Previous miniature ion thruster studies have demonstrated impressive performance using ring-cusp discharges. These studies suggest that the magnetic field must be sufficiently strong to increase primary electron confinement times for ionization, but weak enough to allow plasma electrons to escape and maintain the plasma potential necessary for ionization. To investigate these phenomena, an experiment was developed to allow detailed measurements of the internal structure and characteristics of a miniature ring-cusp discharge. These measurements provide spatially resolved values for plasma density, electron temperature, and plasma potential along a meridian plane. The magnetic field configuration is arranged as a quasi-periodic domain in order to generalize the findings to all multipole discharges. The results show that the magnetic field strength drives the plasma structure, and the dependence on discharge power can be removed with proper scaling of the plasma parameters. The stronger magnetic field results in a higher peak plasma density, but relatively low discharge utilization efficiency. In addition, the potential measurements indicate the likely onset of discharge instability. In contrast, the weaker magnetic field, or baseline configuration, better uses the volume of the chamber. This leads to a higher and more uniform density near the downstream end of the discharge where ion extraction would occur, implying superior discharge utilization.