Challenging space missions include those at very low altitudes, where the atmosphere is source of aerodynamic drag on the spacecraft. To extend such missions lifetime, an efficient propulsion system is required. One solution is Atmosphere-Breathing Electric Propulsion (ABEP). It collects atmospheric particles to be used as propellant for an electric thruster. The system would minimize the requirement of limited propellant availability and can also be applied to any planet with atmosphere, enabling new mission at low altitude ranges for longer times. Challenging is also the presence of reactive chemical species, such as atomic oxygen in Earth orbit. Such species cause erosion of (not only) propulsion system components, i.e. acceleration grids, electrodes, and discharge channels of conventional EP systems. IRS is developing within the DISCOVERER project, an intake and a thruster for an ABEP system. The paper describes the design and implementation of the RF helicon-based inductive plasma thruster (IPT). This paper deals in particular with the design and implementation of a novel antenna called the birdcage antenna, a device well known in magnetic resonance imaging (MRI), and also lately employed for helicon-wave based plasma sources in fusion research. This is aided by the numerical tool XFdtd®. The IPT is based on RF electrodeless operation aided by an externally applied static magnetic field. The IPT is composed by an antenna, a discharge channel, a movable injector, and a solenoid. By changing the operational parameters along with the novel antenna design, the aim is to minimize losses in the RF circuit, and accelerate a quasi-neutral plasma plume. This is also to be aided by the formation of helicon waves within the plasma that are to improve the overall efficiency and achieve higher exhaust velocities. Finally, the designed IPT with a particular focus on the birdcage antenna design procedure is presented.