Helical Toroidal Magnetic Field Configuration and Its Associated Steady-State Axial Frame-Dragging Effect

This paper investigates a helical toroidal magnetic field configuration based on a Bidirectional Closed Opposed Conical Coil (BCOCC). In this configuration, the coil is connected end-to-end forming a closed loop, and the magnetic field lines distribute helically along the toroidal surface, producing a steady-state axial frame-dragging effect, complementary to the time-varying gravitomagnetic signal in Paper I and the time-varying gravitational potential in Paper II. Using geometric parameters of 20° cone angle, 5 cm base radius, 10 turns, and 20 A continuous current, based on the weak-field gravitoelectromagnetic (GEM) approximation with conservative estimation, the magnitude of the steady-state field is approximately 10−18 s−110−18s−1. This paper explicitly notes that the 10−7 s−110−7s−1 magnitude reported in Paper I is an upper-bound estimate based on optimistic parameter combinations including high-Q resonance, optimal coupling conditions, and enhancement factors, rather than a conservative median value. The conservative estimate in this work differs from the upper-bound estimate in Paper I by approximately 11 orders of magnitude, reflecting the significant impact of different parameter assumptions on gravitomagnetic effect estimations.