Abstract: This study utilizes three-dimensional Particle-in-Cell and Monte Carlo Collision (PIC/MCC) simulations to analyze how Poynting vector distributions influence energy conversion processes in the anode layer Hall thruster, considering both axial and radial spatial dimensions under steady-state conditions. The Poynting vector field intensity exhibits gradient distribution characteristics along the axial direction, demonstrating pronounced spatial inhomogeneity. Correlation analysis in the radial dimension reveals that electron energy accumulation is not solely governed by direct electromagnetic acceleration but also involves multiple nonlinear energy transport mechanisms. The strong correlation between ion density, ion energy, and Poynting vector field intensity demonstrates significant synergistic effects between energy transport and ion generation processes. The Poynting vector field intensity modulates electron drift velocity to influence ion density distribution, ultimately resulting in spatially continuous but characteristically delayed energy cascade phenomena. A nonlinear dependency exists between plasma energy and Poynting vector intensity, with the energy transfer process divisible into three phases: energy accumulation, energy saturation, and stable transport. Energy conversion efficiency exhibits an initial increase followed by a decrease as the Poynting vector intensity increases. Optimal energy transfer efficiency is achieved in the moderate intensity range. Therefore, thruster performance optimization should prioritize energy utilization in the moderate Poynting vector intensity region while suppressing energy losses in high-field areas. These findings provide rational configuration recommendations for optimizing the electromagnetic field topology within the thruster, ultimately enhancing overall thruster performance.