# Hybrid Electrostatic-Atomic Accelerometer for Future Space Gravity Missions
## 3 Results and Discussions
### Performance Aspects
#### 3.4.2 Electrostatic Accelerometer  
Global Architecture  
In the frame of NGGM [1], a new design of electrostatic accelerometer, MicroSTAR, with a cubic proof-mass and numeric control loop has been proposed. The main advantage of this proof-mass shape is to have the same performance along the three axes and to provide three adapted angular acceleration measurements, which can be used for attitude control, as was done in the MICROSCOPE mission. The HybridSTAR accelerometer (cf. Figure 28a), the EA foreseen for the hybrid instrument, is a variation of MicroSTAR accelerometer adapted for the needs of the cold atom sensor. With a satellite in an Earth-pointing attitude control mode, the atomic sensor has a loss of contrast in the case of a satellite-fixed mirror for the Raman laser beam, which can lead to the impossibility to provide a long interrogation time measurement. To compensate this effect, HybridSTAR is designed in order to use the proof-mass as a mirror for the Raman laser beam, as well as to allow a rotation of the proof-mass around the cross-track axis to compensate for the satellite rotation. Following this objective, the proof-mass size was increased, and consequently, the electrode plates were changed compared to MicroSTAR. The main differences with the other previous EA accelerometers are the shape of the proof-mass and the dissociation of the stops from the ultra-low expansion glass (ULE) plates. A window was also added on the housing to allow the passage of the Raman laser towards the proof-mass. The dimension of the cubic proof-mass was increased and adapted to the size of the Raman laser (\(\phi=25\) mm). Figure 28b shows the presence of an additional big hole at the center of the electrodes for the passage of the Raman laser beam. The six electrode plates are identical to have a symmetrical core around the proof-mass and for redundancy manufacturing aspects. \begin{table}
\begin{tabular}{c c c} \hline \(x,y,z=0\) & \(v_{x,y,z}=0\) & \(\Omega_{y}=1.16\) mrad/s & \(\Omega_{x,z}=0.1\) mrad/s (max) \\ \hline \(\delta_{x,y,z}=\pm\) 200 \(\mu\)m & \(\delta_{v_{x},y_{y},v_{z}}=\pm\) 1 mm/s & \(\Omega=10^{-6}\) rad\(\cdot\)s\({}^{-2}\) (max, all axes) \\ \hline \end{tabular}
\end{table} 
Table 5: Assumptions on CAI atomic source parameters and satellite rotation parameters. \(\delta_{i}\) refers to the amplitude of variation impacting parameter \(i\). HybridSTAR accelerometer is composed of the following sub-assemblies:  
* A sole plate, which receives the core, the housing, and the hermetic feedthroughs, to ensure the mechanical and electrical interfaces;
* A hermetic housing with the pumping system, to maintain and ensure the vacuum inside the core;
* A core, with a cubic proof-mass polarized with a 5 \(\upmu\)m diameter Platinum wire and six identical electrode plates, providing the same sensitive measurements for the three linear and three angular accelerations;
* A cage, independent of the core, which receives supports with the stops, limiting the free motion of the proof-mass, preventing any contact with the electrode plates. Performance Aspects  
The electrostatic accelerometer was designed to fulfill the requirements of NGGM [1]. In order to have the capability to rotate the proof-mass around the cross-track axis, the design is slightly different for the radial axis, which will be in charge of this rotation. In particular, the detectors along this axis shall be able to see a great motion of the proof-mass. The polarization wire also introduces a different contribution, depending on its direction. This wire is implemented along the radial axis, as this axis is already degraded due to the rotation control of the proof-mass. Figure 29a provides the ASD of the noise of the accelerometer for the along-track axis, as well as the cross-track axis. The polarization voltage is at 10 V and the detection voltage at 5 Vrms. The gap between electrode and proof-mass is 300 \(\upmu\)m. The mass of the PM is about 394 g. Above 0.1 Hz, the main contributor is the detector noise.