Antenna geometry strongly influences electromagnetic-field distribution, mode transition, and plasma-density formation in low-pressure inductively coupled plasma (ICP) sources. This study compares three external antenna configurations in the same 13.56 MHz, 3.0 mTorr argon plasma system: a helical-type antenna, a planar spiral antenna, and a combined spiral–helical antenna. The comparison is based on spatially resolved measurements of plasma density, RF plasma-potential oscillation, and RF magnetic-field components. The helical-type antenna produced a gradual density increase and a source-localized plasma, whereas the planar spiral antenna showed a clearer abrupt transition from a capacitively influenced low-density state to a higher-density inductive state. The combined spiral–helical antenna gave the strongest overall experimental response, producing the highest measured plasma-density values, the best density uniformity among the three configurations, the broadest useful high-density region, and strong suppression of RF plasma-potential oscillation in the high-density regime. The experimental magnetic-field measurements showed that the combined antenna produced a hybrid electromagnetic structure, with a hill-shaped axial RF magnetic-field profile and an off-axis radial-field structure. To support the interpretation, a verified three-dimensional vacuum-field Biot–Savart benchmark was developed under equal-current conditions. The benchmark is used only as a geometry-controlled field comparison and does not include plasma loading, dielectric boundaries, chamber currents, antenna-current variation, capacitive coupling, or self-consistent particle balance. The combined experimental and numerical results show that RF magnetic-field structure and plasma-density distribution are related but not identical, because density formation also depends on induced electric field, plasma-current density, ionization, transport, and wall losses. The work provides guidance for optimizing antenna geometry in controllable, energy-efficient, low-pressure cold plasma sources. This study should be read as a geometry-comparison case study: energy-efficiency gains are inferred from higher plasma density at equal applied RF generator power, not from direct absorbed-power measurements, and the combined-antenna geometry and 3.0 mTorr operating pressure investigated here represent a single tested case rather than a generally optimized design.