Radiation pattern of a ULF space-based antenna for controlled removal of energetic trapped protons

Highly energetic protons trapped in the inner Van Allen belt can disturb spacecraft operations, contaminate scientific measurements, and even cause early termination of missions. Earlier papers proposed that space-based coil antennas in the Electromagnetic Ion Cyclotron (EMIC) wave regime could potentially remove these particles by precipitating them into the atmosphere. Specifically, the designs involve a coil antenna driven in DC but rotating at the desired EMIC frequency (that is, below the proton gyro-frequency), which is capable of generating these waves and could serve as a payload on a scientific mission with the purpose of testing the ideas behind the concept of controlled removal of energetic trapped protons. This paper focuses on the radiation characteristics of this potential payload. We calculate the radiation pattern and radiation resistance of this transmitter operating in the EMIC band, taking into account the response of the plasma. We present a full-wave linear model capable of calculating the radiation pattern and radiation resistance in the far-field region of the rotating coil configuration immersed in a cold magnetized plasma consisting of protons and electrons. The stationary phase method is used to find a solution to the inverse Fourier transform of the radiated fields. The model shows that the power flux is fairly confined within a very small cone around the geomagnetic field lines, which corresponds to the waves´ resonance cone; the corresponding wave number vectors, however, are close to perpendicular to the Poynting flux direction. The radiation resistance is at a maximum for coil axis perpendicular to the geomagnetic field lines, which defines a preferred axis of rotation for the coil constituting the transmitter. Additionally, we show that the radiated power increases with increasing rotation frequency. We present at the end of the paper a brief discussion on thermal effects and other assumptions which should be carefully reconsidered - n future efforts.