Plasma plumes are the end products ejected from electric propulsion after complex ionization and acceleration processes. The physics behind the plasma plumes has attracted significant interest due to their interactions with the critical components of satellites and an increased understanding of the relevant processes. Recently, in the front view from a pulsed plasma thruster (PPT), we observed an unclosed vortex structure in the plasma plume, which led us to reconsider the propagation process and the current flux directions inside a plasma plume. To study this plume structure in depth, a highly sensitive Rogowski coil is used here to obtain the current density of the plume over the operating period of a PPT in 3 perpendicular directions. Vector-time-resolved current flux maps were obtained through experimental measurements and the peak current densities were found to reach 50000 mA/cm² to 250000 mA/cm². From successive 3-D current flux maps, the complete process of current flow inside a transient plasma plume is observed. The vortex plume structure was found to form during the initial discharge period. The plasma in-plume current is shown to be involved by discharge circuit. After the main discharge is completed, the plasma plume tends to circuit-independent and in self-equilibrium.