The gas pixel detector (GPD) dedicated for photoelectric X-ray polarimetry is selected as the focal plane detector for the ESA medium-class mission concept X-ray Imaging and Polarimetry Explorer (XIPE). Here we show the design, assembly, and preliminary test results of a small GPD for the purpose of gas mixture optimization needed for the phase A study of XIPE. The detector is assembled in house at Tsinghua University following a design by the INFN-Pisa group. The improved detector design results in a good uniformity for the electric field. Filled with pure dimethyl ether (DME) at 0.8 atm, the measured energy resolution is 18% at 6 keV and inversely scales with the square root of the X-ray energy. The measured modulation factor is well consistent with that from simulation, up to ~0.6 above 6 keV. The residual modulation is found to be 0.30% +/- 0.15% at 6 keV for the whole sensitive area, which can be translated into a systematic error of less than 1% for polarization measurement at a confidence level of 99%. The position resolution of the detector is about 80 um in FWHM, consistent with previous studies and sufficient for XIPE requirements.
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