We report on the performance of a micro-TPC with a micro pixel chamber($mu$-PIC) readout for a time-resolved neutron position-sensitive detector(PSD). Three-dimensional tracks and the Bragg curves of protons with energies of around 1 MeV were clearly detected by the micro-TPC. More than 95% of gamma-rays of 511 keV were found to be discriminated by simple analysis. Simulation studies showed that the total track length of proton and triton emitted from the $rm {}^{3}He$(n,p(573 keV))$rm {}^{3}H(191 keV)$ reaction is about 1.2 cm, and that both particles have large energy losses ($rm > 200 keV/cm$) in 1 atm Ar+$rm C_{2}H_{6}(10%)$+${}^{3}$He($< 1%$). These values suit the current performance of the micro-TPC, and we conclude that a time-resolved neutron PSD with spatial resolution of sub-millimeters shall be developed as an application of the micro-TPC.
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