# Hybrid Electrostatic-Atomic Accelerometer for Future Space Gravity Missions
### Hybrid Atomic-Electrostatic Accelerometer Concept  
Both atomic and electrostatic technologies have their own drawbacks and advantages in terms of performance. Typically, electrostatic accelerometers offer in space state-of-the-art sensitivity, a bandwidth of typically 1 Hz (\(<\)10 Hz), a measurement range of \(10^{6}\) relative to the achievable sensitivity, and continuous measurements. They suffer nevertheless from bias instabilities mainly due to temperature dependencies, which degrade the long-term stability of the measurement. In cold atom interferometers, the measurement is based on a very well-known and controlled scale factor, determined at first order only by the inter-pulse timing \(T\) and the interferometer laser wavelength and relies on the well-defined energy separation between two atomic states. Atomic interferometers are therefore potentially excellent in terms of accuracy and stability. They suffer nevertheless from a low measurement rate (\(1/T_{c}\)), errors due to dead time measurements (\(T_{c}-2T\)), and a relative low measurement range (shot-to-shot acceleration variations should stay smaller than \(\approx\frac{\pi}{2k_{eff}T^{2}}\), corresponding to an interfringe variation for the atom interferometer; see Figure 1). Hybridizing an atom accelerometer and an electrostatic accelerometer should offer the possibility to take advantage of both technologies and mitigate their respective weaknesses. The atom interferometer could be used to correct the drift of the EA, and simultaneously, the EA could be used to fill the measurement dead times of the atomic sensor. If necessary, the EA could help to determine the fringe index of the interferometer instrument. Such a hybridization scheme is reminiscent of methods already implemented for ground cold atom gravimeters where the atomic sensor is coupled to a classical accelerometer or seismometer \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**EA** & \multicolumn{4}{c}{**Space Missions**} \\ \hline
**Characteristics** & **CHAMP** & **GOCE** & **GRACE-FO** & **NGGM** \\ \hline PM mass (g) & 72 & 320 & 72 & 507 \\ GAP USA (\(\mu\)m) & 75 & 299 & 175 & 300 \\ GAP LSA (\(\mu\)m) & 60 & 32 & 60 & 300 \\ Meas. range USA [m\(\cdot\)s\({}^{-2}\)] & \(\pm 10^{-4}\) & \(\pm 6\times 10^{-6}\) & \(\pm 7\times 10^{-5}\) & \(\pm 10^{-5}\) \\ Meas. range LSA [m\(\cdot\)s\({}^{-2}\)] & \(\pm 10^{-4}\) & \(\pm 5\times 10^{-4}\) & \(\pm 6\times 10^{-4}\) & \(\pm 10^{-5}\) \\ Noise floor USA [m\(\cdot\)s\({}^{-2}\), Hz\({}^{-1/2}\)] & \(2\times 10^{-9}\) & \(2\times 10^{-12}\) & \(10^{-10}\) & \(3\times 10^{-12}\) \\ Noise floor LSA [m\(\cdot\)s\({}^{-2}\).Hz\({}^{-1/2}\)] & \(2\times 10^{-9}\) & \(2\times 10^{-10}\) & \(10^{-9}\) & \(3\times 10^{-12}\) \\ Total Mass [kg] (w. elec.) & 10 (w/o ICU) & 9 & 11 & 15 \\ Total Elec. Cons. [W] & 2 (w/o ICU) & 9 & 11 & 15 \\ Total Volume [L] & 13 (w/o ICU) & 11 & 14 & 16 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main characteristics of the last flying space EAs in CHAMP, COCE, and GRACE-FO and the foreseen EAs for NGGM, the future ESA mission. For CHAMP, the mass and power consumption do not take into account the interface and control unit (ICU). USA and LSA stand, respectively, for ultra-sensitive axis and less-sensitive axis. For instance, in GRACE-FO, the USA are the along-track and radial axes and the LSA is the cross-track axis. Figure 4: Noise performance specifications on the ultra-sensitive axis (USA) of the EAs used in CHAMP, GRACE-FO, GOCE, and foreseen for NGGM. to compensate for the same lack of atomic instruments [40; 45; 46; 47; 48]. Note that the previously demonstrated hybrid instruments on Earth never involved electrostatic instruments similar to the one operating in space since this technology is not in principle adapted to ground operations, the electrostatic forces to compensate for the gravity acceleration being too large. One original aspect of the proposed atomic-electrostatic hybridization is the ability to create a close link between both accelerometers.