We have developed a simple model that is able to describe and predict hysteresis behavior inside Mumetal magnetic shields, when the shields are submitted to ultra-low frequency (<0.01 Hz) magnetic perturbations with amplitudes lower than 60 μT. This predictive model has been implemented in a software to perform an active compensation system. With this compensation the attenuation of longitudinal magnetic fields is increased by two orders of magnitude. The system is now integrated in the cold atom space clock called PHARAO. The clock will fly onboard the International Space Station in the frame of the ACES space mission.

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