# Hybrid Electrostatic-Atomic Accelerometer for Future Space Gravity Missions
## 3 Results and Discussions
### Performance Aspects
The average AC Stark shift should be the remaining contribution if we consider the spatial arm separation of the interferometer, which should be around 2 cm for an interrogation time of 1 s. Considering a Raman beam waist of 1.3 cm and a half angular divergence of 0.1 mrad [79], the relative intensity difference between the extreme points on the interferometer should be \(\approx\)2 \(\times\) 10\({}^{-4}\) and the impact on the acceleration systematics a few 10\({}^{-1}\) m\(\cdot\)s\({}^{-2}\). Note that this estimation does not take into account steeper intensity gradients such as laser speckle. * Misalignments: The measurement axis of the atomic instrument is given by the direction of \(\vec{k}_{eff}\). Any misalignments between this direction and the satellite measurement axis should lead to errors coming from the projection of accelerations. Let us consider first that the Raman mirror is fixed relative to the satellite. In the atomic instrument, the Raman laser is retro-reflected on the mirror, and therefore, the effective wavevector \(\vec{k}_{eff}\) is always orthogonal to the mirror plane. A defect in the retro-reflection will only impact at first approximation the scale factor through a modification of \(\left\|\vec{k}_{eff}\right\|\). A misalignment of the mirror will induce therefore a misalignment of the measurement axis by the same angle. The Raman mirror will constitute the reference for the atomic measurement and, therefore, has to be precisely integrated in the satellite to avoid important misalignment errors. Misalignment errors of the mirror referential relative to the satellite referential should be of the same order of magnitude as the one foreseen for the electrostatic accelerometer in NGGM, typically of \(\approx\)100 \(\upmu\)rad. Angular errors in the mirror mechanical structure itself should be significantly lower, estimated at first sight as \(\approx\)10 \(\upmu\)rad. The main contribution comes from the projection of transverse drag accelerations. We considered for all axes residual linear drag accelerations with amplitudes lower than 10\({}^{-6}\) m\(\cdot\)s\({}^{-2}\) and a noise in the measurement bandwidth (1-100 mHz) lower than 5 \(\times\) 10\({}^{-9}\) m\(\cdot\)s\({}^{-2}\cdot\)Hz\({}^{-1/2}\)[1]. This leads to acceleration errors with a maximum amplitude of 10\({}^{-10}\) m\(\cdot\)s\({}^{-2}\) and a noise of 5 \(\times\) 10\({}^{-13}\) m\(\cdot\)s\({}^{-2}\cdot\)Hz\({}^{-1/2}\) in the measurement bandwidth. * Raman wavefront aberrations: Wavefront aberrations of the Raman laser are identified as a main limitation in cold atom inertial sensors [22; 25; 80; 81; 82; 83]. This is due to the fact that the measurement is derived from the displacement of the free-falling atoms relative to the Raman laser equiphase surfaces. Any distortions of the equiphase surfaces introduce therefore parasitic phase shifts at the interferometer output, which translate into acceleration biases and long-term drifts due to atom kinematic variations (initial atomic position/velocity and temperature). For an atom whose trajectory is not perfectly aligned with the Raman laser, the phases of the three pulses are different, leading to a systematic shift. The resulting phase error at the output of the interferometer depends therefore on the initial density distribution of the atomic cloud, its expansion during the free-fall, and the averaging over the final spatial distribution during the detection process. State-of-the-art determination of the impact of wavefront aberrations on acceleration measurements has been achieved using an evaporatively cooled atomic source, with temperatures down to 50 nK, reaching an uncertainty for the effect of 1.3 \(\times\) 10\({}^{-8}\) m\(\cdot\)s\({}^{-2}\)[25].