Stability of the compact cold atom clock HORACE

HORACE is a compact cold cesium atom clock which is being developed in LNE-SYRTE for space applications and onboard systems. The operation of this clock is different from fountains since the laser cooling, the microwave interrogation and the detection are sequentially performed inside the spherical microwave cavity. We recently achieved short term stability of 5.5 10^-13 tau^-0.5 reaching the 10^-14 level at 3000 sec. We report in this paper recent developments and improvements, particularly on the cooling sequence. We also study the main limitations.