The application of air-core reactors in power systems is extensive and primarily aimed at enhancing system stability, limiting short-circuit currents, and providing reactive power compensation. Currently, the type most commonly used in power systems is the cylindrical-shaped air-core reactor (CAR), known for its stable mechanical structure and mature manufacturing process. However, the external magnetic field generated by this reactor propagates over a considerable distance in the air, which can interfere with the normal operation of many power electronic devices. This paper presents a comparative analysis between a novel annular-shaped air-core bridge arm reactor (AABAR) and the widely used cylindrical-shaped air-core bridge arm reactor (CABAR) within a DC transformer system. The comparison focuses on the magnetic field distribution, including magnetic flux density, magnetic field radiation range, and magnetic field energy, as well as the attenuation characteristics of these physical quantities. The concept of magnetic clearance (MC) is introduced as a quantitative metric. Through finite element simulation software (AEDT 2021 R1), it is demonstrated that the annular-shaped air-core reactor design can significantly improve spatial utilization and reduce the actual usage space of the reactors in DC transformer systems.