NASA's Hall Effect Rocket with Magnetic Shielding (HERMeS) 12.5kW Technology Demonstration Unit-1 (TDU-1) has been the subject of extensive technology maturation in preparation for flight system development. The TDU-1 thruster implements a magnetically shielded field topology and has demonstrated the elimination of the discharge channel erosion. Extensive wear testing the TDU Hall thrusters has identified the thruster front pole covers as the next life limiting component. This effort aims to explore and investigate alternate magnetic field topologies to assess whether reductions in the front pole cover erosion can be attained while still maintaining very low erosion rates on the discharge channel walls. NASA GRC and JPL have begun a magnetic field topology characterization and optimization study by designing four candidate magnetic field topologies that reduce the effectiveness of the shielding along the discharge channel walls with the intent to also reduce the erosion rates along the pole covers. Three of the four candidate magnetic field topologies have been manufactured subjected to an extensive test campaign that includes performance, plume, and stability characterization. In Phase I of the testing campaign, the thruster's oscillation magnitude and Laser Induced fluorescence (LIF) measurements of the plasma plume were performed for the three candidate topologies. In Phase I, the thruster's oscillation magnitude and LIF measurements were performed for the three candidate topologies. Phase I test results found that the B1 configuration attained lower oscillation levels than B0. Additionally, LIF measurements along the discharge chamber centerline found that upstream retraction of the thruster's peak magnetic field does result in an upstream shift of the acceleration zone but the magnitude of the shift does not correspond one-to-one to the shift in the location of the peak radial magnetic field magnitude. Phase II test segment will include performing performance, stability, plume, and erosion measurements for the various candidate magnetic field topologies.