Limitations to the short term frequency stability in a compact cold atom clock

The HORACE device is a compact cold atom clock where about 10⁸ cesium atoms are laser cooled at a few μK, then interrogated and detected directly in a 20 cm³ spherical microwave cavity. The optimization of the short term stability with the cooling and interrogation durations is presented, leading to an estimation of the Allan deviation of σ_y(τ) -1 10^-13 τ ^{- 1}2 /on earth and σ_y(τ) = 7 10^-14 τ^-frac12; in space. The quantum projection noise, the Dick effect and the detection laser noises are taken into account. The calculations are based on a preliminary model for the recapture of cold atoms, in reasonable agreement with measurements.