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During beam injection the components of the magnetic field inside the magnets decay in time. At the re-start of the ramping, this decay is cancelled resulting in a fast change of the harmonics called "snapback". This sudden variation affects mainly the sextupole and decapole components and can induce significant changes in the machine chromaticity, thus causing particle beam loss. Standard magnetic measurements with rotating coils do not have a sufficient time resolution to properly characterize the snapback phenomenon. A system based on Hall probes has been developed from an existing prototype to measure with a moderate acquisition frequency (3-10 Hz) the decay and snapback of the sextupole and, for the first time, of the decapole fields. The present system also provides local measurements of these field harmonics along a wavelength of the superconducting cable twist pitch. In this paper, we describe the assembly features of this detector and of the measurement chain. The performances are demonstrated based on preliminary measurements performed on the LHC pre-series dipoles in operating conditions.