The gravitational interaction of antimatter and matter has never been directly probed. ALPHA-g is a novel experiment that aims to perform the first measurement of the antihydrogen gravitational mass. A fundamental requirement for this new apparatus is a position sensitive particle detector around the antihydrogen trap which provides information about antihydrogen annihilation location. The proposed detector is a radial Time Projection Chamber, or rTPC, whose concept is being developed at TRIUMF. A simulation of the detector and the development of the reconstruction software, used to determine the antihydrogen annihilation point, is presented alongside with the expected performance of the rTPC.

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