The topology of the applied magnetic field is an important design aspect of
Hall thrusters. For modern Hall thrusters, the field topology most often
features curved lines with a concave (negative) curvature upstream of the field
peak and a convex (positive) curvature downstream. Additionally, the advent of
the magnetic shielding technique has resulted in the design of Hall thrusters
with non-conventional magnetic fields that exhibit high degrees of concavity
upstream of the field's peak. We carry out a rigorous and detailed study of the
effects that the magnetic field's curvature has on the plasma properties and
the underlying processes in a 2D configuration representative of a Hall
thruster's radial-azimuthal cross-section. The analyses are performed for
plasma discharges of three propellants: xenon, krypton, and argon. For each
propellant, we have carried out high-fidelity reduced-order particle-in-cell
(PIC) simulations with various degrees of positive and negative curvatures of
the magnetic field. Corresponding 1D radial PIC simulations were also performed
for xenon to compare the observations between 1D and 2D simulations. We
observed that there are distinct differences in the plasma phenomena between
the cases with positive and negative field curvatures. The instability spectra
in the cases of positive curvature is mostly dominated by the Electron
Cyclotron Drift Instability, whereas the Modified Two Stream Instability is
dominant in the negative-curvature cases. The distribution of the plasma
properties, particularly the electron and ion temperatures, and the
contribution of various mechanisms to electrons' cross-field transport showed
notable variations with the field's curvature, especially between the positive
and the negative values. Finally, the magnetic field curvature was observed to
majorly influence the ion beam divergence along the radial and azimuthal
coordinates.Comment: 25 pages, 24 figure