Current $gamma$-ray telescopes suffer from a gap in sensitivity in the energy range between 100keV and 100MeV, and no polarisation measurement has ever been done on cosmic sources above 1MeV. Past and present e$^+$e$^-$ pair telescopes are limited at lower energies by the multiple scattering of electrons in passive tungsten converter plates. This results in low angular resolution, and, consequently, a drop in sensitivity to point sources below 1GeV. The polarisation information, which is carried by the azimuthal angle of the conversion plane, is lost for the same reasons. HARPO (Hermetic ARgon POlarimeter) is an R&D program to characterise the operation of a gaseous detector (a Time Projection Chamber or TPC) as a high angular-resolution and sensitivity telescope and polarimeter for $gamma$ rays from cosmic sources. It represents a first step towards a future space instrument in the MeV-GeV range. We built and characterised a 30cm cubic demonstrator [SPIE 91441M], and put it in a polarised $gamma$-ray beam at the NewSUBARU accelerator in Japan. Data were taken at photon energies from 1.74MeV to 74MeV, and with different polarisation configurations. We describe the experimental setup in beam. We then describe the software we developed to reconstruct the photon conversion events, with special focus on low energies. We also describe the thorough simulation of the detector used to compare results. Finally we will present the performance of the detector as extracted from this analysis and preliminary measurements of the polarisation asymmetry. This beam-test qualification of a gas TPC prototype in a $gamma$-ray beam could open the way to high-performance $gamma$-ray astronomy and polarimetry in the MeV-GeV energy range in the near future.
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