Abstract: The auroral arc is a common form of aurora. Its formation involves three processes: the transfer of disturbed energy from the source region to the acceleration region via Alfvén waves, the generation of acceleration structures within the acceleration region, and the acceleration of electrons to produce aurora. Observations indicate that the auroral arc corresponds to a quasi-static parallel electric field with a U-shaped structure, with a clear concentration of the electric field at the bottom of the U-shaped structure. Regarding how the initial energy input evolves into a quasi-static electric field with a U-shaped structure, simulation studies based on existing auroral particle acceleration theories have not yet fully reproduced results that are fully consistent with the observed characteristics. This suggests that the existing theory may still lack a description of a key energy conversion process. Our research indicates that the core of this process lies precisely in the modified electron acoustic wave unique to the transition region. Based on this, we have constructed a dynamic theoretical model that incorporates, for the first time, the coupling of modified electron acoustic waves and kinetic Alfvén waves. The model's output is in good agreement with the observed characteristics of the U-shaped structure, directly revealing the decisive role of modified electron acoustic waves in the formation and evolution of the quasi-static electric field. This achievement provides a new physical foundation for improving the theory of auroral particle acceleration.