Extremely Low Frequency Electric Field Emissions for Space Applications: Measuring and Modeling Techniques

Introduction

The need to measure electromagnetic fields and particle population in space plasmas has led to several space missions (Benkhoff, Casteren, Hayakawa, Fujimoto, Laakso, Novara, Ferri, Middleton, & Ziethe, 2010; Drinkwater, Floberghagen, Haagmans, Muzi, & Popescu, 2003; Scheeres, Marzari, Tomasella, & Vanzani, 1998; Escoubet, Schmidt, & Goldstein, 1997; Antonucci, Armano, Audley, Auger, Benedetti, Binetruy, Boatella et al., 2011; Müller, Marsden, Cyr & Gilbert, 2013; Bayle, Lorenzoni, Blancquaert, Langlois, Walloschek, Portigliotti, & Capuano, 2011), such as GOCE, EXOMARS, Rosetta, Cluster, BepiColombo, LISA and Solar Orbiter, which aim to facilitate these measurements. The payload of these missions is necessarily sensitive to electric and magnetic fields and require stringent electromagnetic cleanliness with emphasis to random and periodic AC electric and magnetic field variations in frequency and time domain. This necessity for cleanliness occurs due to the sensitivity of the measuring instruments that they are placed on the spacecraft’s boom. From the perspective of extremely low frequency (ELF) electric cleanliness, these instruments are meant to measure slow time- variant electric fields, equivalent to frequencies not higher than 250 KHz (THOR mission). Test limits for radiated AC electric field emissions in terms of spectral density and amplitude level which derives from the spectral density in case of THOR mission are depicted in Figures 2 and 3. Regarding these Figures, it is understood that the unintended emissions from spacecraft’s units shall not exceed these limits. An example of such an emission is depicted in Figure 1, presenting radiated emissions of a PCDU unit from GOCE mission.

In the process of ensuring compliance with the strict requirements, both characterization of the sources and the accurate prediction of emissions are vital for the design and position arrangement of the equipment inside the spacecraft structure. Equivalent dipole modeling (EDM) has been demonstrated to be very efficient and robust in characterizing electromagnetic emissions from radiating elements (Obiekezie, Thomas, Nothofer, Greedy, Arnaut & Sewell, 2014). Basic modeling requires well defined and characterized problem especially focused on the localization and identification of the equivalent dipoles. Additionally, optimization techniques offer ways of determining the best solution with limited computational resources (Obiekezie et al, 2014). For extremely low frequencies it is safe to assume that the electric field, especially when the near field is of interest, can be described by a quasi-static formulation. In this case, source reconstruction can be achieved either using equivalent current densities or electric dipoles with specific position and moments. Both methods are suitable and the differences between using current densities and electric dipole moments are negligible. Given the fact that the electromagnetic fields from a dipole moment can be expressed in detail and the exact distributions of current and voltages can be described in a completely equivalent manner using dipole moments, a Multi-Frequency Electric Dipole Model methodology (MFEDM) is proposed. The novelty in the proposed MFEDM technique consists of the modeling of LF AC electric field variations assigning an equivalent dipole source for every frequency sample. The proposed methodology is able to solve the equivalent inverse problem assuming that the magnitude of each frequency component is the corresponding electrostatic field value. An iteration of this process for all frequency samples results to the full MFEDM model.

Figure 1.

Indicative ELF Electric Emissions of PCDU (14 KHz -100 MHz part) from GOCE mission (published with permission of TAS- I, ESA)