  High-power magnetically shielded Hall thrusters have recently emerged to meet
the needs of the next-generation space missions. Even though a few such
thrusters are currently undergoing their late-stage development campaigns, many
unanswered questions yet exist concerning the behavior and evolution of the
plasma in these large-size thrusters that feature an unconventional magnetic
field topology. Noting the complex, multi-dimensional nature of plasma
processes in Hall thrusters, high-fidelity particle-in-cell simulations are
optimal tools to study the intricate plasma behavior. Nonetheless, the
significant computational cost of traditional PIC schemes renders simulating
high-power thrusters without any physics-altering speed-up factors unfeasible.
Thus, in this article, we demonstrate the applicability of the novel
reduced-order PIC scheme for a cost-efficient, self-consistent study of the
high-power Hall thrusters by performing simulations of a 20 kW magnetically
shielded Hall thruster along the axial-azimuthal and radial-azimuthal
coordinates. The axial-azimuthal simulations are performed for three operating
conditions in a rather simplified representation of the thruster's inherently
3D configuration. Nevertheless, we resolved self-consistently an unprecedented
650 us of the discharge evolution without any ad-hoc electron mobility model,
capturing several breathing cycles and approximating the experimental
performance parameters with an accuracy of 70 to 80 % across the operating
conditions. The radial-azimuthal simulations casted further light on the
evolution of the azimuthal instabilities and the resulting variations in the
electrons' cross-field mobility and the plasma-wall interactions. Particularly,
we observed the development of a long-wavelength, relatively low-frequency wave
mode near the exit plane of the thruster's channel that induces a notable
electron transport.
