manipulating only the strongly magnetized electrons. The plasma potential distribution shows an axial-azimuthal variation; a low magnetic field region results in spatial potential saturation further downstream. The plasma density structure shows a 1D-like azimuthal variation with less axial deformation. A dense region is observed near the location of B > - > 0, where electrons are expected to undergo the B and curvature drift toward the anode where neutrals are introduced. The potential structure is in close correlation to the Hall parameter distribution, indicating that electron dynamics plays a primary role in plasma structure formation, and via multiple consecutive stepwise physical steps, it eventually affects the density structure formation. In the z- θ space, the cross-field transport by E × B and diamagnetic drifts dominantly determines the electron flow and increases the overall axial electron mobility due to the azimuthal inhomogeneity. It is shown that most of the current is carried by the largest structure, but as the macroscopic structure fades out downstream, small structures grow and share the current. By considering the conservation laws, we show that a relation between azimuthal distributions of physical properties is formed to conserve the axial flux by a balance of specific forces, a balance between the resistive force and the magnetic force in the near-anode region and a balance between the electric/pressure force and the magnetic force in the acceleration and plume region, which differs from the Boltzmann relation satisfied in the radial dimension. Based on this principle, with a simplified test case having a uniform plasma density distribution, we show an analytic relation between azimuthal distributions of the magnetic field and the plasma potential and confirm the relation by a 2D hybrid simulation.
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