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The BGIP is a proposal for a new, non-destructive beam profile monitor for the future Large Hadron Collider (LHC). This device provides the rms beam size value by means of the analysis of the velocity spectrum of the rest gas ions created and accelerated by the beam itself. After a thorough computer simulation study of the related physics, a first prototype of the BGIP has been conceived, built up and installed in the SPS main ring during 1999. This paper contains a short presentation of the simulation work and a description of the test set-up. The first experimental results are presented and compared with theoretical computations. [ABSTRACT FROM AUTHOR]